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Auction Mechanism for P2P Local Energy Trading considering Physical Constraints
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Energy Procedia 158 Energy Procedia 00(2019) (2017)6613–6618 000–000 www.elsevier.com/locate/procedia
10th International Conference on Applied Energy (ICAE2018), 22-25 August 2018, Hong Kong, 10th International Conference on Applied Energy China(ICAE2018), 22-25 August 2018, Hong Kong, China
Auction Mechanism for P2P Local Energy Trading considering The 15th International Symposium District Heating and Cooling Auction Mechanism for P2P LocalonEnergy Trading considering Physical Constraints Physical Constraints AssessingChou the feasibility of using the heat demand-outdoor Hon Leong, Chenghong Gu, and Furong Li Chou Hon for Leong, Chenghong Gu, and Furong temperature function a long-term district heat Li demand forecast Department of Electronic & Electrical Engineering, University of Bath, Bath, BA2 7AY, United Kingdom Department of Electronic & Electrical Engineering, University of Bath, Bath, BA2 7AY, United Kingdom
I. Andrića,b,c*, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc a IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal Abstract b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France Abstract c
Département Systèmes Énergétiques et Environnement - IMT Atlantique, Alfred Kastler, 44300 approaches Nantes, Franceto increase Peer to Peer (P2P) Energy trading in a lower voltage distribution system 4isrue one of the effective Peer to Peerenergy (P2P) penetration Energy trading a lower voltage distribution system is one of the approaches to increase renewable fromindecentralized generators (DG). In this paper, an effective energy auction is proposed as a renewable penetrationoffrom decentralized (DG). In this apaper, an energy proposed as a marketplaceenergy and mechanism the market design generators is established to ensure fair and efficientauction biddingis in the auction. marketplace and mechanism the important market design established to To ensure fair problem, and efficient bidding inGame the auction. An optimal bidding strategy isofvery to theisenergy auction. solvea this the Bayesian Theory Abstract An optimal as bidding strategyinisthe very important to the solve this problem, the Bayesian Theory is adopted the strategy energy auction to energy enable auction. efficientTo and cost-effective bidding for eachGame buyer. This isDistrict adopted as the strategy in the energy auction to enable efficient and cost-effective bidding for each buyer. This paper proposes a procedure for the energy auction to ensure that the power losses are within acceptable range. heating networks are commonly addressed in the literature as one of the most effective solutions for decreasingAn the paper proposes a procedure for energy auction to systems ensure thehigh power losses of are within acceptable range. An algorithm transform the power loss issue toThese become partthat of bidding strategy Bayesian Game through Theory. greenhousetogas emissions from thethe building sector. require investments which are returned theThe heat algorithm tototransform theclimate power lossmaximized issueand to become part bidding strategy of distribution Bayesian Theory. The proposed method showed that it has the utility forofprosumer on aheat typical network. sales. Due the ischanged conditions building renovation policies, demand in the Game future could decrease, proposed method is showed thatperiod. it has maximized the utility for prosumer on a typical distribution network. prolonging the investment return
Copyright © 2018ofElsevier Ltd.isAll rights reserved. main paper to Elsevier assess the feasibility of using the heat demand – outdoor temperature function for heat demand ©The 2019 Thescope Authors.this Published by Ltd. Copyright © 2018 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility the scientific committee of theas10ath International Conference Applied Energy forecast. The access districtarticle of Alvalade, inofLisbon (Portugal), was used case study. The district on is consisted of 665 This is an open under thelocated CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) th International Conference on Applied Energy Selection and peer-review under responsibility of the scientific committee of the 10 (ICAE2018). buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and threeEnergy. district Peer-review under responsibility of the scientific committee of ICAE2018 – The 10th International Conference on Applied (ICAE2018). renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were Keywords: Energy Trading, Game VCG Auction, Power losses ; comparedP2P with results from Bayesian a dynamic heatTheory, demand model, previously developed and validated by the authors. Keywords: P2P Energy Trading, Bayesian Game Theory, VCG Auction, Power losses ; of error could be acceptable for some applications The results showed that when only weather change is considered, the margin (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation 1.scenarios, Introduction the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). 1.The Introduction value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the decrease in the an number of heating hours of 22-139h duringbuildings the heatingand season (depending on the combination weather and Nowadays, increasing number commercial households have installed their of own energy Nowadays, an increasing of commercial and households have installed their own energy renovation scenarios considered). On theand other hand, function intercept increased for 7.8-12.7% per decade (depending on the generation or storage to save number energy increase cleanbuildings energy generation for a decarbonized future. Furthermore, coupled scenarios). Thetovalues suggested be options used to modify the function parameters the scenarios considered, and generation or storage save energy andcould increase clean energy generation for decarbonized future. Furthermore, decentralization of energy generation gives more to energy consumers as awell asfor increases the energy security improve the accuracy of heat demand estimations. decentralization of energy generation gives more options to energy consumers as well as increases the energy security and resilience [1]. These distributed energy resources (DERs) could form a small scale network as known as a
and resilience [1]. These distributed energy resources microgrid, enabling the energy to be transferred within or(DERs) betweencould them.form a small scale network as known as a © 2017 Theenabling Authors.the Published by Elsevier Ltd. microgrid, energy to be transferred within or between them. This Peer-to-Peer (P2P) energy transfer allows DERs to utilize the surplus to meet local demand. Most DERs are Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and This Peer-to-Peer (P2P) energy transfer allows DERs to utilize the surplus to meetoflocal demand. DERs are very challenging to accommodate in the energy system due to the high degree volatility andMost intermittency. Cooling. very challenging to accommodate in the energy system due to the high degree of volatility and intermittency. Furthermore, the injection of DERs to the distribution network has also induced instability [2]. Furthermore, injection of DERs the distribution network has also induced instability [2]. Keywords: Heatthe demand; Forecast; Climateto change 1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility the scientific 1876-6102 Copyright © 2018 Elsevier Ltd. All of rights reserved. committee of the 10th International Conference on Applied Energy (ICAE2018). Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied Energy (ICAE2018). 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 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of ICAE2018 – The 10th International Conference on Applied Energy. 10.1016/j.egypro.2019.01.045
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Chou Hon Leong et al. / Energy Procedia 158 (2019) 6613–6618 Author name / Energy Procedia 00 (2018) 000–000
To address these problems, a virtual energy trading platform has been designed to allow consumers and prosumers to physically trade electricity in a P2P model at a microgrid. Prosumers with surplus energy are able to sell it to local demand to make extra profits and maximize energy utilization within the community. It provides a socio-economic incentive for individual households and the communities to invest in distributed energy technologies. This paper has divided into three main sections. A literature review of the current research on P2P energy trading and introduction of Vickrey-Clarke-Groves (VCG) Auction for energy trading. The formulation of Bayesian bidding solution for energy auction. A case study of the P2P trading system via a Bayesian Game theoretic approach. 2. Section I – Literature review and energy market design A large volume of existing research and studies on local P2P energy trading focuses on market design and pricing strategies and mechanism. In [3], N. Liu proposed an energy sharing model with price-based demand response for P2P trading. In [4], an integrated design of marketplace included the architectures and layers in commercial activities, control system, ICT applications and power grid monitoring control. In [5], a competition model of stored energy trade between demand responses aggregators in a non-cooperative game theoretical approached has investigated. This paper focuses on the overall P2P energy trading procedures and the Bayesian strategic bidding solution integrated with physical constraints during the local energy trade. 2.1 Energy Trading Market Structure From the market’s point of view, as the costs of renewable energy and energy storage technologies are declining, more people could afford to install their own DGs [6]. It becomes viable to establish a trading platform for individual prosumers to participate in the local energy market in a Peer to Peer fashion. Base on the model in [7], this paper will focus on Microgrid market setup, which includes the Market Mechanism, the Pricing Mechanism and the Information System. The Distribution System Operator (DSO) will monitor and regulate energy trading activities and ensure it will not bring significant disruption to the distribution networks. Therefore, every trading has to be checked and approved by the DSO before proceeding. 2.3 Energy Market Structure This paper proposes a flowchart to regulate energy trading activities from the beginning till the completion, as seen in figure 1. The flowchart consisted of four main components, the registry for energy sellers, energy Auction, energy balancing by the DSO and the negotiation for the seller and buyers if necessary.
Figure 1 A proposed flow diagram for peer to peer energy trading procedures.
1. Every seller must register with DSO for energy trading, the registration door opens for 30 minutes before the trading; sellers should submit the amount of real energy (kWh), reactive power (kVArh) that are prepared to be injected into distribution network (DN).
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2. After door closure, no registration will be accepted and the DSO will provide brief power flow analysis results to individual seller, including the power losses that the seller will bring to the DN. It will give 30 minutes for sellers to arrange an energy auction, and submit the notification of the energy transaction details to the DSO. 3. The energy auction holds in Vickrey-Clarke-Groves (VCG) auction style. See the explanation in Section 2.3. 4. The preliminary notification (PN) is an initial notice that the sellers to the DSO regarding the completion of the auction, including successful bid price, the amount of real energy to be traded, and the amount of reactive power to be injected. 5. In the energy balancing, the DSO exanimates every PN on a first-come-first-serve basis. The exanimation includes the power flow analysis of the DN and the impact brought by the new transaction. The DSO will decide whether accept the preliminary notification based on the results of the exanimation and this process should take no longer than 5 minutes. If the DSO accepted the PN, the transaction between the seller and buyer will be validated and processed after the Gate Closure. 6. If the PN does not pass the examination by DSO, it will return the notification submitted to the sellers. On a case-by-case basis, the return notification will either be a rejection or a conditional modification request (CMR). The rejection means that the auction has to be disqualified and the seller has to hold the auction again if the seller insisted to trade energy. The CMR will usually be a request for a change of the certain set of variants in order to pass the examination, such as the amount of real and reactive power injection to the DN. 7. In the negotiation, the seller and buyers will decide whether accept the CMR in 5 minutes. If yes, they will return the request to DSO and process the energy transaction after the Gate Closure; otherwise, the result will be equivalent to a rejection. 8. All validated transactions will be listed and proceed after Gate Closure. A new registration will be opened for the next hour slot transactions. 2.3 Vickrey Clarke Groves Auction The Vickrey Clarke Groves (VCG) Auction is proposed for the energy trading in this paper. It is a first price sealed bidding auction for multiple items [11]. VCG Auction can encourage prosumers to bid at a rational price [10]. The seller will have a certain amount of energy that is ready for trade and the energy information will be broadcasted to every buyer. The buyers could bid the amount of energy they want at any price. The bidding list will prioritize the bid in a descending order with the respective amount of energy. The seller will firstly trade with the bidder who has the highest bid price and then the second highest, etc. It will end either all energy has been sold or no more bidders want to purchase energy or the auction excesses the time limit. When some equal bids occur, either one of the following scenarios will take place: a.)If there is sufficient energy for all equal bid bidders: all bidders will receive the amount of energy in their bids. b.)If there is no sufficient energy for all equal bid bidders: all bidders will share the amount of energy proportional to their energy bids. When there is no sufficient energy for the bidder who has the last successful bid, the seller could provide remaining energy to that bidder. 3. Section II - Formulation of Bayesian Equilibrium solution In this section, we developed the Bayesian Equilibrium (BE) solution for VCG auction in energy trading. Including the formulation of function for utility, power losses and the algorithm of the Bayesian strategic bidding. 3.1 Bayesian Game Theory Consider a VCG auction first price sealed bid auction. A seller offers energy es for bidding and there is a number of n bidders, donated as i = 1,2,3…n and the other bidders, donated as j =1,2,3…n, j ≠ i. Bidder i has a valuation vi for certain amount of energy ei as well as the others bidder j. Therefore, if bidder i wins the bid and pays the bid prices at bi, the general utility function for the bidder i is ui (vi – bi). The valuation for each bidder is independently and uniformly distributed on [0,1]. The Bayesian game theoretic algorithm for VCG Auction consists of 4 elements, the action spaces, the type spaces, the beliefs and the utility function. The action spaces are the action that the bidder submits a bid bi, and the type space is the bidder’s valuation vi [9]. The function of valuation for each bidder is consisted by two different variants, the
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electricity retail price Q, and the saving from the energy trade, the saving rate Ci in percentage. Assumed all the consumers in the DN are paying Q, and the Q becomes the common information for all bidders in the auction. The private information is the Ci. And therefore, the valuation function can be formed as: (1) 𝑣𝑣𝑖𝑖 (𝐶𝐶𝑖𝑖 ) = (1 − 𝐶𝐶𝑖𝑖 ) The beliefs for the bidders are that the valuation is independently and uniformly distributed on [0,1], and it assumed all bidders in the energy auction are rational, i.e. they are pursuing to maximize the profit and minimize the energy cost. Therefore, they will not bid higher than Q, where Q is 1 in the uniform distribution [0, Q]. And the utility function in different scenarios can be formed as: 𝑒𝑒𝑖𝑖 (𝑄𝑄 − 𝑏𝑏𝑖𝑖 ), 𝑖𝑖𝑖𝑖 𝑏𝑏𝑖𝑖 > 𝑏𝑏𝑗𝑗 , 𝑒𝑒𝑠𝑠 ≥ 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 (𝑄𝑄 − 𝑏𝑏𝑖𝑖 ), 𝑖𝑖𝑖𝑖 𝑏𝑏𝑖𝑖 = 𝑏𝑏𝑗𝑗 , 𝑒𝑒𝑠𝑠 ≥ 𝑒𝑒𝑖𝑖 + ∑ 𝑒𝑒𝑗𝑗
𝑒𝑒𝑚𝑚 (𝑄𝑄 − 𝑏𝑏𝑖𝑖 ), 𝑒𝑒𝑚𝑚 =
𝑢𝑢𝑖𝑖 (𝑏𝑏𝑖𝑖 , 𝑏𝑏𝑗𝑗 ; 𝑄𝑄; 𝑒𝑒𝑖𝑖 , 𝑒𝑒𝑗𝑗 , 𝑒𝑒𝑠𝑠 ) =
𝑒𝑒𝑖𝑖 𝑒𝑒𝑠𝑠
𝑒𝑒𝑖𝑖 +∑ 𝑒𝑒𝑗𝑗
, 𝑖𝑖𝑖𝑖 𝑏𝑏𝑖𝑖 = 𝑏𝑏𝑗𝑗 , 0 < 𝑒𝑒𝑠𝑠 < 𝑒𝑒𝑖𝑖 + ∑ 𝑒𝑒𝑗𝑗
𝑒𝑒𝑖𝑖 (𝑄𝑄 − 𝑏𝑏𝑖𝑖 ), 𝑖𝑖𝑖𝑖 𝑏𝑏𝑖𝑖 < 𝑏𝑏𝑗𝑗 , 0 < 𝑒𝑒𝑖𝑖 ≤ 𝑒𝑒𝑠𝑠 𝑒𝑒𝑠𝑠 (𝑄𝑄 − 𝑏𝑏𝑖𝑖 ), 𝑖𝑖𝑖𝑖 𝑏𝑏𝑖𝑖 < 𝑏𝑏𝑗𝑗 , 0 < 𝑒𝑒𝑠𝑠 ≤ 𝑒𝑒𝑖𝑖 0, 𝑖𝑖𝑖𝑖 𝑏𝑏𝑖𝑖 < 𝑏𝑏𝑖𝑖 , 0 ≥ 𝑒𝑒𝑠𝑠
{
(2)
Where the em is the modified amount of energy due to the equal bids, the modification would correct the amount of bid energy proportion to the weigh of the energy which they are going to share. All bidders are risk neutral. However, the probability to win the auction is related to the number of bidders in the auction. The larger the number of bidders is, the higher the probability to have others bidders submit a high bid. In the uniform distribution [0, Q], the probability that the bidder i is higher than the others bidder j is the bid itself on the uniform distribution [bi,Q] [8]. Therefore, the probability function in n bidders scenario can be formulated as: (3) 𝑏𝑏𝑖𝑖 × 𝑏𝑏𝑖𝑖 × 𝑏𝑏𝑖𝑖 × 𝑏𝑏𝑖𝑖 × ⋯ = 𝑏𝑏𝑖𝑖𝑛𝑛−1 Hence, the general utility function ui (vi, bi) for bidder i is (𝑣𝑣𝑖𝑖 − 𝑏𝑏𝑖𝑖 ) 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 {𝑏𝑏𝑖𝑖 > 𝑏𝑏𝑗𝑗 } = 𝑏𝑏𝑖𝑖𝑛𝑛−1 (𝑣𝑣𝑖𝑖 − 𝑏𝑏𝑖𝑖 ) (4) The BE for the bid is 𝑑𝑑 { 𝑏𝑏𝑖𝑖𝑛𝑛−1 (𝑣𝑣𝑖𝑖 − 𝑏𝑏𝑖𝑖 ) } (5) and the solution of
𝑑𝑑𝑢𝑢𝑖𝑖 𝑑𝑑𝑏𝑏𝑖𝑖
is
𝑑𝑑𝑏𝑏𝑖𝑖
𝑛𝑛−1
𝑏𝑏𝑖𝑖 = × 𝑣𝑣𝑖𝑖 (6) 𝑛𝑛 In the n bidder’s scenario, the BE occurs when all bidders submit the bid equal to the fraction (n - 1) / n of their
value, vi. For bidder j, the best response to bidder i's strategy is bj = vj (n -1) / n, i ≠ j.
3.2 Power loss and utility factor function However, the above Bayesian utility functions have not included the power loss constraints where the energy seller incurred. The energy market design we proposed has included a feedback of brief power flow analysis result, therefore the seller could inform the bidders of the amount of power loss would take place during the energy trading, and buyers have to afford the full cost of power loss. The power loss ∆𝑒𝑒𝑙𝑙 can be translated into an energy cost Cp, and added into the utility function. ∆𝑒𝑒𝑙𝑙 ∆𝑒𝑒𝑙𝑙 > 0 𝑒𝑒 𝐶𝐶𝑝𝑝 (∆𝑒𝑒𝑙𝑙 , 𝑒𝑒𝑠𝑠 ) = { 𝑠𝑠 (7) 0 ∆𝑒𝑒𝑙𝑙 ≤ 0
The modified utility factor function αi is the following 𝑏𝑏𝑖𝑖𝑛𝑛−1 (𝑄𝑄 − 𝑏𝑏𝑖𝑖 − 𝐶𝐶𝑝𝑝 ) (8) The utility factor is the utility before multiply by the energy bid price and amount of energy. Therefore, we can summarize the BE biding solution into an algorithm, see table 1.
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Table 1 An algorithm for Bayesian Equilibrium bid. Algorithm The Seller sets the energy Es for bid. 1: 2: The n bidders initializes the bidding with their valuation 𝒗𝒗𝒊𝒊 (𝟏𝟏 − 𝑪𝑪𝒊𝒊 ), quantity of energy to bid 𝒆𝒆𝒊𝒊 = {𝒆𝒆𝟏𝟏 , 𝒆𝒆𝟐𝟐, 𝒆𝒆𝟑𝟑 … 𝒆𝒆𝒏𝒏 } and the bid price 𝒃𝒃𝒊𝒊 = {𝒃𝒃𝟏𝟏 , 𝒃𝒃𝟐𝟐, 𝒃𝒃𝟑𝟑 … 𝒃𝒃𝒏𝒏 } , where n is the total number of the bidder who participated in the auction. Meanwhile, seller will also inform the bidders that the cost of power loss to pay. ∆𝑒𝑒𝑙𝑙 ∆𝑒𝑒𝑙𝑙 > 0 𝐶𝐶𝑝𝑝 (∆𝑒𝑒𝑙𝑙 , 𝑒𝑒𝑠𝑠 ) = { 𝑒𝑒𝑠𝑠 3: 4: 5: 6: 7: 8: 9: 10:
0 ∆𝑒𝑒𝑙𝑙 ≤ 0 The bidders position their bid and utility factor function onto a Bayesian Equilibrium 𝑏𝑏𝑖𝑖𝑛𝑛−1 [𝑄𝑄 − 𝑏𝑏𝑖𝑖 − 𝐶𝐶𝑝𝑝 ], where 𝑏𝑏𝑖𝑖 = (1 − 𝑛𝑛)𝑣𝑣𝑖𝑖 /𝑛𝑛 . If utility factor function αi (Q, vi, bi, Cp, n) > 0 , submit the bid If utility factor function αi (Q, vi, bi, Cp, n) ≤ 0 , then Optimise the Valuation function by minimizing the Ci to satisfy αi (Q, vi, bi, Cp, n ) > 0, where Ci ≥ 0. If αi > 0 submits the new bid If αi ≤ 0 not to bid End if End if
4. Section III - Case study of IEEE 33-bus distribution system The IEEE 33-bus distribution system is used to model the proposed P2P energy trading system, where two types of players, prosumer and consumer are included. Assumed all prosumers have renewable energy generator and energy storage system. We only simulate P2P energy trading with one seller and multi-buyers. The auction will stop when there is no surplus energy or unmet local energy demand, or the auction excesses the time limit. In figure 2, node 6 offers 4kWh electricity to sell in the distribution network. Nodes 4, 7, 15, 22 and 30 participate in the auction for the 4kWh electricity. Assumed the retail price of the electricity is 14.37 p/kWh from the current energy supplier.
Figure 2 Single-line diagram of IEEE 33-bus distribution system with 6 prosumers.
4.1 Results In table 2, the bidders submit their bid price and the required amount of energy from 0 to 1, in term of the proportion of the retail energy price and the available energy. The power losses incur by energy trade is 0.6 kWh, it is about 15% of the available energy from the seller. Bus nodes 4 and 7 submit them without following BE solution. And the rest submit their bids in a BE solution. The successful bids are nodes 7, 15 and 30 and the received energy is 0.2, 0.4 and 0.4 respectively. The reason of received energy at 30 nodes has been adjusted because energy available to node 30 does not satisfy the energy bid and therefore it has been reduced to what it has remained. Table 2 The results of the simulated auction according to the algorithm in table 1. Node
Ci
bi
Prioritization
ei
Received ei
αi
4* 7* 15 22 30
0 0.2 0.1
0.6 0.8 0.8 0.64 0.75
5 1 1 4 3
0.8 0.2 0.4 0.7 0.6
0 0.2 0.4 0 0.4
0 0.11 0.22 0 0.21
*Not a Bayesian strategic bidding.
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Figure 3 Comparison of utility factor vs. various number of bidders with (left) and without (right) power losses constraint.
Figure 3 shows the utility factor of the bidder i’s best response to bidder j's strategy in various number of bidders scenarios; In figure 3 (right), the Bayesian Equilibrium’s u(b(Ci = 0)) without power loss constraints always has the highest payoff, the optimal solution of BE for the bid is 0.8 when n=5. However, in figure 3 (left), the power losses constraint alters the result of utility factors as the number of bidder increases, it will give a negatives utility in the BE due to the power loss constraint in the utility factor function. Nodes 30 and 22 have positioned their bid the BE, and both bidders modified the bid by adjusting the variant of Ci to 0.1 and 0.2 respectively in order to maximize the utility and avoid negative utility. When the number of bidders is at 7 or more, the utility goes to negative, therefore optimization of Ci is needed to prevent negative utility. 5. Conclusion Energy trading in P2P fashion is one of the accessible methods to increase the decentralized energy penetration for the future smart grid. The VCG auction with Bayesian game theory approach has provided strategic method and algorithm to allocate the energy resources. The case study of shown the Bayesian strategic bidding solution have maximized the utility for prosumer and prevented the negative utility for bidders when there are more than 7 bidders in the auction when the power losses are at 15%. Multi-seller and multi-buyer in a VCG auction energy trade with game theory approach would be carried out for the future research work in order to further exanimate the model for real practices. References [1] Strbac G, Aunedi M, Pudjianto D, Djapic P, Teng F, Sturt A, et al. Strategic assessment of the role and value of energy storage systems in the UK low carbon energy future. Energy Futures Lab Report Carbon Trust 2012 Available at: 〈www. carbontrust.com/media/129310/energystorage-systems-role-value-strategicassessment.pdf〉. [2] T. Liu, X. Tan, B. Sun, Y. Wu, X. Guan, D.H.K. Tsang, Energy management of cooperative microgrids with P2P energy sharing in distribution networks, in: 2015 IEEE International Conference on Smart Grid Communications (SmartGridComm), 2015, pp. 410-415. [3] N. Liu, X. Yu, C. Wang, C. Li, L. Ma, J. Lei, Energy-Sharing Model With Price-Based Demand Response for Microgrids of Peer-to-Peer Prosumers, IEEE Transactions on Power Systems, 32 (2017) 3569-3583. [4] C. Zhang, J. Wu, Y. Zhou, M. Cheng, C. Long, Peer-to-Peer energy trading in a Microgrid, Applied Energy, 220 (2018) 1-12. [5] M. Motalleb, R. Ghorbani, Non-cooperative game-theoretic model of demand response aggregator competition for selling stored energy in storage devices, Applied Energy, 202 (2017) 581-596. [6] C.L. Azimoh, B.S. Paul, C. Mbohwa, Declining cost of renewable energy technology: An opportunity for increasing electricity access in subSaharan Africa, in: 2017 IEEE Electrical Power and Energy Conference (EPEC), 2017, pp. 1-6. [7] E. Mengelkamp, J. Gärttner, K. Rock, S. Kessler, L. Orsini, C. Weinhardt, Designing microgrid energy markets: A case study: The Brooklyn Microgrid, Applied Energy, 210 (2018) 870-880. [8] D.E. Campbell, Incentives: Motivation and the economics of information, Cambridge University Press, 2018, pp. 353-358. [9] R. Gibbons, Game theory for applied economists, Princeton University Press, 1992, pp. 155-159. [10] C.S. PING Jian, ZHANG Ning, YAN Zheng, YAO Liangzhong, Decentralized Transactive Mechanism in Distribution Network Based on Smart Contract, Proceeding of the CSEE, 37 (2017) 3682-3690. [11] D. Fudenberg, J. Tirole, Game theory, The MIT Press, Cambridge, Massachusetts, 1991, pp. 223.
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10th International Conference on Applied Energy (ICAE2018), 22-25 August 2018, Hong Kong, 10th International Conference on Applied Energy China(ICAE2018), 22-25 August 2018, Hong Kong, China
Auction Mechanism for P2P Local Energy Trading considering The 15th International Symposium District Heating and Cooling Auction Mechanism for P2P LocalonEnergy Trading considering Physical Constraints Physical Constraints AssessingChou the feasibility of using the heat demand-outdoor Hon Leong, Chenghong Gu, and Furong Li Chou Hon for Leong, Chenghong Gu, and Furong temperature function a long-term district heat Li demand forecast Department of Electronic & Electrical Engineering, University of Bath, Bath, BA2 7AY, United Kingdom Department of Electronic & Electrical Engineering, University of Bath, Bath, BA2 7AY, United Kingdom
I. Andrića,b,c*, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc a IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal Abstract b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France Abstract c
Département Systèmes Énergétiques et Environnement - IMT Atlantique, Alfred Kastler, 44300 approaches Nantes, Franceto increase Peer to Peer (P2P) Energy trading in a lower voltage distribution system 4isrue one of the effective Peer to Peerenergy (P2P) penetration Energy trading a lower voltage distribution system is one of the approaches to increase renewable fromindecentralized generators (DG). In this paper, an effective energy auction is proposed as a renewable penetrationoffrom decentralized (DG). In this apaper, an energy proposed as a marketplaceenergy and mechanism the market design generators is established to ensure fair and efficientauction biddingis in the auction. marketplace and mechanism the important market design established to To ensure fair problem, and efficient bidding inGame the auction. An optimal bidding strategy isofvery to theisenergy auction. solvea this the Bayesian Theory Abstract An optimal as bidding strategyinisthe very important to the solve this problem, the Bayesian Theory is adopted the strategy energy auction to energy enable auction. efficientTo and cost-effective bidding for eachGame buyer. This isDistrict adopted as the strategy in the energy auction to enable efficient and cost-effective bidding for each buyer. This paper proposes a procedure for the energy auction to ensure that the power losses are within acceptable range. heating networks are commonly addressed in the literature as one of the most effective solutions for decreasingAn the paper proposes a procedure for energy auction to systems ensure thehigh power losses of are within acceptable range. An algorithm transform the power loss issue toThese become partthat of bidding strategy Bayesian Game through Theory. greenhousetogas emissions from thethe building sector. require investments which are returned theThe heat algorithm tototransform theclimate power lossmaximized issueand to become part bidding strategy of distribution Bayesian Theory. The proposed method showed that it has the utility forofprosumer on aheat typical network. sales. Due the ischanged conditions building renovation policies, demand in the Game future could decrease, proposed method is showed thatperiod. it has maximized the utility for prosumer on a typical distribution network. prolonging the investment return
Copyright © 2018ofElsevier Ltd.isAll rights reserved. main paper to Elsevier assess the feasibility of using the heat demand – outdoor temperature function for heat demand ©The 2019 Thescope Authors.this Published by Ltd. Copyright © 2018 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility the scientific committee of theas10ath International Conference Applied Energy forecast. The access districtarticle of Alvalade, inofLisbon (Portugal), was used case study. The district on is consisted of 665 This is an open under thelocated CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) th International Conference on Applied Energy Selection and peer-review under responsibility of the scientific committee of the 10 (ICAE2018). buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and threeEnergy. district Peer-review under responsibility of the scientific committee of ICAE2018 – The 10th International Conference on Applied (ICAE2018). renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were Keywords: Energy Trading, Game VCG Auction, Power losses ; comparedP2P with results from Bayesian a dynamic heatTheory, demand model, previously developed and validated by the authors. Keywords: P2P Energy Trading, Bayesian Game Theory, VCG Auction, Power losses ; of error could be acceptable for some applications The results showed that when only weather change is considered, the margin (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation 1.scenarios, Introduction the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). 1.The Introduction value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the decrease in the an number of heating hours of 22-139h duringbuildings the heatingand season (depending on the combination weather and Nowadays, increasing number commercial households have installed their of own energy Nowadays, an increasing of commercial and households have installed their own energy renovation scenarios considered). On theand other hand, function intercept increased for 7.8-12.7% per decade (depending on the generation or storage to save number energy increase cleanbuildings energy generation for a decarbonized future. Furthermore, coupled scenarios). Thetovalues suggested be options used to modify the function parameters the scenarios considered, and generation or storage save energy andcould increase clean energy generation for decarbonized future. Furthermore, decentralization of energy generation gives more to energy consumers as awell asfor increases the energy security improve the accuracy of heat demand estimations. decentralization of energy generation gives more options to energy consumers as well as increases the energy security and resilience [1]. These distributed energy resources (DERs) could form a small scale network as known as a
and resilience [1]. These distributed energy resources microgrid, enabling the energy to be transferred within or(DERs) betweencould them.form a small scale network as known as a © 2017 Theenabling Authors.the Published by Elsevier Ltd. microgrid, energy to be transferred within or between them. This Peer-to-Peer (P2P) energy transfer allows DERs to utilize the surplus to meet local demand. Most DERs are Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and This Peer-to-Peer (P2P) energy transfer allows DERs to utilize the surplus to meetoflocal demand. DERs are very challenging to accommodate in the energy system due to the high degree volatility andMost intermittency. Cooling. very challenging to accommodate in the energy system due to the high degree of volatility and intermittency. Furthermore, the injection of DERs to the distribution network has also induced instability [2]. Furthermore, injection of DERs the distribution network has also induced instability [2]. Keywords: Heatthe demand; Forecast; Climateto change 1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility the scientific 1876-6102 Copyright © 2018 Elsevier Ltd. All of rights reserved. committee of the 10th International Conference on Applied Energy (ICAE2018). Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied Energy (ICAE2018). 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 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of ICAE2018 – The 10th International Conference on Applied Energy. 10.1016/j.egypro.2019.01.045
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Chou Hon Leong et al. / Energy Procedia 158 (2019) 6613–6618 Author name / Energy Procedia 00 (2018) 000–000
To address these problems, a virtual energy trading platform has been designed to allow consumers and prosumers to physically trade electricity in a P2P model at a microgrid. Prosumers with surplus energy are able to sell it to local demand to make extra profits and maximize energy utilization within the community. It provides a socio-economic incentive for individual households and the communities to invest in distributed energy technologies. This paper has divided into three main sections. A literature review of the current research on P2P energy trading and introduction of Vickrey-Clarke-Groves (VCG) Auction for energy trading. The formulation of Bayesian bidding solution for energy auction. A case study of the P2P trading system via a Bayesian Game theoretic approach. 2. Section I – Literature review and energy market design A large volume of existing research and studies on local P2P energy trading focuses on market design and pricing strategies and mechanism. In [3], N. Liu proposed an energy sharing model with price-based demand response for P2P trading. In [4], an integrated design of marketplace included the architectures and layers in commercial activities, control system, ICT applications and power grid monitoring control. In [5], a competition model of stored energy trade between demand responses aggregators in a non-cooperative game theoretical approached has investigated. This paper focuses on the overall P2P energy trading procedures and the Bayesian strategic bidding solution integrated with physical constraints during the local energy trade. 2.1 Energy Trading Market Structure From the market’s point of view, as the costs of renewable energy and energy storage technologies are declining, more people could afford to install their own DGs [6]. It becomes viable to establish a trading platform for individual prosumers to participate in the local energy market in a Peer to Peer fashion. Base on the model in [7], this paper will focus on Microgrid market setup, which includes the Market Mechanism, the Pricing Mechanism and the Information System. The Distribution System Operator (DSO) will monitor and regulate energy trading activities and ensure it will not bring significant disruption to the distribution networks. Therefore, every trading has to be checked and approved by the DSO before proceeding. 2.3 Energy Market Structure This paper proposes a flowchart to regulate energy trading activities from the beginning till the completion, as seen in figure 1. The flowchart consisted of four main components, the registry for energy sellers, energy Auction, energy balancing by the DSO and the negotiation for the seller and buyers if necessary.
Figure 1 A proposed flow diagram for peer to peer energy trading procedures.
1. Every seller must register with DSO for energy trading, the registration door opens for 30 minutes before the trading; sellers should submit the amount of real energy (kWh), reactive power (kVArh) that are prepared to be injected into distribution network (DN).
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2. After door closure, no registration will be accepted and the DSO will provide brief power flow analysis results to individual seller, including the power losses that the seller will bring to the DN. It will give 30 minutes for sellers to arrange an energy auction, and submit the notification of the energy transaction details to the DSO. 3. The energy auction holds in Vickrey-Clarke-Groves (VCG) auction style. See the explanation in Section 2.3. 4. The preliminary notification (PN) is an initial notice that the sellers to the DSO regarding the completion of the auction, including successful bid price, the amount of real energy to be traded, and the amount of reactive power to be injected. 5. In the energy balancing, the DSO exanimates every PN on a first-come-first-serve basis. The exanimation includes the power flow analysis of the DN and the impact brought by the new transaction. The DSO will decide whether accept the preliminary notification based on the results of the exanimation and this process should take no longer than 5 minutes. If the DSO accepted the PN, the transaction between the seller and buyer will be validated and processed after the Gate Closure. 6. If the PN does not pass the examination by DSO, it will return the notification submitted to the sellers. On a case-by-case basis, the return notification will either be a rejection or a conditional modification request (CMR). The rejection means that the auction has to be disqualified and the seller has to hold the auction again if the seller insisted to trade energy. The CMR will usually be a request for a change of the certain set of variants in order to pass the examination, such as the amount of real and reactive power injection to the DN. 7. In the negotiation, the seller and buyers will decide whether accept the CMR in 5 minutes. If yes, they will return the request to DSO and process the energy transaction after the Gate Closure; otherwise, the result will be equivalent to a rejection. 8. All validated transactions will be listed and proceed after Gate Closure. A new registration will be opened for the next hour slot transactions. 2.3 Vickrey Clarke Groves Auction The Vickrey Clarke Groves (VCG) Auction is proposed for the energy trading in this paper. It is a first price sealed bidding auction for multiple items [11]. VCG Auction can encourage prosumers to bid at a rational price [10]. The seller will have a certain amount of energy that is ready for trade and the energy information will be broadcasted to every buyer. The buyers could bid the amount of energy they want at any price. The bidding list will prioritize the bid in a descending order with the respective amount of energy. The seller will firstly trade with the bidder who has the highest bid price and then the second highest, etc. It will end either all energy has been sold or no more bidders want to purchase energy or the auction excesses the time limit. When some equal bids occur, either one of the following scenarios will take place: a.)If there is sufficient energy for all equal bid bidders: all bidders will receive the amount of energy in their bids. b.)If there is no sufficient energy for all equal bid bidders: all bidders will share the amount of energy proportional to their energy bids. When there is no sufficient energy for the bidder who has the last successful bid, the seller could provide remaining energy to that bidder. 3. Section II - Formulation of Bayesian Equilibrium solution In this section, we developed the Bayesian Equilibrium (BE) solution for VCG auction in energy trading. Including the formulation of function for utility, power losses and the algorithm of the Bayesian strategic bidding. 3.1 Bayesian Game Theory Consider a VCG auction first price sealed bid auction. A seller offers energy es for bidding and there is a number of n bidders, donated as i = 1,2,3…n and the other bidders, donated as j =1,2,3…n, j ≠ i. Bidder i has a valuation vi for certain amount of energy ei as well as the others bidder j. Therefore, if bidder i wins the bid and pays the bid prices at bi, the general utility function for the bidder i is ui (vi – bi). The valuation for each bidder is independently and uniformly distributed on [0,1]. The Bayesian game theoretic algorithm for VCG Auction consists of 4 elements, the action spaces, the type spaces, the beliefs and the utility function. The action spaces are the action that the bidder submits a bid bi, and the type space is the bidder’s valuation vi [9]. The function of valuation for each bidder is consisted by two different variants, the
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electricity retail price Q, and the saving from the energy trade, the saving rate Ci in percentage. Assumed all the consumers in the DN are paying Q, and the Q becomes the common information for all bidders in the auction. The private information is the Ci. And therefore, the valuation function can be formed as: (1) 𝑣𝑣𝑖𝑖 (𝐶𝐶𝑖𝑖 ) = (1 − 𝐶𝐶𝑖𝑖 ) The beliefs for the bidders are that the valuation is independently and uniformly distributed on [0,1], and it assumed all bidders in the energy auction are rational, i.e. they are pursuing to maximize the profit and minimize the energy cost. Therefore, they will not bid higher than Q, where Q is 1 in the uniform distribution [0, Q]. And the utility function in different scenarios can be formed as: 𝑒𝑒𝑖𝑖 (𝑄𝑄 − 𝑏𝑏𝑖𝑖 ), 𝑖𝑖𝑖𝑖 𝑏𝑏𝑖𝑖 > 𝑏𝑏𝑗𝑗 , 𝑒𝑒𝑠𝑠 ≥ 𝑒𝑒𝑖𝑖 𝑒𝑒𝑖𝑖 (𝑄𝑄 − 𝑏𝑏𝑖𝑖 ), 𝑖𝑖𝑖𝑖 𝑏𝑏𝑖𝑖 = 𝑏𝑏𝑗𝑗 , 𝑒𝑒𝑠𝑠 ≥ 𝑒𝑒𝑖𝑖 + ∑ 𝑒𝑒𝑗𝑗
𝑒𝑒𝑚𝑚 (𝑄𝑄 − 𝑏𝑏𝑖𝑖 ), 𝑒𝑒𝑚𝑚 =
𝑢𝑢𝑖𝑖 (𝑏𝑏𝑖𝑖 , 𝑏𝑏𝑗𝑗 ; 𝑄𝑄; 𝑒𝑒𝑖𝑖 , 𝑒𝑒𝑗𝑗 , 𝑒𝑒𝑠𝑠 ) =
𝑒𝑒𝑖𝑖 𝑒𝑒𝑠𝑠
𝑒𝑒𝑖𝑖 +∑ 𝑒𝑒𝑗𝑗
, 𝑖𝑖𝑖𝑖 𝑏𝑏𝑖𝑖 = 𝑏𝑏𝑗𝑗 , 0 < 𝑒𝑒𝑠𝑠 < 𝑒𝑒𝑖𝑖 + ∑ 𝑒𝑒𝑗𝑗
𝑒𝑒𝑖𝑖 (𝑄𝑄 − 𝑏𝑏𝑖𝑖 ), 𝑖𝑖𝑖𝑖 𝑏𝑏𝑖𝑖 < 𝑏𝑏𝑗𝑗 , 0 < 𝑒𝑒𝑖𝑖 ≤ 𝑒𝑒𝑠𝑠 𝑒𝑒𝑠𝑠 (𝑄𝑄 − 𝑏𝑏𝑖𝑖 ), 𝑖𝑖𝑖𝑖 𝑏𝑏𝑖𝑖 < 𝑏𝑏𝑗𝑗 , 0 < 𝑒𝑒𝑠𝑠 ≤ 𝑒𝑒𝑖𝑖 0, 𝑖𝑖𝑖𝑖 𝑏𝑏𝑖𝑖 < 𝑏𝑏𝑖𝑖 , 0 ≥ 𝑒𝑒𝑠𝑠
{
(2)
Where the em is the modified amount of energy due to the equal bids, the modification would correct the amount of bid energy proportion to the weigh of the energy which they are going to share. All bidders are risk neutral. However, the probability to win the auction is related to the number of bidders in the auction. The larger the number of bidders is, the higher the probability to have others bidders submit a high bid. In the uniform distribution [0, Q], the probability that the bidder i is higher than the others bidder j is the bid itself on the uniform distribution [bi,Q] [8]. Therefore, the probability function in n bidders scenario can be formulated as: (3) 𝑏𝑏𝑖𝑖 × 𝑏𝑏𝑖𝑖 × 𝑏𝑏𝑖𝑖 × 𝑏𝑏𝑖𝑖 × ⋯ = 𝑏𝑏𝑖𝑖𝑛𝑛−1 Hence, the general utility function ui (vi, bi) for bidder i is (𝑣𝑣𝑖𝑖 − 𝑏𝑏𝑖𝑖 ) 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 {𝑏𝑏𝑖𝑖 > 𝑏𝑏𝑗𝑗 } = 𝑏𝑏𝑖𝑖𝑛𝑛−1 (𝑣𝑣𝑖𝑖 − 𝑏𝑏𝑖𝑖 ) (4) The BE for the bid is 𝑑𝑑 { 𝑏𝑏𝑖𝑖𝑛𝑛−1 (𝑣𝑣𝑖𝑖 − 𝑏𝑏𝑖𝑖 ) } (5) and the solution of
𝑑𝑑𝑢𝑢𝑖𝑖 𝑑𝑑𝑏𝑏𝑖𝑖
is
𝑑𝑑𝑏𝑏𝑖𝑖
𝑛𝑛−1
𝑏𝑏𝑖𝑖 = × 𝑣𝑣𝑖𝑖 (6) 𝑛𝑛 In the n bidder’s scenario, the BE occurs when all bidders submit the bid equal to the fraction (n - 1) / n of their
value, vi. For bidder j, the best response to bidder i's strategy is bj = vj (n -1) / n, i ≠ j.
3.2 Power loss and utility factor function However, the above Bayesian utility functions have not included the power loss constraints where the energy seller incurred. The energy market design we proposed has included a feedback of brief power flow analysis result, therefore the seller could inform the bidders of the amount of power loss would take place during the energy trading, and buyers have to afford the full cost of power loss. The power loss ∆𝑒𝑒𝑙𝑙 can be translated into an energy cost Cp, and added into the utility function. ∆𝑒𝑒𝑙𝑙 ∆𝑒𝑒𝑙𝑙 > 0 𝑒𝑒 𝐶𝐶𝑝𝑝 (∆𝑒𝑒𝑙𝑙 , 𝑒𝑒𝑠𝑠 ) = { 𝑠𝑠 (7) 0 ∆𝑒𝑒𝑙𝑙 ≤ 0
The modified utility factor function αi is the following 𝑏𝑏𝑖𝑖𝑛𝑛−1 (𝑄𝑄 − 𝑏𝑏𝑖𝑖 − 𝐶𝐶𝑝𝑝 ) (8) The utility factor is the utility before multiply by the energy bid price and amount of energy. Therefore, we can summarize the BE biding solution into an algorithm, see table 1.
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Table 1 An algorithm for Bayesian Equilibrium bid. Algorithm The Seller sets the energy Es for bid. 1: 2: The n bidders initializes the bidding with their valuation 𝒗𝒗𝒊𝒊 (𝟏𝟏 − 𝑪𝑪𝒊𝒊 ), quantity of energy to bid 𝒆𝒆𝒊𝒊 = {𝒆𝒆𝟏𝟏 , 𝒆𝒆𝟐𝟐, 𝒆𝒆𝟑𝟑 … 𝒆𝒆𝒏𝒏 } and the bid price 𝒃𝒃𝒊𝒊 = {𝒃𝒃𝟏𝟏 , 𝒃𝒃𝟐𝟐, 𝒃𝒃𝟑𝟑 … 𝒃𝒃𝒏𝒏 } , where n is the total number of the bidder who participated in the auction. Meanwhile, seller will also inform the bidders that the cost of power loss to pay. ∆𝑒𝑒𝑙𝑙 ∆𝑒𝑒𝑙𝑙 > 0 𝐶𝐶𝑝𝑝 (∆𝑒𝑒𝑙𝑙 , 𝑒𝑒𝑠𝑠 ) = { 𝑒𝑒𝑠𝑠 3: 4: 5: 6: 7: 8: 9: 10:
0 ∆𝑒𝑒𝑙𝑙 ≤ 0 The bidders position their bid and utility factor function onto a Bayesian Equilibrium 𝑏𝑏𝑖𝑖𝑛𝑛−1 [𝑄𝑄 − 𝑏𝑏𝑖𝑖 − 𝐶𝐶𝑝𝑝 ], where 𝑏𝑏𝑖𝑖 = (1 − 𝑛𝑛)𝑣𝑣𝑖𝑖 /𝑛𝑛 . If utility factor function αi (Q, vi, bi, Cp, n) > 0 , submit the bid If utility factor function αi (Q, vi, bi, Cp, n) ≤ 0 , then Optimise the Valuation function by minimizing the Ci to satisfy αi (Q, vi, bi, Cp, n ) > 0, where Ci ≥ 0. If αi > 0 submits the new bid If αi ≤ 0 not to bid End if End if
4. Section III - Case study of IEEE 33-bus distribution system The IEEE 33-bus distribution system is used to model the proposed P2P energy trading system, where two types of players, prosumer and consumer are included. Assumed all prosumers have renewable energy generator and energy storage system. We only simulate P2P energy trading with one seller and multi-buyers. The auction will stop when there is no surplus energy or unmet local energy demand, or the auction excesses the time limit. In figure 2, node 6 offers 4kWh electricity to sell in the distribution network. Nodes 4, 7, 15, 22 and 30 participate in the auction for the 4kWh electricity. Assumed the retail price of the electricity is 14.37 p/kWh from the current energy supplier.
Figure 2 Single-line diagram of IEEE 33-bus distribution system with 6 prosumers.
4.1 Results In table 2, the bidders submit their bid price and the required amount of energy from 0 to 1, in term of the proportion of the retail energy price and the available energy. The power losses incur by energy trade is 0.6 kWh, it is about 15% of the available energy from the seller. Bus nodes 4 and 7 submit them without following BE solution. And the rest submit their bids in a BE solution. The successful bids are nodes 7, 15 and 30 and the received energy is 0.2, 0.4 and 0.4 respectively. The reason of received energy at 30 nodes has been adjusted because energy available to node 30 does not satisfy the energy bid and therefore it has been reduced to what it has remained. Table 2 The results of the simulated auction according to the algorithm in table 1. Node
Ci
bi
Prioritization
ei
Received ei
αi
4* 7* 15 22 30
0 0.2 0.1
0.6 0.8 0.8 0.64 0.75
5 1 1 4 3
0.8 0.2 0.4 0.7 0.6
0 0.2 0.4 0 0.4
0 0.11 0.22 0 0.21
*Not a Bayesian strategic bidding.
Chou Hon Leong et al.Procedia / Energy00 Procedia 158 (2019) 6613–6618 Author name / Energy (2018) 000–000
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Figure 3 Comparison of utility factor vs. various number of bidders with (left) and without (right) power losses constraint.
Figure 3 shows the utility factor of the bidder i’s best response to bidder j's strategy in various number of bidders scenarios; In figure 3 (right), the Bayesian Equilibrium’s u(b(Ci = 0)) without power loss constraints always has the highest payoff, the optimal solution of BE for the bid is 0.8 when n=5. However, in figure 3 (left), the power losses constraint alters the result of utility factors as the number of bidder increases, it will give a negatives utility in the BE due to the power loss constraint in the utility factor function. Nodes 30 and 22 have positioned their bid the BE, and both bidders modified the bid by adjusting the variant of Ci to 0.1 and 0.2 respectively in order to maximize the utility and avoid negative utility. When the number of bidders is at 7 or more, the utility goes to negative, therefore optimization of Ci is needed to prevent negative utility. 5. Conclusion Energy trading in P2P fashion is one of the accessible methods to increase the decentralized energy penetration for the future smart grid. The VCG auction with Bayesian game theory approach has provided strategic method and algorithm to allocate the energy resources. The case study of shown the Bayesian strategic bidding solution have maximized the utility for prosumer and prevented the negative utility for bidders when there are more than 7 bidders in the auction when the power losses are at 15%. Multi-seller and multi-buyer in a VCG auction energy trade with game theory approach would be carried out for the future research work in order to further exanimate the model for real practices. References [1] Strbac G, Aunedi M, Pudjianto D, Djapic P, Teng F, Sturt A, et al. Strategic assessment of the role and value of energy storage systems in the UK low carbon energy future. Energy Futures Lab Report Carbon Trust 2012 Available at: 〈www. carbontrust.com/media/129310/energystorage-systems-role-value-strategicassessment.pdf〉. [2] T. Liu, X. Tan, B. Sun, Y. Wu, X. Guan, D.H.K. Tsang, Energy management of cooperative microgrids with P2P energy sharing in distribution networks, in: 2015 IEEE International Conference on Smart Grid Communications (SmartGridComm), 2015, pp. 410-415. [3] N. Liu, X. Yu, C. Wang, C. Li, L. Ma, J. Lei, Energy-Sharing Model With Price-Based Demand Response for Microgrids of Peer-to-Peer Prosumers, IEEE Transactions on Power Systems, 32 (2017) 3569-3583. [4] C. Zhang, J. Wu, Y. Zhou, M. Cheng, C. Long, Peer-to-Peer energy trading in a Microgrid, Applied Energy, 220 (2018) 1-12. [5] M. Motalleb, R. Ghorbani, Non-cooperative game-theoretic model of demand response aggregator competition for selling stored energy in storage devices, Applied Energy, 202 (2017) 581-596. [6] C.L. Azimoh, B.S. Paul, C. Mbohwa, Declining cost of renewable energy technology: An opportunity for increasing electricity access in subSaharan Africa, in: 2017 IEEE Electrical Power and Energy Conference (EPEC), 2017, pp. 1-6. [7] E. Mengelkamp, J. Gärttner, K. Rock, S. Kessler, L. Orsini, C. Weinhardt, Designing microgrid energy markets: A case study: The Brooklyn Microgrid, Applied Energy, 210 (2018) 870-880. [8] D.E. Campbell, Incentives: Motivation and the economics of information, Cambridge University Press, 2018, pp. 353-358. [9] R. Gibbons, Game theory for applied economists, Princeton University Press, 1992, pp. 155-159. [10] C.S. PING Jian, ZHANG Ning, YAN Zheng, YAO Liangzhong, Decentralized Transactive Mechanism in Distribution Network Based on Smart Contract, Proceeding of the CSEE, 37 (2017) 3682-3690. [11] D. Fudenberg, J. Tirole, Game theory, The MIT Press, Cambridge, Massachusetts, 1991, pp. 223.