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Grid Influenced Peer-to-Peer Energy Trading

Wayes Tushar, Tapan Kumar Saha, Chau Yuen, Thomas Morstyn, Nahid-Al-Masood, H. Vincent Poor, Richard Bean

arXiv:1908.09449v1eess.SYcs.GT

TL;DR

The paper addresses how P2P energy trading can help a centralized power system reduce prosumer-related peak demand while retaining benefits for prosumers. It formulates a cooperative Stackelberg game in which CPS pricing prompts coalition-based P2P trading, and reports a unique stable equilibrium with favorable numerical outcomes for prosumers.

  • Problem

    P2P trading must fit and complement existing centralized energy systems, while schemes should engage prosumers beyond purely economic incentives.

  • Method

    The paper formulates a cooperative Stackelberg game with the CPS as leader and prosumers forming double-auction-based coalitions for P2P trading.

  • Results

    The proposed game has a unique and stable Stackelberg equilibrium, with a closed-form leader strategy and stable prosumer coalitions.

  • Takeaways & Limitations

    Numerical case studies report that prosumers gain 22% more average revenue than selling surplus to the CPS, while noncooperative participation raises average cost by 50% versus P2P trading.

Abstract

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This paper proposes a peer-to-peer energy trading scheme that can help the centralized power system to reduce the total electricity demand of its customers at the peak hour. To do so, a cooperative Stackelberg game is formulated, in which the centralized power system acts as the leader that needs to decide on a price at the peak demand period to incentivize prosumers to not seeking any energy from it. The prosumers, on the other hand, act as followers and respond to the leader's decision by forming suitable coalitions with neighboring prosumers in order to participate in P2P energy trading to meet their energy demand. The properties of the proposed Stackelberg game are studied. It is shown that the game has a unique and stable Stackelberg equilibrium, as a result of the stability of prosumers' coalitions. At the equilibrium, the leader chooses its strategy using a derived closed-form expression, while the prosumers choose their equilibrium coalition structure. An algorithm is proposed that enables the centralized power system and the prosumers to reach the equilibrium solution. Numerical case studies demonstrate the beneficial properties of the proposed scheme.

NOMENCLATURE

The paper frames P2P energy trading as a way to complement centralized power systems by engaging prosumers in market and coalition-based energy management. Its proposed cooperative Stackelberg scheme targets peak-demand reduction while accounting for grid compatibility and prosumer participation.

  • NOMENCLATURE: P2P energy trading enables customers to trade with prosumers and the grid, with potential benefits including renewable-energy use, cost reduction, and peak-load shaving.The literature also associates P2P trading with prosumer empowerment and lower network operation and investment costs.
  • NOMENCLATURE: Existing P2P studies address financial market models, physical-network constraints, and mechanisms for engaging prosumers.Examples include blockchain markets, transaction-loss allocation, decentralization, heterogeneous energy products, federated power plants, and motivational approaches.
  • NOMENCLATURE: Integrating P2P trading into current energy policy requires mechanisms that fit and complement grid-connected centralized systems.The paper identifies benefits to the centralized power system as one way to demonstrate this suitability.
  • NOMENCLATURE: The proposed scheme uses a centralized power system as Stackelberg leader and prosumers as followers who form coalitions for P2P trading at peak demand.The leader selects a price to reduce prosumer supply from the CPS, while followers use double-auction-based coalition formation to meet demand without CPS energy.
  • NOMENCLATURE: The paper models a network containing a CPS and prosumers with generation capability, P2P participation, and two-way communication and power flow.Prosumer demand may be met by solar generation, storage, peer purchases, or grid purchases, while the CPS must meet total customer demand.
  • NOMENCLATURE: When prosumer demand exceeds a CPS threshold, the CPS sends a high price signal intended to encourage prosumers to manage energy among themselves.The stated objective is to make ED(t) = 0 for selected prosumers through the CPS's pricing decision.

A. Utility Function of the Prosumer

The prosumer utility model combines satisfaction from energy use with the revenues or costs of trading with the CPS or other prosumers. It distinguishes grid transactions from P2P transactions and shows how CPS pricing affects grid purchases.

  • A. Utility Function of the Prosumer: Prosumer utility combines logarithmic energy-use utility with trading revenue or cost determined by traded quantity and price.The formulation applies to transactions with either the CPS or another prosumer.
  • A. Utility Function of the Prosumer: The model uses α_n(t) for energy-use preference and distinguishes grid buying, grid selling, and P2P prices.The traded quantities include energy exchanged with the CPS and with other peers.
  • A. Utility Function of the Prosumer: A prosumer buying from the CPS does not simultaneously perform P2P trading in the specified system.When e_n,g(t) > 0, e_n,p(t) = 0, and conversely.
  • A. Utility Function of the Prosumer: The CPS price affects the prosumer's optimal grid-purchased energy, so a sufficiently high price can redirect demand toward alternative venues.The paper identifies this price response as the mechanism motivating P2P participation.

B. Cost Function of the CPS

The CPS cost function combines sales revenue with costs incurred when demand exceeds a predefined threshold. The CPS therefore selects pricing parameters to reduce excess demand and encourage alternative energy trading.

  • B. Cost Function of the CPS: The CPS net cost includes revenue from selling prosumer energy and a cost component for meeting demand beyond its predefined threshold.The excess-demand cost can represent network-constraint violations or starting an additional generator.
  • B. Cost Function of the CPS: CPS cost occurs only when demand exceeds the defined threshold, making prosumer demand reduction the relevant pricing objective.The CPS chooses a suitable price when ED(t) > ET(t) to encourage purchases from alternatives rather than from the CPS.
  • B. Cost Function of the CPS: The CPS adjusts pricing parameters a and b according to total demand and threshold conditions to support secured and sustainable trading operation.The parameters are used to alter prosumer demand when ED(t) exceeds ET(t).
  • B. Cost Function of the CPS: The CPS can set its selling price high enough to influence prosumers not to purchase energy during peak hours.The paper derives a maximum CPS price that a prosumer needs to pay and uses it to characterize this incentive.
  • B. Cost Function of the CPS: After the price is set, prosumers are expected to meet demand through P2P responses rather than relying on CPS energy.The subsequent cooperative Stackelberg game captures these decisions when ED(t) > ET(t).

III. COOPERATIVE STACKELBERG GAME

The cooperative Stackelberg game models CPS pricing as the leader's decision and coalition-based P2P trading as the prosumers' response. Its equilibrium requires stable coalitions and no profitable unilateral strategy changes.

  • III. COOPERATIVE STACKELBERG GAME: The game contains the CPS and prosumers, with the CPS choosing a peak-hour price and prosumers cooperating in response.The strategic form includes prosumer utilities, CPS cost, traded energy, CPS price, and P2P price.
  • III. COOPERATIVE STACKELBERG GAME: Prosumers act as followers whose strategies include traded P2P energy and the per-unit P2P trading price.Their utility is defined for selling or buying energy with other prosumers and the CPS.
  • III. COOPERATIVE STACKELBERG GAME: At the cooperative Stackelberg equilibrium, the CPS and prosumers have no incentive to switch strategies to improve cost or utility.The CPS seeks to reduce its energy trading with prosumers to zero when ED(t) > ET(t), while deficient prosumers obtain energy from surplus prosumers.
  • III. COOPERATIVE STACKELBERG GAME: The equilibrium followers' strategies establish a Dhp-stable coalition structure in which players do not benefit from splitting and forming another coalition.Stability is defined at a given time slot by the absence of an improving coalition deviation.

A. Leader’s Strategy

The CPS selects a peak-period selling price, and prosumers respond by forming coalitions through a double-auction-based coalition formation game. The followers’ coalition structure is sought as a stable response to the CPS strategy.

  • A. Leader’s Strategy: The CPS’s equilibrium selling price is selected according to the derived strategy in (13).The parameters a* and b* may come from historical scenario data or an additional optimization, subject to condition (10).
  • A. Leader’s Strategy: Prosumers form a coalition structure in response to p*_g,s(t), seeking a Dhp-stable outcome.The resulting coalition-formation game models followers’ strategy selection after the CPS decision.
  • A. Leader’s Strategy: A double auction is used because buyers and sellers independently submit reservation prices and bids to determine trading price and energy quantities.The auction supports interactive P2P decisions among prosumers.

1) Double auction between prosumers:

The proposed double auction uses prosumer bids to determine the auction price, participating buyers and sellers, and traded energy quantities. Prosumers excluded from the auction can trade at a mid-market rate.

  • 1) Double auction between prosumers:: The auction involves sellers with surplus energy, buyers needing energy, and an auctioneer that determines price and trading quantities.The auctioneer may be a third party or an automated information system such as blockchain.
  • 1) Double auction between prosumers:: At each time slot, sellers and buyers submit reservation prices and energy amounts for the auction.Seller prices are ordered ascending, while buyer prices are ordered descending as specified in (14).
  • 1) Double auction between prosumers:: The auctioneer constructs aggregated supply and demand curves and identifies their intersection to obtain pmax.The proposed scheme assumes pauc = pmax.
  • 1) Double auction between prosumers:: Prosumers satisfying {pauc : pn,s ≥ pn,b} trade energy within the auction-price coalition.The participating sets are Ba and Sa, bounded by the buyer and seller populations.
  • 1) Double auction between prosumers:: Each seller’s auction-market allocation is influenced by the energy demand of the buyers.When total surplus exceeds deficiency, sellers may face an unsold-energy burden distributed according to the study’s selected scheme.
  • 1) Double auction between prosumers:: Dynamic pricing is identified as established in P2P literature and pilot trials despite limited current use for residential electricity rates.
  • 1) Double auction between prosumers:: Prosumers excluded by the auction condition form another P2P coalition that trades at the mid-market clearing price.The passage notes that this mid-market rate is used in a P2P pilot project.

2) Formation of different coalition:

Coalitions form according to prosumers’ trading decisions at selected time slots, with auction-price and mid-market groups created through the proposed algorithm. The algorithm accounts for forecast demand, auction participation, and feasible within-coalition trading.

  • 2) Formation of different coalition:: Coalition formation reflects prosumers’ decisions to socially interact for energy trading in selected time slots.The process applies when prosumers cannot trade their energy with the grid at the relevant CPS price.
  • 3) Coalition formation algorithm:: Each instructed prosumer first selects an auction-market energy amount and reservation price.The auctioneer then uses submitted prices and quantities to determine pauc and the participating sets Ba and Sa.
  • 3) Coalition formation algorithm:: The coalition formation procedure is presented as an algorithm for forming a stable coalition structure for P2P trading.
  • 3) Coalition formation algorithm:: The CPS forecasts total prosumer demand at each time slot before deciding whether coalition formation proceeds.If forecast demand is below ED(t), the algorithm terminates; otherwise the CPS sets p*_g,s(t).
  • 3) Coalition formation algorithm:: The algorithm forms one coalition from Ba ∪ Sa and a second from the remaining prosumers.The two groups trade within their respective coalitions at auction and mid-market prices.
  • 3) Coalition formation algorithm:: The auction-price coalition determines traded energy using (15), while the mid-market coalition follows the process described in.Within-coalition partner selection may use standard techniques or a pool-based auction.
  • 3) Coalition formation algorithm:: If coalition deficiency exceeds surplus, deficient prosumers may reschedule activities or buy from a third party at a different price.A large neighborhood storage is given as an example of a third party.

IV. PROPERTIES OF THE STACKELBERG GAME

The proposed auction is strategy-proof, which supports stability of the prosumers’ coalition structure. Consequently, the cooperative Stackelberg game has a unique and stable CSE.

  • IV. PROPERTIES OF THE STACKELBERG GAME: The CPS’s strategy yields a unique outcome for any b satisfying (10), so CSE uniqueness and stability reduce to coalition stability.
  • IV. PROPERTIES OF THE STACKELBERG GAME: The auction mechanism is strategy-proof: prosumers reveal their true strategies and do not cheat or deviate during trading.This property is stated as Theorem 1.
  • IV. PROPERTIES OF THE STACKELBERG GAME: A seller that changes its revealed auction quantity cannot improve without creating an impossible burden allocation under the scheme.The proof uses the equal burden shared by seller prosumers and their revealed trading quantities.
  • IV. PROPERTIES OF THE STACKELBERG GAME: Buyers likewise must adhere to their revealed strategies, so unilateral cheating does not improve their trading outcome.
  • IV. PROPERTIES OF THE STACKELBERG GAME: At each time slot, the follower response partitions prosumers into two Dhp-stable coalitions.No player has an incentive to leave its coalition for greater benefit.
  • IV. PROPERTIES OF THE STACKELBERG GAME: The proposed cooperative Stackelberg game Γ possesses a unique and stable CSE.This follows from the stable follower partitions responding to the CPS’s unique decision.

B. Prosumer-Centric Property

The scheme is presented as prosumer-centric because P2P trading offers stable, economically beneficial choices while communicating benefits through positive outcomes.

  • Prosumer-centric properties: A stable coalition solution leaves prosumers with no incentive to choose an alternative strategy instead of cooperating in P2P trading.This supports the scheme’s transitivity and dominance properties.
  • Prosumer-centric properties: Unique and stable coalition and trading-price outcomes make P2P trading economically beneficial when grid trading prices are high.This satisfies the rational-economic property.
  • Prosumer-centric properties: The scheme benefits both the grid by reducing peak demand and prosumers by reducing their grid energy-purchase costs in each P2P trading time slot.The shared beneficial outcome also provides a peripheral path for communicating with prosumers.
  • Prosumer-centric properties: The proposed P2P energy trading scheme is characterized as a prosumer-centric technique.This conclusion is stated as Corollary 2.

V. CASE STUDIES

The case studies evaluate a 12-prosumer residential network with rooftop solar and randomized energy surpluses, deficiencies, and bidding prices.

  • Case-study setup: The numerical case studies use a residential network with 12 prosumers, each assumed to have a 5 kWp solar panel.Energy surplus and deficiency are randomly selected from [2,9].
  • Case-study setup: Energy surpluses and deficiencies are randomly chosen from [2,9], while bidding prices range from [11,15] cents per kWh.The values may differ under different generation and consumption patterns at different locations.
  • Case-study setup: The bidding range is set above the 10-cent-per-kWh FiT price and below the 28-cent-per-kWh grid selling price at off-peak hours.Residential solar data comes from Redback Technologies in Australia.

A. Benefit to the CPS

The CPS raises its selling price when prosumer demand exceeds a threshold, steering prosumers toward P2P trading and reducing peak-period costs. The case studies report benefits for the CPS and prosumers, including lower costs, higher seller revenue, and feasible computation.

  • CPS pricing strategy: 28 cents per kWh is the CPS’s standard off-peak rate when total prosumer demand remains below the threshold.When demand exceeds the threshold, the CPS raises its price; at time slots 3 and 4 it is 19.6 times higher, and at slot 6 it is 12.5 times higher.
  • CPS revenue: When demand is below the threshold, the CPS earns revenue exceeding 500 cents at numerous listed time slots.The reported revenue occurs at time slots 1, 2, 5, 7–12, 14, 16–18, and 20–22.
  • CPS cost under high demand: When demand exceeds the threshold, the CPS’s cost increases significantly because it must maintain reserve capacity or operate new generation units.At time slot 6, the cost reaches around 600 cents, with similar increases at time slots 4, 13, 15, and 19.
  • CPS cost reduction: The CPS’s high price signal directs prosumers to P2P trading, reducing the CPS’s cost to zero because no excess energy needs to be generated.This behavior is presented as the proposed scheme’s response when prosumer demand is above the threshold.
  • Effect of participation: Without P2P participation, CPS cost rises substantially with the number of prosumers, whereas it remains zero when prosumers respond to the price signal through P2P trading.The increase without P2P is attributed mainly to higher total demand served by the CPS.
  • Overall case-study benefits: P2P participation reduces average cost per prosumer by $61.58 and CPS cost by $285.25 for the considered parameter values.The study also reports that cost per prosumer increases as the number of prosumers increases, and states that the proposed algorithm has feasible computational complexity.

VI. CONCLUSION

The paper develops a cooperative Stackelberg framework for peak-hour P2P energy trading, combining a closed-form CPS decision with prosumers’ coalition formation. It identifies demand uncertainty and noncooperative prosumer behavior as directions for further investigation.

  • The scheme combines a centralized power system leader with prosumer followers in a cooperative Stackelberg game.
  • The leader’s decision-making process is captured by a closed-form expression.
  • Future work should examine how uncertain prosumer demand and noncooperative behavior affect the CPS’s decision-making process.
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