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The impact of social network on the adoption of real-time electricity pricing mechanism
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www.elsevier.com/locate/procedia
Energy Procedia 142 Energy Procedia 00(2017) (2017)3154–3159 000–000 www.elsevier.com/locate/procedia
9th International Conference on Applied Energy, ICAE2017, 21-24 August 2017, Cardiff, UK
The impact of social network on the adoption of real-time electricity The 15th International Symposium on District Heating and Cooling pricing mechanism Assessing thea, feasibility of using demand-outdoor Ge Wang Qi Zhanga*, Hailong Lib ,the Yanheat Lia, Siyuan Chena temperature function for a long-term district heat demand forecast Academy of Chinese Energy Strategy, China University of Petroleum-Beijing, Changping, Beijing 102249, China a
b
a,b,c
I. Andrić
School of Business, Society and Technology, Mälardalens University, Sweden
*, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc
a Abstract IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal b
Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France
c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 ruepricing Alfred Kastler, Nantes, France The option menu of electricity tariffs is a compromise way for introducing real-time (RTP) 44300 to consumers while remain the alternative fixed pricing (FP). Since it is difficult for a consumer to evaluate RTP and FP two tariffs because of the information asymmetry, and the acquaintances’ opinions may play an important role when making a choice. This study aims to evaluate the impact of the social network on the diffusion of real-time electricity price using evolutionary game theoretical analysis. Consumers Abstract with heterogeneities in demand response capability and relationships in the social network are considered in an electricity market RTP and FP simultaneously. The consumers who adopt RTP can response to the varying price by shifting their electricity District heating networkstheir are expenditures commonly addressed in the literature one As of athe most effective solutions for decreasing the consumption to minimize and inversely influence theas price. case study, hundreds of scenarios of different greenhouse gas emissions buildingstructures sector. These systemsrules require investments which are returned the heat initial conditions including from socialthe networks and update werehigh analyzed and inter-compared usingthrough the developed sales. The Dueresults to theshow changed climate conditions renovation policies, demand in the of future decrease, model. that: (i) the higher degree and of thebuilding consumers social network, theheat slower the diffusion RTP;could (ii) increasing prolonging the investment return period. the proportion of consumers with high demand response capability can promote the adoption of RTP, implying the worth of The main the scope of this paper is tohome assess the feasibility usingexogenous the heat demand – outdoor temperature function formutation heat demand promoting utilization of smart technology; (iii) of a small probability (e.g. 1%) of the tariff choice can forecast. the Thediffusion district of of RTP, Alvalade, located (Portugal), was can usedbeasuseful. a case study. The district is consisted of 665 accelerate indicating thatintheLisbon advertisement of RTP buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district scenariosPublished were developed (shallow, ©renovation 2017 The Authors. by Elsevier Ltd. intermediate, deep). To estimate the error, obtained heat demand values were compared with results from a dynamic heat demand model,of previously developed and validatedon byApplied the authors. Peer-review under responsibility of the scientific committee the 9th International Conference Energy. The results showed that when only weather change is considered, the margin of error could be acceptable for some applications (the errorEvolutionary in annual demand wasnetwork; lower than 20% price; for allDemand weather scenarios considered). However, after introducing renovation Keywords: game; Social Real-time response scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and 1.decrease Introduction renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and The electricity market reforms in China have been deregulating the retail markets and introducing the electricity improve the accuracy of heat demand estimations.
© 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and * Corresponding author. Tel.: +86-010-89731752. Cooling. E-mail address: [email protected]
Keywords: Heat demand; Forecast; Climate change 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 9th International Conference on Applied Energy.
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling.
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 9th International Conference on Applied Energy . 10.1016/j.egypro.2017.12.383
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Ge Wang et al. / Energy Procedia 142 (2017) 3154–3159 Author name / Energy Procedia 00 (2017) 000–000
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retailers as new participants in the electricity market. In light of the deregulation process, the electricity pricing mechanism is likely to shift from fixed pricing to market-oriented real-time pricing without governments’ interfering. Real-time pricing has been regarded as one of the most efficient pricing strategies to motivate consumers to reshape their loads curve by shifting the electricity consumption from peak time to off-peak time [1]. Previous studies indicate that consumers with a certain level of demand response capability can reduce their expenditure on electricity consumption under real-time pricing [2], while electricity producers can also reduce cost with a smaller peak-valley ratio. However, due to the inherent asymmetry of information in the electricity pricing, it still remains uncertain that if consumers are willingness to take part in a real-time pricing program or stay in the fixed pricing. The behaviors of consumers can influence each other through social contact. Note the connections between people in a community, researchers have found that the social influence can drive consumers’ energy consumption behavior [3,4]. Since it is difficult for a consumer to evaluate the two tariffs because of the information asymmetry, his/her acquaintances’ opinions may play an important role when making a choice. Therefore, the purpose of this study is to evaluate the impact of interactions between individuals through the social network on the adoption of real-time electricity pricing mechanism by using a social-network evolutionary game model. The evolutionary game model can take into consideration the consumers’ self-learning, the information diffusion within the consumers’ social network as well as the consumers’ choice mutations caused by advertisements propagation. In this study, the consumers are different in demand response capability levels which is measured by the ability of responding to electricity price fluctuation. The adoption of real-time electricity pricing mechanism a social network consists of heterogeneous consumers are investigated by using the proposed model. The impact of the degree of the social network, the composition of different types of consumers and the advertising efforts (measured by choice mutations probability) are analyzed through the case study and sensitivity analysis. 2. Methodology The evolution process of consumers’ electricity tariff choices can be described as follows. (1) Self-learning: In the beginning of each period, each consumer compares the electricity expenditure and the corresponding pricing mechanism in his/her memorized periods, and calculate his/her self-learning effect; (2) Social influence: The consumers observes the acquaintances’ choice and calculate his/her social influence. Calculate the comprehensive effect of self-learning and social influence and if the comprehensive effect exceed a threshold, the consumer will change his/her choice; (3) Advertising effect: If the consumer’ choice is fixed pricing, he/she will have a probability to change his/her choice as the result of advertisements propagation; (4) Real-time electricity market: All the consumers who choose real-time pricing in this period will be involved in the real-time electricity market. Their expenditures on electricity consumption will be obtained at the end of this period. The proposed social-network evolutionary game model includes two parts. The first part is the social network module, which processes the self-learning, social influence and advertising effect parts. The output of the social network module is that which parts of consumers will take part in the real-time pricing in electricity market. The second part is the real-time electricity market module, in which, consumers participate in a game in the real-time pricing market and every consumer pursues his/her own minimal expenditure on electricity consumption. The output of the real-time electricity market module is the equilibrium real-time price and consumers’ expenditure. 2.1. Social network module Individuals in a social network are represented as nodes in a complex network and the connections between people who know each other are represented as edges between nodes. In case of a undirected network with N nodes, we assume that node i is connected to ki neighbors, where i=1, . . . ,N. In this study, the topology of the social network is assumed to be a scale-free graph [5], in which small-world effects coexist with a large heterogeneity in neighborhood size [6].
Ge Wang et al. / Energy Procedia 142 (2017) 3154–3159 Author name / Energy Procedia 00 (2017) 000–000
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3
The self-learning effect is measured as equation (1), which is the normalization of the consumer’s expenditure in last period.
(
sle𝑖𝑖,𝑡𝑡 = (expenditure𝑖𝑖,𝑡𝑡−1 − max
𝑘𝑘∈[𝑡𝑡−1−𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚_𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝,𝑡𝑡−1]
min
𝑘𝑘∈[𝑡𝑡−1−𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚_𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝,𝑡𝑡−1]
expenditure𝑖𝑖,𝑘𝑘 −
expenditure𝑖𝑖,𝑘𝑘 ) /
min
𝑘𝑘∈[𝑡𝑡−1−𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚_𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝,𝑡𝑡−1]
expenditure𝑖𝑖,𝑘𝑘 )
(1)
Here sle𝑖𝑖,𝑡𝑡 is the self-learning effect of consumer i in period t. expenditure𝑖𝑖,𝑡𝑡−1 , expenditure𝑖𝑖,𝑘𝑘 are the electricity consumption expenditure of consumer i in period t-1 and period k. 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚_𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 is measuring the consumers’ memory capability. The social influence is measured as equation (2): si𝑖𝑖,𝑡𝑡 = ∑𝑗𝑗∈𝑘𝑘𝑖𝑖 ,𝑐𝑐ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜(𝑗𝑗𝑡𝑡)≠𝑐𝑐ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜(𝑖𝑖𝑡𝑡) 1 / ∑𝑗𝑗∈𝑘𝑘𝑖𝑖 1
(2)
Where si𝑖𝑖,𝑡𝑡 is the social influence effect of consumer i in period t. The binary variable 𝑐𝑐ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜(𝑖𝑖𝑡𝑡 ) is the choice of consumer i in period t. 𝑐𝑐ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜(𝑖𝑖𝑡𝑡 ) = 1 means the consumer i choose real-time pricing and 𝑐𝑐ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜(𝑖𝑖𝑡𝑡 ) = 0 means the consumer i choose fixed pricing. It is assumed that each consumer has his/her unique judgement on the importance of self-learning and social influence, which can be expressed as a weight 𝛾𝛾. The comprehensive effect of self-learning and social influence can be expressed as 𝛾𝛾 × sle𝑖𝑖,𝑡𝑡 + (1 − 𝛾𝛾) × si𝑖𝑖,𝑡𝑡 . When the comprehensive effect exceeds a threshold h, the consumer will change his choice, as described by equation (3). 𝑐𝑐ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑒𝑒(𝑖𝑖𝑡𝑡 ) = {
𝑐𝑐ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜(𝑖𝑖𝑡𝑡−1 ), 𝑖𝑖𝑖𝑖 [𝛾𝛾 × sle𝑖𝑖,𝑡𝑡 + (1 − 𝛾𝛾) × si𝑖𝑖,𝑡𝑡 ] ≤ ℎ 1 − 𝑐𝑐ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜(𝑖𝑖𝑡𝑡−1 ), 𝑖𝑖𝑖𝑖 [𝛾𝛾 × sle𝑖𝑖,𝑡𝑡 + (1 − 𝛾𝛾) × si𝑖𝑖,𝑡𝑡 ] > ℎ
(3)
2.2. Real-time electricity market module Consumers are bilaterally connected to the retailer. Power retailers gather the consumption data and set the realtime price based on the wholesale hourly power consumption. Residents respond to the hourly price by shifting their power load in form of submitting new demand bids and the retailer set a new price again. Such procedure will be repeated until equilibrium. The consumers’ houses consist of controllable, non-controllable electric appliances and central control appliance. Controllable appliances refer to appliances or human tasks which can be performed at any time of the day or within a particular time interval while non-controllable appliances refer to those whose operation time is fixed. A case in point is that washing machine is controllable, however, air-condition is usually non-controllable. For each consumer, his/her objective is to minimize the expenditure, which is described as equation (4). min ∑ℎ 𝑝𝑝𝑟𝑟ℎ × [∑𝑐𝑐 𝑐𝑐𝑎𝑎𝑖𝑖,𝑐𝑐,ℎ + 𝑁𝑁𝑁𝑁𝐿𝐿𝑖𝑖,ℎ ] , ∀𝑖𝑖
(4)
∑ℎ 𝑐𝑐𝑎𝑎𝑖𝑖,𝑐𝑐,ℎ = 𝑅𝑅𝑃𝑃𝑖𝑖,𝑐𝑐 𝑐𝑐𝑎𝑎𝑖𝑖,𝑐𝑐,ℎ ≤ 𝑅𝑅𝑃𝑃𝑖𝑖,𝑐𝑐 , ∀𝑆𝑆𝑆𝑆𝐴𝐴i,c ≤ 𝑡𝑡 ≤ 𝑆𝑆𝑆𝑆𝑂𝑂i,c 𝑐𝑐𝑎𝑎𝑖𝑖,𝑐𝑐,ℎ ≡ 0, ∀𝑡𝑡 < 𝑆𝑆𝑆𝑆𝐴𝐴i,c 𝑜𝑜𝑜𝑜 𝑡𝑡 > 𝑆𝑆𝑆𝑆𝑂𝑂i,c
(5) (6) (7)
Here, 𝑝𝑝𝑟𝑟ℎ is the real-time electricity price, 𝑐𝑐𝑎𝑎𝑖𝑖,𝑐𝑐,ℎ is the power consumed by one controllable appliance and 𝑁𝑁𝑁𝑁𝐿𝐿𝑖𝑖,ℎ is the non-controllable load. Each controllable appliance can only work once for one hour (which is the length of one entire time interval) in the given interval, which is described by equation (5)-(7).
Author name / Energy Procedia 00 (2017) 000–000 Ge Wang et al. / Energy Procedia 142 (2017) 3154–3159
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Here 𝑅𝑅𝑃𝑃𝑖𝑖,𝑐𝑐 is the rated power of one controllable appliance. 𝑆𝑆𝑆𝑆𝐴𝐴i,c is the earliest start time of one controllable appliance and 𝑆𝑆𝑆𝑆𝑂𝑂i,c is the latest stop time of one controllable appliance. An average-cost based pricing scheme is used as is described by equation (8). The 𝐹𝐹𝐹𝐹𝐿𝐿h is the electricity power load of consumers who choose fixed pricing, which is set to be exogenous constant. α and β are coefficients. And the fixed price equals to α+β. 𝑝𝑝𝑟𝑟ℎ = 𝛼𝛼 × {∑𝑖𝑖[∑𝑐𝑐 𝑐𝑐𝑎𝑎𝑖𝑖,𝑐𝑐,ℎ + 𝑁𝑁𝑁𝑁𝐿𝐿𝑖𝑖,ℎ ] + 𝐹𝐹𝐹𝐹𝐿𝐿h }/ {
∑ℎ[∑𝑖𝑖 𝑁𝑁𝑁𝑁𝐿𝐿𝑖𝑖,ℎ +𝐹𝐹𝐹𝐹𝐿𝐿h ]+∑𝑖𝑖 ∑𝑐𝑐 𝑅𝑅𝑃𝑃𝑖𝑖,𝑐𝑐 24
(8)
} + 𝛽𝛽
2.3. Tools The social network module is coded as a multi-agent model using Python programming language. The real-time electricity market module is coded as mixed complementarity problem (MCP), and solved by PATH solver on General Algebraic Modeling System (GAMS). The two modules are linked by Python. 3. Data 3.1. Consumers The residential load consists two parts, the non-controllable load (NCL) and controllable load(CAL). The noncontrollable load and the initial distribution of the controllable load are depicted in Fig. 1. In this study, three types of consumers differing in ability of responding to price change have been taken into consideration. Without loss of generality, it is assumed that the length of the time interval in which energy consumption can be shifted is during 24 hours for the consumer type 1, 5 hours for the consumer type 2, 1 hour for the consumer type 3, respectively. Taking consumer type 2 as an example to illustrate the meaning of the time interval length, if a type 2 consumer is accustomed to using washing machine at 1:00 pm before going to work in the afternoon, he can choose to shift the operation in time interval 11:00 am to 3:00 pm, of which 1:00 pm is the midpoint. In particular, type 1 consumer can shift his load to any other hour within the day and type 3 consumer cannot shift any load. There are 500 consumers considered in this study and they share the same non-controllable load and initial controllable load. 3.2. Social network The default value of the parameters of the social network is shown in Table 1. When conducting the sensitivity analyses of one parameter, the other parameters are set as the default value. The proportion of type 2 consumers is one minus the proportion of type 1 consumers and the proportion of type 3 consumers.
Table 1. Default parameters of the social network
Fig. 1. One consumer’ power load
Network’s degree
Consumer’s threshold
Advertising effect (probability)
Proportion of type 1 consumers
Proportion of type 3 consumers
3
0.3
1%
0.2
0.2
Author name / Energy Procedia 00 (2017) 000–000
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4. Result The impact of the social network’s mean degree, advertising effect and the composition of different types of consumers on the adoption of real-time electricity pricing mechanism are investigated in this study by simulation and sensitivity analysis. The simulation period is 100. The impact of social network’s degree is shown in Fig 2(a). It is indicated that with the degree increased, the adoption speed of real-time pricing mechanism decreased. The reason is that real-time pricing mechanism is a new opinion for the social-network. The more frequent the consumers communicate with each other, the more chances the new opinion being eliminated by the dominant old opinion (fixed pricing mechanism) in the social influence process. (a)
Degree=3
Degree=5
Degree=7
Probability=0
Probability=1%
Probability=10%
(b)
Fig. 2. (a) The impact of social network’s degree on the diffusion of RTP. (b) The impact of advertising effect on the diffusion of RTP.
As shown in Fig. 2(b), the advertising effect is significantly related to the adoption speed of real-time pricing mechanism. Such mutation probability, as the result of advertisements propagation, is the source of real-time pricing mechanism. The results show that the investment on advertising is useful and essential for promoting the penetration of real-time pricing. (a)
Initial proportion of Type 1 consumer=0
Initial proportion of Type 1 consumer=0.2
Initial proportion of Type 1 consumer=0.4
6
Ge Wang et al. / Energy Procedia 142 (2017) 3154–3159 Author name / Energy Procedia 00 (2017) 000–000
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(b)
Initial proportion of Type 3 consumer=0
Initial proportion of Type 3 consumer=0.2
Initial proportion of Type 3 consumer=0.4
Fig. 3. (a) The impact of initial proportion of type 1 consumers on the diffusion of RTP. (b) The impact of initial proportion of type 3 consumers on the diffusion of RTP.
The impacts of the proportion of type 1 consumers and type 3 consumers are shown in Fig 3(a) and Fig 3(b) respectively. It is shown that increasing the proportion of type 1 consumers, who have the highest demand response capability, and decreasing the proportion of type 3 consumers, who have the lowest demand response capability, can promote the adoption of real-time pricing mechanism. However, increasing the proportion of type 1 consumers is more efficient. The reason is that the consumers with higher demand response capability can benefit more from realtime pricing mechanism and thus are more likely to form a stable information source of real-time pricing mechanism. 5. Conclusion In the present study, the impacts of the social network on the adoption of real-time electricity pricing mechanism are investigated by using a social-network evolutionary game model. The results shows that: (i) the higher degree of the consumers social network, the slower the diffusion of real-time pricing, which shows that it is not necessary to provide a platform for communication; (ii) increasing the proportion of consumers with high demand response capability can promote the adoption of RTP, implying the worth of promoting the utilization of smart home technology; (iii) a small exogenous probability (e.g. 1%) of the tariff choice mutation can accelerate the diffusion of RTP, indicating that the advertisement of RTP can be a useful tool. References [1] Chen Z, Wu L, Fu Y. Real-Time Price-Based Demand Response Management for Residential Appliances via Stochastic Optimization and
Robust Optimization. IEEE Transactions on Smart Grid 2012;3:1822–31. [2] Wang G, Zhang Q, Li H, McLellan BC, Chen S, Li Y, et al. Study on the promotion impact of demand response on distributed PV penetration by using non-cooperative game theoretical analysis. Applied Energy 2017;185:1869–78. [3] Du F, Zhang J, Li H, Yan J, Galloway S, Lo KL. Modelling the impact of social network on energy savings. Applied Energy 2016;178:56–65. [4] Jain RK, Gulbinas R, Taylor JE, Culligan PJ. Can social influence drive energy savings? Detecting the impact of social influence on the energy consumption behavior of networked users exposed to normative eco-feedback. Energy and Buildings 2013;66:119–27. [5] Barabási A-L. Scale-Free Networks: A Decade and Beyond. Science 2009;325:412–3. [6] Santos FC, Santos MD, Pacheco JM. Social diversity promotes the emergence of cooperation in public goods games. Nature 2008;454:213–6.
ScienceDirect Availableonline onlineatatwww.sciencedirect.com www.sciencedirect.com Available Energy Procedia 00 (2017) 000–000
ScienceDirect ScienceDirect
www.elsevier.com/locate/procedia
Energy Procedia 142 Energy Procedia 00(2017) (2017)3154–3159 000–000 www.elsevier.com/locate/procedia
9th International Conference on Applied Energy, ICAE2017, 21-24 August 2017, Cardiff, UK
The impact of social network on the adoption of real-time electricity The 15th International Symposium on District Heating and Cooling pricing mechanism Assessing thea, feasibility of using demand-outdoor Ge Wang Qi Zhanga*, Hailong Lib ,the Yanheat Lia, Siyuan Chena temperature function for a long-term district heat demand forecast Academy of Chinese Energy Strategy, China University of Petroleum-Beijing, Changping, Beijing 102249, China a
b
a,b,c
I. Andrić
School of Business, Society and Technology, Mälardalens University, Sweden
*, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc
a Abstract IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal b
Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France
c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 ruepricing Alfred Kastler, Nantes, France The option menu of electricity tariffs is a compromise way for introducing real-time (RTP) 44300 to consumers while remain the alternative fixed pricing (FP). Since it is difficult for a consumer to evaluate RTP and FP two tariffs because of the information asymmetry, and the acquaintances’ opinions may play an important role when making a choice. This study aims to evaluate the impact of the social network on the diffusion of real-time electricity price using evolutionary game theoretical analysis. Consumers Abstract with heterogeneities in demand response capability and relationships in the social network are considered in an electricity market RTP and FP simultaneously. The consumers who adopt RTP can response to the varying price by shifting their electricity District heating networkstheir are expenditures commonly addressed in the literature one As of athe most effective solutions for decreasing the consumption to minimize and inversely influence theas price. case study, hundreds of scenarios of different greenhouse gas emissions buildingstructures sector. These systemsrules require investments which are returned the heat initial conditions including from socialthe networks and update werehigh analyzed and inter-compared usingthrough the developed sales. The Dueresults to theshow changed climate conditions renovation policies, demand in the of future decrease, model. that: (i) the higher degree and of thebuilding consumers social network, theheat slower the diffusion RTP;could (ii) increasing prolonging the investment return period. the proportion of consumers with high demand response capability can promote the adoption of RTP, implying the worth of The main the scope of this paper is tohome assess the feasibility usingexogenous the heat demand – outdoor temperature function formutation heat demand promoting utilization of smart technology; (iii) of a small probability (e.g. 1%) of the tariff choice can forecast. the Thediffusion district of of RTP, Alvalade, located (Portugal), was can usedbeasuseful. a case study. The district is consisted of 665 accelerate indicating thatintheLisbon advertisement of RTP buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district scenariosPublished were developed (shallow, ©renovation 2017 The Authors. by Elsevier Ltd. intermediate, deep). To estimate the error, obtained heat demand values were compared with results from a dynamic heat demand model,of previously developed and validatedon byApplied the authors. Peer-review under responsibility of the scientific committee the 9th International Conference Energy. The results showed that when only weather change is considered, the margin of error could be acceptable for some applications (the errorEvolutionary in annual demand wasnetwork; lower than 20% price; for allDemand weather scenarios considered). However, after introducing renovation Keywords: game; Social Real-time response scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and 1.decrease Introduction renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and The electricity market reforms in China have been deregulating the retail markets and introducing the electricity improve the accuracy of heat demand estimations.
© 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and * Corresponding author. Tel.: +86-010-89731752. Cooling. E-mail address: [email protected]
Keywords: Heat demand; Forecast; Climate change 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 9th International Conference on Applied Energy.
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling.
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 9th International Conference on Applied Energy . 10.1016/j.egypro.2017.12.383
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retailers as new participants in the electricity market. In light of the deregulation process, the electricity pricing mechanism is likely to shift from fixed pricing to market-oriented real-time pricing without governments’ interfering. Real-time pricing has been regarded as one of the most efficient pricing strategies to motivate consumers to reshape their loads curve by shifting the electricity consumption from peak time to off-peak time [1]. Previous studies indicate that consumers with a certain level of demand response capability can reduce their expenditure on electricity consumption under real-time pricing [2], while electricity producers can also reduce cost with a smaller peak-valley ratio. However, due to the inherent asymmetry of information in the electricity pricing, it still remains uncertain that if consumers are willingness to take part in a real-time pricing program or stay in the fixed pricing. The behaviors of consumers can influence each other through social contact. Note the connections between people in a community, researchers have found that the social influence can drive consumers’ energy consumption behavior [3,4]. Since it is difficult for a consumer to evaluate the two tariffs because of the information asymmetry, his/her acquaintances’ opinions may play an important role when making a choice. Therefore, the purpose of this study is to evaluate the impact of interactions between individuals through the social network on the adoption of real-time electricity pricing mechanism by using a social-network evolutionary game model. The evolutionary game model can take into consideration the consumers’ self-learning, the information diffusion within the consumers’ social network as well as the consumers’ choice mutations caused by advertisements propagation. In this study, the consumers are different in demand response capability levels which is measured by the ability of responding to electricity price fluctuation. The adoption of real-time electricity pricing mechanism a social network consists of heterogeneous consumers are investigated by using the proposed model. The impact of the degree of the social network, the composition of different types of consumers and the advertising efforts (measured by choice mutations probability) are analyzed through the case study and sensitivity analysis. 2. Methodology The evolution process of consumers’ electricity tariff choices can be described as follows. (1) Self-learning: In the beginning of each period, each consumer compares the electricity expenditure and the corresponding pricing mechanism in his/her memorized periods, and calculate his/her self-learning effect; (2) Social influence: The consumers observes the acquaintances’ choice and calculate his/her social influence. Calculate the comprehensive effect of self-learning and social influence and if the comprehensive effect exceed a threshold, the consumer will change his/her choice; (3) Advertising effect: If the consumer’ choice is fixed pricing, he/she will have a probability to change his/her choice as the result of advertisements propagation; (4) Real-time electricity market: All the consumers who choose real-time pricing in this period will be involved in the real-time electricity market. Their expenditures on electricity consumption will be obtained at the end of this period. The proposed social-network evolutionary game model includes two parts. The first part is the social network module, which processes the self-learning, social influence and advertising effect parts. The output of the social network module is that which parts of consumers will take part in the real-time pricing in electricity market. The second part is the real-time electricity market module, in which, consumers participate in a game in the real-time pricing market and every consumer pursues his/her own minimal expenditure on electricity consumption. The output of the real-time electricity market module is the equilibrium real-time price and consumers’ expenditure. 2.1. Social network module Individuals in a social network are represented as nodes in a complex network and the connections between people who know each other are represented as edges between nodes. In case of a undirected network with N nodes, we assume that node i is connected to ki neighbors, where i=1, . . . ,N. In this study, the topology of the social network is assumed to be a scale-free graph [5], in which small-world effects coexist with a large heterogeneity in neighborhood size [6].
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The self-learning effect is measured as equation (1), which is the normalization of the consumer’s expenditure in last period.
(
sle𝑖𝑖,𝑡𝑡 = (expenditure𝑖𝑖,𝑡𝑡−1 − max
𝑘𝑘∈[𝑡𝑡−1−𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚_𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝,𝑡𝑡−1]
min
𝑘𝑘∈[𝑡𝑡−1−𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚_𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝,𝑡𝑡−1]
expenditure𝑖𝑖,𝑘𝑘 −
expenditure𝑖𝑖,𝑘𝑘 ) /
min
𝑘𝑘∈[𝑡𝑡−1−𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚_𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝,𝑡𝑡−1]
expenditure𝑖𝑖,𝑘𝑘 )
(1)
Here sle𝑖𝑖,𝑡𝑡 is the self-learning effect of consumer i in period t. expenditure𝑖𝑖,𝑡𝑡−1 , expenditure𝑖𝑖,𝑘𝑘 are the electricity consumption expenditure of consumer i in period t-1 and period k. 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚_𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 is measuring the consumers’ memory capability. The social influence is measured as equation (2): si𝑖𝑖,𝑡𝑡 = ∑𝑗𝑗∈𝑘𝑘𝑖𝑖 ,𝑐𝑐ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜(𝑗𝑗𝑡𝑡)≠𝑐𝑐ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜(𝑖𝑖𝑡𝑡) 1 / ∑𝑗𝑗∈𝑘𝑘𝑖𝑖 1
(2)
Where si𝑖𝑖,𝑡𝑡 is the social influence effect of consumer i in period t. The binary variable 𝑐𝑐ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜(𝑖𝑖𝑡𝑡 ) is the choice of consumer i in period t. 𝑐𝑐ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜(𝑖𝑖𝑡𝑡 ) = 1 means the consumer i choose real-time pricing and 𝑐𝑐ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜(𝑖𝑖𝑡𝑡 ) = 0 means the consumer i choose fixed pricing. It is assumed that each consumer has his/her unique judgement on the importance of self-learning and social influence, which can be expressed as a weight 𝛾𝛾. The comprehensive effect of self-learning and social influence can be expressed as 𝛾𝛾 × sle𝑖𝑖,𝑡𝑡 + (1 − 𝛾𝛾) × si𝑖𝑖,𝑡𝑡 . When the comprehensive effect exceeds a threshold h, the consumer will change his choice, as described by equation (3). 𝑐𝑐ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑒𝑒(𝑖𝑖𝑡𝑡 ) = {
𝑐𝑐ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜(𝑖𝑖𝑡𝑡−1 ), 𝑖𝑖𝑖𝑖 [𝛾𝛾 × sle𝑖𝑖,𝑡𝑡 + (1 − 𝛾𝛾) × si𝑖𝑖,𝑡𝑡 ] ≤ ℎ 1 − 𝑐𝑐ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜(𝑖𝑖𝑡𝑡−1 ), 𝑖𝑖𝑖𝑖 [𝛾𝛾 × sle𝑖𝑖,𝑡𝑡 + (1 − 𝛾𝛾) × si𝑖𝑖,𝑡𝑡 ] > ℎ
(3)
2.2. Real-time electricity market module Consumers are bilaterally connected to the retailer. Power retailers gather the consumption data and set the realtime price based on the wholesale hourly power consumption. Residents respond to the hourly price by shifting their power load in form of submitting new demand bids and the retailer set a new price again. Such procedure will be repeated until equilibrium. The consumers’ houses consist of controllable, non-controllable electric appliances and central control appliance. Controllable appliances refer to appliances or human tasks which can be performed at any time of the day or within a particular time interval while non-controllable appliances refer to those whose operation time is fixed. A case in point is that washing machine is controllable, however, air-condition is usually non-controllable. For each consumer, his/her objective is to minimize the expenditure, which is described as equation (4). min ∑ℎ 𝑝𝑝𝑟𝑟ℎ × [∑𝑐𝑐 𝑐𝑐𝑎𝑎𝑖𝑖,𝑐𝑐,ℎ + 𝑁𝑁𝑁𝑁𝐿𝐿𝑖𝑖,ℎ ] , ∀𝑖𝑖
(4)
∑ℎ 𝑐𝑐𝑎𝑎𝑖𝑖,𝑐𝑐,ℎ = 𝑅𝑅𝑃𝑃𝑖𝑖,𝑐𝑐 𝑐𝑐𝑎𝑎𝑖𝑖,𝑐𝑐,ℎ ≤ 𝑅𝑅𝑃𝑃𝑖𝑖,𝑐𝑐 , ∀𝑆𝑆𝑆𝑆𝐴𝐴i,c ≤ 𝑡𝑡 ≤ 𝑆𝑆𝑆𝑆𝑂𝑂i,c 𝑐𝑐𝑎𝑎𝑖𝑖,𝑐𝑐,ℎ ≡ 0, ∀𝑡𝑡 < 𝑆𝑆𝑆𝑆𝐴𝐴i,c 𝑜𝑜𝑜𝑜 𝑡𝑡 > 𝑆𝑆𝑆𝑆𝑂𝑂i,c
(5) (6) (7)
Here, 𝑝𝑝𝑟𝑟ℎ is the real-time electricity price, 𝑐𝑐𝑎𝑎𝑖𝑖,𝑐𝑐,ℎ is the power consumed by one controllable appliance and 𝑁𝑁𝑁𝑁𝐿𝐿𝑖𝑖,ℎ is the non-controllable load. Each controllable appliance can only work once for one hour (which is the length of one entire time interval) in the given interval, which is described by equation (5)-(7).
Author name / Energy Procedia 00 (2017) 000–000 Ge Wang et al. / Energy Procedia 142 (2017) 3154–3159
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Here 𝑅𝑅𝑃𝑃𝑖𝑖,𝑐𝑐 is the rated power of one controllable appliance. 𝑆𝑆𝑆𝑆𝐴𝐴i,c is the earliest start time of one controllable appliance and 𝑆𝑆𝑆𝑆𝑂𝑂i,c is the latest stop time of one controllable appliance. An average-cost based pricing scheme is used as is described by equation (8). The 𝐹𝐹𝐹𝐹𝐿𝐿h is the electricity power load of consumers who choose fixed pricing, which is set to be exogenous constant. α and β are coefficients. And the fixed price equals to α+β. 𝑝𝑝𝑟𝑟ℎ = 𝛼𝛼 × {∑𝑖𝑖[∑𝑐𝑐 𝑐𝑐𝑎𝑎𝑖𝑖,𝑐𝑐,ℎ + 𝑁𝑁𝑁𝑁𝐿𝐿𝑖𝑖,ℎ ] + 𝐹𝐹𝐹𝐹𝐿𝐿h }/ {
∑ℎ[∑𝑖𝑖 𝑁𝑁𝑁𝑁𝐿𝐿𝑖𝑖,ℎ +𝐹𝐹𝐹𝐹𝐿𝐿h ]+∑𝑖𝑖 ∑𝑐𝑐 𝑅𝑅𝑃𝑃𝑖𝑖,𝑐𝑐 24
(8)
} + 𝛽𝛽
2.3. Tools The social network module is coded as a multi-agent model using Python programming language. The real-time electricity market module is coded as mixed complementarity problem (MCP), and solved by PATH solver on General Algebraic Modeling System (GAMS). The two modules are linked by Python. 3. Data 3.1. Consumers The residential load consists two parts, the non-controllable load (NCL) and controllable load(CAL). The noncontrollable load and the initial distribution of the controllable load are depicted in Fig. 1. In this study, three types of consumers differing in ability of responding to price change have been taken into consideration. Without loss of generality, it is assumed that the length of the time interval in which energy consumption can be shifted is during 24 hours for the consumer type 1, 5 hours for the consumer type 2, 1 hour for the consumer type 3, respectively. Taking consumer type 2 as an example to illustrate the meaning of the time interval length, if a type 2 consumer is accustomed to using washing machine at 1:00 pm before going to work in the afternoon, he can choose to shift the operation in time interval 11:00 am to 3:00 pm, of which 1:00 pm is the midpoint. In particular, type 1 consumer can shift his load to any other hour within the day and type 3 consumer cannot shift any load. There are 500 consumers considered in this study and they share the same non-controllable load and initial controllable load. 3.2. Social network The default value of the parameters of the social network is shown in Table 1. When conducting the sensitivity analyses of one parameter, the other parameters are set as the default value. The proportion of type 2 consumers is one minus the proportion of type 1 consumers and the proportion of type 3 consumers.
Table 1. Default parameters of the social network
Fig. 1. One consumer’ power load
Network’s degree
Consumer’s threshold
Advertising effect (probability)
Proportion of type 1 consumers
Proportion of type 3 consumers
3
0.3
1%
0.2
0.2
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4. Result The impact of the social network’s mean degree, advertising effect and the composition of different types of consumers on the adoption of real-time electricity pricing mechanism are investigated in this study by simulation and sensitivity analysis. The simulation period is 100. The impact of social network’s degree is shown in Fig 2(a). It is indicated that with the degree increased, the adoption speed of real-time pricing mechanism decreased. The reason is that real-time pricing mechanism is a new opinion for the social-network. The more frequent the consumers communicate with each other, the more chances the new opinion being eliminated by the dominant old opinion (fixed pricing mechanism) in the social influence process. (a)
Degree=3
Degree=5
Degree=7
Probability=0
Probability=1%
Probability=10%
(b)
Fig. 2. (a) The impact of social network’s degree on the diffusion of RTP. (b) The impact of advertising effect on the diffusion of RTP.
As shown in Fig. 2(b), the advertising effect is significantly related to the adoption speed of real-time pricing mechanism. Such mutation probability, as the result of advertisements propagation, is the source of real-time pricing mechanism. The results show that the investment on advertising is useful and essential for promoting the penetration of real-time pricing. (a)
Initial proportion of Type 1 consumer=0
Initial proportion of Type 1 consumer=0.2
Initial proportion of Type 1 consumer=0.4
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Ge Wang et al. / Energy Procedia 142 (2017) 3154–3159 Author name / Energy Procedia 00 (2017) 000–000
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(b)
Initial proportion of Type 3 consumer=0
Initial proportion of Type 3 consumer=0.2
Initial proportion of Type 3 consumer=0.4
Fig. 3. (a) The impact of initial proportion of type 1 consumers on the diffusion of RTP. (b) The impact of initial proportion of type 3 consumers on the diffusion of RTP.
The impacts of the proportion of type 1 consumers and type 3 consumers are shown in Fig 3(a) and Fig 3(b) respectively. It is shown that increasing the proportion of type 1 consumers, who have the highest demand response capability, and decreasing the proportion of type 3 consumers, who have the lowest demand response capability, can promote the adoption of real-time pricing mechanism. However, increasing the proportion of type 1 consumers is more efficient. The reason is that the consumers with higher demand response capability can benefit more from realtime pricing mechanism and thus are more likely to form a stable information source of real-time pricing mechanism. 5. Conclusion In the present study, the impacts of the social network on the adoption of real-time electricity pricing mechanism are investigated by using a social-network evolutionary game model. The results shows that: (i) the higher degree of the consumers social network, the slower the diffusion of real-time pricing, which shows that it is not necessary to provide a platform for communication; (ii) increasing the proportion of consumers with high demand response capability can promote the adoption of RTP, implying the worth of promoting the utilization of smart home technology; (iii) a small exogenous probability (e.g. 1%) of the tariff choice mutation can accelerate the diffusion of RTP, indicating that the advertisement of RTP can be a useful tool. References [1] Chen Z, Wu L, Fu Y. Real-Time Price-Based Demand Response Management for Residential Appliances via Stochastic Optimization and
Robust Optimization. IEEE Transactions on Smart Grid 2012;3:1822–31. [2] Wang G, Zhang Q, Li H, McLellan BC, Chen S, Li Y, et al. Study on the promotion impact of demand response on distributed PV penetration by using non-cooperative game theoretical analysis. Applied Energy 2017;185:1869–78. [3] Du F, Zhang J, Li H, Yan J, Galloway S, Lo KL. Modelling the impact of social network on energy savings. Applied Energy 2016;178:56–65. [4] Jain RK, Gulbinas R, Taylor JE, Culligan PJ. Can social influence drive energy savings? Detecting the impact of social influence on the energy consumption behavior of networked users exposed to normative eco-feedback. Energy and Buildings 2013;66:119–27. [5] Barabási A-L. Scale-Free Networks: A Decade and Beyond. Science 2009;325:412–3. [6] Santos FC, Santos MD, Pacheco JM. Social diversity promotes the emergence of cooperation in public goods games. Nature 2008;454:213–6.