Transactive Energy Auction with Hidden User Information in Microgrid

📝 Abstract

This research proposes a novel auction mechanism for transactive energy exchange between buyers and sellers, modeled as agents in a microgrid. The mechanism is implemented by a separate microgrid controller (MC) agent, and requires big data flow with the other agents through an iterative bidding process. Although private user information remains hidden to the MC, a theoretical analysis shows that under the assumption of convexity of the agents utilities, the proposed auction is still able to maximize the social welfare (SW), i.e. the aggregate utilities of the agents. In addition, it is shown that the mechanism exhibits the key desirable features of individual rationality and weak budget balance, guaranteeing that neither the payoff to any agent nor the net monetary revenue after termination, is negative. The proposed approach also incorporates a mechanism to redistribute the sellers shares in a fair manner. As an example, a maximum entropy based fair redistribution scheme is addressed. The theoretical analysis reported here is accompanied by extensive set of simulations that illustrate the various aspects of the proposed mechanism.

💡 Analysis

This research proposes a novel auction mechanism for transactive energy exchange between buyers and sellers, modeled as agents in a microgrid. The mechanism is implemented by a separate microgrid controller (MC) agent, and requires big data flow with the other agents through an iterative bidding process. Although private user information remains hidden to the MC, a theoretical analysis shows that under the assumption of convexity of the agents utilities, the proposed auction is still able to maximize the social welfare (SW), i.e. the aggregate utilities of the agents. In addition, it is shown that the mechanism exhibits the key desirable features of individual rationality and weak budget balance, guaranteeing that neither the payoff to any agent nor the net monetary revenue after termination, is negative. The proposed approach also incorporates a mechanism to redistribute the sellers shares in a fair manner. As an example, a maximum entropy based fair redistribution scheme is addressed. The theoretical analysis reported here is accompanied by extensive set of simulations that illustrate the various aspects of the proposed mechanism.

📄 Content

1

Abstract— This research proposes a novel auction mechanism for transactive energy exchange between buyers and sellers, modeled as agents in a microgrid. The mechanism is implemented by a separate microgrid controller (MC) agent, and requires big data flow with the other agents through an iterative bidding process. Although private user information remains hidden to the MC, a theoretical analysis shows that under the assumption of convexity of the agents’ utilities, the proposed auction is still able to maximize the social welfare (SW), i.e. the aggregate utilities of the agents. In addition, it is shown that the mechanism exhibits the key desirable features of individual rationality and weak budget balance; guaranteeing that neither the payoff to any agent nor the net monetary revenue after termination, is negative. The proposed approach also incorporates a mechanism to redistribute the sellers’ shares in a fair manner. As an example, a maximum entropy based fair redistribution scheme is addressed. The theoretical analysis reported here is accompanied by extensive set of simulations that illustrate the various aspects of the proposed mechanism.

Index Terms—microgrid; agents; trading; auction; bid; social welfare, fairness

NOMENCLATURE

𝒟 Set of buyer agents 𝒮 Set of seller agents 𝑁𝑏 Number of buyer agents, where 𝑁𝑏= |𝒟| 𝑁𝑠 Number of seller agents, where 𝑁𝑠= |𝒮| 𝑖 Index of a buyer, where 𝑖∈𝒟 𝑗 Index of a seller, where 𝑗∈𝒮 𝑢𝑖 Utility function of the 𝑖𝑡ℎ buyer 𝑢𝑖 ′ Marginal utility of the 𝑖𝑡ℎ buyer 𝑔𝑗 Generation capacity of the 𝑗𝑡ℎ seller 𝑣𝑗 Utility function of the 𝑗𝑡ℎ seller 𝑣𝑗 ′ Marginal utility of the 𝑗𝑡ℎ seller 𝑑𝑖 Demand delivered to the 𝑖th buyer 𝑏𝑖 Buying price bid placed by the 𝑖th buyer 𝑐𝑖 Buying per unit price payed by the 𝑖th buyer 𝑎𝑗 Availability declared by 𝑗th seller 𝑠𝑗 Supply amount assigned to the 𝑗th seller 𝑐𝑗 Minimum per unit selling price by the 𝑗th seller 𝑝 The minimum per unit buying and maximum per unit selling price of energy Θ SW optimization problem (SWOP) objective function ℒΘ Lagrangian of the SWOP
𝜆𝑖 Dual variable in ℒΘ, corresponding to 𝑝𝑑𝑖≤𝑏𝑖 𝛼𝑗 Dual variable in ℒΘ, corresponding to 𝑠𝑗< 𝑎𝑗 𝜇 Dual variable in ℒΘ, corresponding to ∑ 𝑑𝑖 𝑖∈𝒟 = ∑ 𝑠𝑗 𝑗∈𝒮

This work was supported by the National Science Foundation-CPS under Grants CNS-1136040 and CNS-1544705. 𝑑𝑖 ∗ 𝑑𝑖 at equilibrium as the efficient solution of the SWOP 𝑠𝑗 ∗ 𝑠𝑗 at equilibrium as the efficient solution of the SWOP 𝜆𝑖 ∗ 𝜆𝑖 at equilibrium in the SWOP 𝛼𝑗 ∗ 𝛼𝑗 at equilibrium in the SWOP 𝜇∗ 𝜇 at equilibrium in the SWOP Φ MC optimization problem (MCOP) objective function ℒΦ Lagrangian of the MCOP 𝛾𝑖 Dual variable in ℒΦ, corresponding to 𝑝𝑑𝑖≤𝑏𝑖 𝛽𝑗 Dual variable in ℒΦ, corresponding to 𝑠𝑗< 𝑎𝑗 𝜈 Dual variable in ℒΦ, corresponding to ∑ 𝑑𝑖 𝑖∈𝒟 = ∑ 𝑠𝑗 𝑗∈𝒮

𝑑𝑖 † 𝑑𝑖 at equilibrium as the solution of the MCOP 𝑠𝑗 † 𝑠𝑗 at equilibrium as the solution of the MCOP 𝛾𝑖 † 𝛾𝑖 at equilibrium in the MCOP 𝛽𝑗 † 𝛽𝑗 at equilibrium in the MCOP 𝜈† 𝜈 at equilibrium in the MCOP 𝜁 Dual variable of constraint 𝑠𝑗≥0 in seller’s problem 𝜋𝑖 Buyers payoff from the auction 𝜋𝑗 Sellers payoff from the auction 𝜋𝑀𝑀 Microgrid controllers’ benefit 𝐹 Fairness term function 𝜂 Fairness term coefficient ℒWF Lagrangian of the FROP 𝑠𝑗 𝑟 The sellers’ redistributed supply 𝑆 Sum of the redistributed supply of all sellers 𝑅 Total sellers’ revenue 𝑐𝑗 𝑟 The sellers’ redistributed selling price 𝛽𝑗 𝑟 Dual variable in ℒWF for 𝑠𝑗 𝑟≤𝑎𝑗 𝜈𝑟 Dual variable in ℒWF for ∑ 𝑠𝑗 𝑟= 𝑆 𝑗∈𝒮

𝐾 Solution constant for the FROP 𝜅𝐹 Price of fairness
I. INTRODUCTION HE advent of alternative energy sources is causing a paradigm change in the operation of the energy grid [1]. It has shifted the generation of electricity away from a few large power plants towards several smaller individual units that are equipped with PV panels and other means to produce electricity from renewable sources. Although at present this energy is typically utilized to meet the individual units’ own energy needs, it is envisaged that with greater penetration of PV-equipped homes in future, along with the development of more efficient solar panels, individual homes would be able to deliver energy to the grid [2]. Being positioned closer to other consumer units, these PV-equipped units are better placed to supply energy to the latter during exigent situations [3]. Complete isolation of a microgrid is an extreme example of such a case. Under these circumstances, the microgrid should M.Nazif Faqiry, IEEE Student Member, Sanjoy Das Transactive Energy Auction with Hidden User Information in Microgrid T

2 allow bidirectional energy transactions between the units

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