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A Coalition Formation Game Framework for Peer-to-Peer Energy Trading

Wayes Tushar, Tapan K. Saha, Chau Yuen, M. Imran Azim, Thomas Morstyn, H. Vincent Poor, Dustin Niyato, Richard Bean

arXiv:2001.08588v1eess.SPcs.GTeess.SY

TL;DR

P2P energy trading needs a sustainable, prosumer-centric way to coordinate cooperation and battery use. The paper addresses this with a coalition formation game that lets prosumers choose trading states and form suitable groups; it reports stable, optimal coalitions and prosumer-centric outcomes, supported by real-data case studies.

  • Problem

    The paper asks how P2P trading can sustain prosumer cooperation while ensuring that prosumers are the main beneficiaries.

  • Method

    A coalition formation game compares prosumers’ benefits across battery-use states and helps them form suitable P2P trading groups.

  • Results

    The resulting coalition structure is stable and optimal, and the P2P trading scheme is prosumer-centric.

  • Takeaways & Limitations

    The scheme can enable prosumers without storage to participate in and benefit from P2P trading.

Abstract

from arXiv · show

This paper studies social cooperation backed peer-to-peer energy trading technique by which prosumers can decide how they can use their batteries opportunistically for participating in the peer-to-peer trading. The objective is to achieve a solution in which the ultimate beneficiaries are the prosumers, i.e., a prosumer-centric solution. To do so, a coalition formation game is designed, which enables a prosumer to compare its benefit of participating in the peer-to-peer trading with and without using its battery and thus, allows the prosumer to form suitable social coalition groups with other similar prosumers in the network for conducting peer-to-peer trading. The properties of the formed coalitions are studied, and it is shown that 1) the coalition structure that stems from the social cooperation between participating prosumers at each time slot is both stable and optimal, and 2) the outcomes of the proposed peer- to-peer trading scheme is prosumer-centric. Case studies are conducted based on real household energy usage and solar generation data to highlight how the proposed scheme can benefit prosumers through exhibiting prosumer-centric properties.

NOMENCLATURE

The nomenclature defines energy, battery, pricing, utility, coalition, and prosumer-state symbols used throughout the framework.

  • Coalition notation identifies prosumer sets, coalition providers and receivers, coalition value, stability symbols, and the coalition formation game.
  • Battery variables specify capacity, available capacity, charging and discharging rates, state of charge, and degradation cost.
  • Energy variables distinguish solar generation, household demand, battery charging and discharging, surplus, deficiency, and total demand.
  • Market variables define buying, selling, charging, discharging, threshold, and state-specific P2P prices.
  • Utility notation distinguishes prosumer utility in state 1, charging and discharging utility in state 2, coalition utility, and satisfaction parameters.

I. INTRODUCTION

The introduction motivates prosumer-centric P2P energy trading and proposes coalition formation to coordinate battery participation. The scheme targets stable, socially optimal coalitions validated with real consumer data.

  • The framework addresses the challenge of sustaining cooperation and participation in decentralized P2P trading where prosumers should receive the benefits.
  • The paper proposes a coalition-formation P2P trading scheme that uses social cooperation to achieve prosumer-centric outcomes.
  • Each prosumer selects whether to trade with or without battery participation and forms a suitable coalition based on its state-specific benefit.
  • The coalition structure is reported as stable and socially optimal, delivering prosumer-centric outcomes.
  • Numerical simulations using real consumer data validate the proposed scheme’s coalition properties.
  • The model makes decisions at the current time slot, supporting settings without historical PV-generation and demand patterns.

II. SYSTEM MODEL

The system model represents a two-layer P2P network in which prosumers exchange energy through a virtual layer while managing solar generation, demand, and batteries. Prosumers choose between non-trading battery use and battery-enabled trading at each time slot.

  • The network comprises a physical energy-transfer layer and a virtual communication and trading layer connecting prosumers.
  • Each prosumer’s surplus or deficiency is determined from solar generation, household demand, and battery charging or discharging.
  • Battery degradation cost contributes to the differing benefits of state 1 and state 2, so prosumers can change states across time slots.
  • Prosumer n can sell surplus energy or buy deficient energy from the centralized power system or other prosumers.
  • State 1 excludes battery charging or discharging for trading, whereas state 2 permits battery use to buy or sell energy in the P2P market.
  • A prosumer without a battery remains in state 1, while smart-meter functions track generation, consumption, state of charge, battery operation, and trades.

1) Utility of prosumer at state 1:

State 1 prosumers are modeled as grid-tied solar prosumers without battery participation, while state 2 prosumers use battery charging or discharging utilities to guide trading decisions.

  • State 1 prosumers do not charge or discharge their batteries and trade solar energy with another prosumer or the grid.
  • State 2 charging and discharging utilities account for energy benefits, prices, battery degradation, and satisfaction parameters.
  • Battery charging and discharging are bounded by rated battery limits, available capacity, energy surplus or deficit, and network transfer constraints.
  • The utility functions use decreasing marginal benefit to model prosumer decisions as battery state of charge approaches available capacity.
  • Prosumers form socially cooperative groups with neighboring prosumers at different time slots to maximize utility through P2P trading.

III. PROBLEM FORMULATION FOR P2P TRADING

The problem formulation models each prosumer’s state choice as an individual decision shaped by energy conditions, prices, task urgency, and achievable utility, then derives charging-price behavior.

  • III. PROBLEM FORMULATION FOR P2P TRADING: Prosumer state choice depends on solar production, energy demand, energy price, task urgency, and utility from neighboring prosumers.
  • III. PROBLEM FORMULATION FOR P2P TRADING: Each prosumer independently chooses its state without central control and the formulation identifies when battery participation becomes attractive.
  • A. Decision of a prosumer to charge and discharge the battery: For a given charging price pc(t), the preferred charging amount en,c(t)* is obtained by maximizing the charging utility Un,c(t).
  • 1) Price condition for charging a battery:: The charging decision is summarized in Table II as part of the prosumer’s state-selection strategy.
  • 1) Price condition for charging a battery:: When pc(t) equals pn,c(t), the prosumer does not charge its battery because the preferred charging amount is zero.
  • 1) Price condition for charging a battery:: When pc(t) exceeds pn,c(t), the prosumer does not charge because the preferred charging amount is negative.
  • 1) Price condition for charging a battery:: When pc(t) is below pn,c(t), the charging utility is positive and the prosumer charges its battery.

2) Price condition for discharging a battery:

Discharging decisions compare the P2P discharge price with each prosumer’s minimum motivating price, after which prosumers organize into utility-seeking coalitions through Pareto-based merge and split rules.

  • 2) Price condition for discharging a battery:: A prosumer does not discharge when pd(t) equals pn,d(t) or falls below it.
  • 2) Price condition for discharging a battery:: A prosumer discharges its battery when pd(t) exceeds its minimum motivating price pn,d(t).
  • 2) Price condition for discharging a battery:: Battery trading decisions are influenced by battery capacity and state of charge through the charging and discharging price conditions.
  • B. Coalition formation framework: Figures illustrate cooperation among similar-state prosumers and state decisions driven by price and available energy across time slots.
  • B. Coalition formation framework: A coalition formation game Γ is defined by participating players and a coalition value assigned to each coalition.
  • B. Coalition formation framework: Prosumers compare coalitions using individual utilities under Pareto order rather than coalition value alone.
  • B. Coalition formation framework: Merge and split rules let prosumers combine or divide coalitions when the resulting arrangement is Pareto-preferred.
  • B. Coalition formation framework: Coalitions are reorganized iteratively as prosumers seek higher utilities, including by leaving a coalition or acting independently.

C. Coalition formation algorithm

The algorithm dynamically groups prosumers according to whether they participate with or without battery charging or discharging, reconfiguring coalitions each time slot to maximize prosumer benefit.

  • Dynamic reconfiguration: Coalitions dynamically split and merge each time slot as prosumers change states, allowing the structure to adapt to storage conditions and benefits.The state of charge links decisions across time slots, although the same coalition can persist when it remains beneficial.
  • Pricing and coalition eligibility: Battery charging and discharging prices include degradation costs and incentives, while participants without battery trading do not incur the additional degradation component.These pricing conditions exclude simultaneous trades between non-battery participants and prosumers charging or discharging batteries.
  • Coalition outcome: The resulting structure separates prosumers according to compatible battery-use decisions, preventing trades between non-battery participants and simultaneous battery users under the proposed prices.The scheme remains intended to support prosumer-centric participation and battery-use decisions.

D. Trading of energy

The trading framework forms stable coalitions whose members exchange energy through prices derived from aggregate battery supply and demand, with the resulting partition claimed to be Pareto optimal.

  • Battery-energy trading: State 2 providers and receivers trade battery energy within coalitions, balancing total discharged and charged energy so that E_d(t) = E_c(t).Charging and discharging prices are calculated by equating the relevant energy and pricing relationships.
  • Scope boundary: The framework omits selling state-2 battery energy directly to the CPS because the manuscript associates that model with limited prosumer benefits.The authors state that CPS participation as a negotiated peer could extend the model.
  • Stability and optimality: The proposed coalition structure is stable and Pareto optimal at every time slot, with no prosumer benefiting from switching coalitions.The proof links stability to utility-maximizing choices and Pareto ordering.
  • Stability and optimality: The unique two-coalition partition maximizes each prosumer’s individual benefit and therefore the sum of participating prosumers’ benefits.The paper identifies this as D_c stability and uses it to establish Pareto optimality.

B. Prosumer-Centric Property

The paper defines a prosumer-centric scheme through stable coalitions and utilities satisfying three motivational-psychology models, then argues that its coalition game meets those conditions.

  • Evaluation framework: The study examines rational economic, elaboration likelihood, and positive reinforcement models to assess whether the trading scheme supports prosumer participation.These models are presented as relevant behavioral perspectives for evaluating technology participation.
  • Definition: A P2P scheme is prosumer-centric when its coalition structure is stable and each prosumer’s utility satisfies rational-economic, elaboration-likelihood, and positive-reinforcement models.The paper uses these conditions as its formal definition of prosumer-centricity.
  • Evaluation framework: The proposed scheme satisfies the stability requirement through Theorem 1, leaving the motivational-psychology conditions as the remaining basis for prosumer-centricity.The paper introduces three models and evaluates whether the trading scheme exhibits their properties.

1) Rational economic model:

The rational-economic argument treats monetary utility as a primary participation motive and links coalition formation to improved benefits, while the case studies use real household and solar data.

  • Rational economic model: Prosumer coalition and battery-use decisions are driven by economic utility, particularly buying and selling prices, within the proposed trading framework.The paper states that economic benefit plays a key role in selecting a stable coalition.
  • Rational economic model: The proposed scheme is presented as satisfying the rational-economic model because Algorithm 1 lets prosumers choose battery participation based on their utility.The relevant choice is whether to charge or discharge batteries for trading.
  • Motivational consequences: Cooperative P2P participation is reported as more beneficial than non-cooperative trading, supporting positive reinforcement through better utility from repeated cooperation.The paper connects improved utility with encouragement to cooperate again in future energy trading.
  • Motivational consequences: The framework uses improved net benefit as a peripheral-path incentive for convincing prosumers to participate in P2P trading.The paper characterizes this as supporting the elaboration-likelihood model.
  • Overall conclusion: The proposed scheme is reported to satisfy all three motivational models and therefore exhibit prosumer-centric properties.The rational-economic discussion is supported with case studies using real solar-generation and household-consumption data sampled every 15 minutes.
  • Scope and motivation: Battery degradation may discourage extensive battery sharing, so the model is especially framed as relevant to users willing to share storage despite that cost.The paper also notes users’ interests in environmental benefits, lower energy costs, and grid independence.

1) Stability of coalition:

At each time slot, prosumers form coalitions for P2P trading, and the resulting structure remains stable while allowing opportunistic battery use and improved or equal net benefits.

  • Stability of coalition: Fig. 3 shows prosumers selecting different coalition structures across three time snapshots, including cases with no battery charging or discharging.In one case, all ten prosumers form a grand coalition; in others, coalitions change across time slots while covering all ten prosumers.
  • Stability of coalition: Each time slot produces a unique outcome with two coalitions, and prosumers have no incentive to deviate before the next trading slot.The stability follows from the Pareto order and the coalition-formation design.
  • Benefits to prosumers: Net-benefit improvements vary across prosumers and time slots, reaching 15260 for prosumer one at time slot 40 and 825 at time slot 82.The improvement is zero in the morning for prosumer one, reflecting differing generation and demand patterns.
  • Benefits to prosumers: P2P trading improves net benefits for most selected time slots and is at least as good as the FiT scheme in the remaining slots.Net benefit is defined as utility minus the cost of trading energy.
  • Benefits to prosumers: Battery use is opportunistic: prosumers trade battery energy when beneficial, while P2P benefits can persist during slots with no battery-energy trading.The cited example reports battery trading during slots 25–45 but none during slots 50–60, while benefits remain evident in slots 50–60.

3) Prosumer-centric property:

The proposed scheme is prosumer-centric because cooperation is generally more beneficial than FiT participation without harming prosumers, while outcomes vary with prosumer characteristics and weather.

  • Prosumer-centric property: Cooperation is more beneficial most of the time and never detrimental to prosumers compared with participating in the FiT scheme.The paper links this property to rational economic and elaboration likelihood characteristics of its motivational psychology model.
  • Prosumer-centric property: Benefits differ across prosumers and weather conditions, with prosumers 2, 3, 5, and 9 receiving higher average benefits than prosumers 7 and 8.Longer sunshine periods are associated with greater P2P-trading benefits in the reported cases.
  • Prosumer-centric property: Sunny days produce consistent performance improvements over FiT, whereas completely cloudy days provide the same benefit as FiT.On cloudy days, prosumers lack surplus solar energy and use stored energy to meet their own demand.
  • Prosumer-centric property: The computational burden is described as negligible because prosumer decisions use simple rules and calculations based on available information.The paper notes that complexity may increase for very large numbers of prosumers.
  • Prosumer-centric property: The coalition-formation game lets each prosumer decide opportunistically whether to place its battery in the P2P market while preserving stable coalition outcomes.Case studies use Australian household energy-use and solar-generation data.
  • Prosumer-centric property: The scheme can benefit prosumers without storage and supports intelligent battery use while considering battery degradation costs.These conclusions are reported from the paper’s case studies.
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