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Energy Storage Sharing in Smart Grid: A Modified Auction Based Approach

Wayes Tushar, Bo Chai, Chau Yuen, Shisheng Huang, David Smith, H. Vincent Poor, Zaiyue Yang

arXiv:1512.07700v1eess.SY

TL;DR

The paper studies how residential units and shared facility controllers can jointly share energy-storage capacity in a smart community. It proposes a modified Vickrey-style auction with a Stackelberg game to determine price and shared capacity, and reports incentive compatibility, individual rationality, and a unique equilibrium supported by numerical experiments.

  • Problem

    Residential units must decide whether and how much energy-storage capacity to share with shared facility controllers, while existing studies often overlook this joint-sharing opportunity.

  • Method

    A modified Vickrey auction uses a Stackelberg game between an auctioneer and residential units to determine the auction price and storage allocation.

  • Results

    The proposed auction possesses incentive compatibility and individual rationality, leveraged by a unique Stackelberg equilibrium; numerical case studies evaluate the scheme.

  • Takeaways & Limitations

    The scheme enables residential units and shared facility controllers to participate in joint storage ownership while deciding the price and shared capacity through the auction process.

Abstract

from arXiv · show

This paper studies the solution of joint energy storage (ES) ownership sharing between multiple shared facility controllers (SFCs) and those dwelling in a residential community. The main objective is to enable the residential units (RUs) to decide on the fraction of their ES capacity that they want to share with the SFCs of the community in order to assist them storing electricity, e.g., for fulfilling the demand of various shared facilities. To this end, a modified auction-based mechanism is designed that captures the interaction between the SFCs and the RUs so as to determine the auction price and the allocation of ES shared by the RUs that governs the proposed joint ES ownership. The fraction of the capacity of the storage that each RU decides to put into the market to share with the SFCs and the auction price are determined by a noncooperative Stackelberg game formulated between the RUs and the auctioneer. It is shown that the proposed auction possesses the incentive compatibility and the individual rationality properties, which are leveraged via the unique Stackelberg equilibrium (SE) solution of the game. Numerical experiments are provided to confirm the effectiveness of the proposed scheme.

I. INTRODUCTION

The paper addresses storage space and cost constraints by proposing joint ownership that lets residential units share part of their energy storage with shared facility controllers. A modified auction captures their interaction and determines sharing and pricing while targeting benefits for both parties.

  • Motivation: Shared facility controllers may require large, costly storage whose capacity can remain unused because facility usage is random.Residential-unit storage is also costly and primarily used for household savings, motivating a solution that addresses both parties’ constraints.
  • Proposed direction: The proposed scheme leases a fraction of each residential unit’s storage to shared facility controllers while the remaining capacity serves the unit’s own purposes.The paper presents this arrangement as joint energy-storage ownership within a smart-grid community.
  • Motivation: Each residential unit can choose whether to participate and what fraction of its energy storage to share with shared facility controllers.The scheme gives residential units a decision role in joint ownership rather than treating storage as owned and used by only one entity.
  • Contribution: The Stackelberg-based auction is designed to benefit storage owners while maintaining maximum cost savings for shared facility controllers.The introduction also states that the scheme has incentive compatibility and individual rationality properties and provides a distributed algorithm reaching the desired solution.
  • Contribution: The modified auction captures interaction between shared facility controllers and residential units through auction determination, payment, and allocation rules.Unlike much prior work, the scheme explicitly models interaction between storage owners and facility controllers.

III. SYSTEM MODEL

The system model represents a smart community in which residential units with energy storage share capacity with shared facility controllers through an auction-based market. Residential units choose reservation prices and sharing fractions while retaining storage for their own needs, under device- and degradation-related considerations.

  • Residential units: Each residential unit may be a home, apartment unit, or aggregated group, and can store grid or renewable electricity in its energy-storage device.Residential units may also perform demand-response management according to real-time grid prices.
  • Storage demand: Shared facility controllers require extra storage when they lack storage or cannot accommodate all excess electricity from sporadic generation and consumption.The model allows intermittent profiles such as hybrid solar and wind generation.
  • Residential-unit decisions: Each residential unit i offers x_i of its storage capacity for sharing, while b_i bounds the shareable space and d_i is reserved for its own future needs.The retained capacity can support essential loads during disruptions or periods of high electricity prices.
  • Residential-unit decisions: Residential units choose reservation prices r_i, and withdraw offered capacity when the received price p_t falls below r_i.The model treats shared storage space and energy interchangeably and incorporates storage capacity and device-specific parameters.
  • Auction market: The market captures interactions among N residential units and M shared facility controllers over participation, shared capacity, pricing, and joint storage ownership.The sharing amount reflects a trade-off between expected economic benefits and each unit’s reluctance to share its storage.
  • Model qualification: Charging and discharging lifetime degradation is not necessarily valid for every electromechanical storage system, including redox-flow systems.This qualification limits the applicability of degradation assumptions across storage technologies.

IV. AUCTION BASED ES OWNERSHIP

The proposed scheme modifies a Vickrey auction for joint ES ownership between RUs and SFCs. It uses determination, payment, and allocation rules to identify participants, set prices, and allocate shared storage.

  • The modified Vickrey auction lets multiple RUs and SFCs decide independently whether to participate in joint ES sharing.Participating RUs can choose the amount of ES space they share when the auction price is below their reservation price.
  • The auction has three elements: RUs act as owners, SFCs as customers, and a third party as auctioneer.RUs seek economic benefits from sharing storage, while SFCs offer a price for jointly using it.
  • The determination rule identifies the maximum auction price and the numbers of participating SFCs and RUs.The payment rule sets the customer price, and the allocation rule assigns shared ES spaces to SFCs.
  • The auction process first determines participating sets after finding the upper price bound, then executes payment and allocation.Figure 3 presents the Vickrey price, maximum auction price, and participant counts.

A. Determination Rule

The determination rule uses ordered RU reservation prices and SFC bids to construct aggregate supply and demand curves. Their intersection determines the price bound and eligible participant counts.

  • RUs submit reservation prices and desired shared-storage quantities, while SFC bids and required quantities are ordered for auction processing.RU reservation prices are arranged increasingly, and SFC bidding prices decreasingly.
  • The auctioneer generates aggregate supply and demand curves from the ordered RU and SFC information.Supply represents RU reservation prices against offered ES, while demand represents SFC bids against required ES.
  • The intersection of the curves identifies SFC K and RU J satisfying aK ≥ rJ and determines the participating counts.The intersection also determines the maximum auction price pmax.
  • Agents outside the selected sets are excluded because joint ES ownership is detrimental for them under am < ri.For truthful auction operation, K −1 SFCs and J −1 RUs participate; otherwise SFC K and RU J may also participate.

B. Payment Rule

The payment rule models price selection and RU storage decisions as a Stackelberg game. The auctioneer chooses the price to maximize SFC savings, while RUs choose shared storage to maximize their utilities.

  • The auction price balances the Vickrey price, which may not benefit all RUs, against the maximum price, which may be detrimental to some SFCs.The scheme seeks a price that benefits participating RUs while remaining cost-effective for SFCs.
  • The auctioneer chooses pt to maximize average SFC cost savings, while each RU chooses xi in response to that price.The RU decision accounts for its utility, reluctance parameter, and reservation price.
  • Each RU’s utility combines revenue from sharing storage with a reluctance penalty that increases with the shared amount.The reluctance parameter αi measures unwillingness to share, and higher αi lowers net benefit for the same ES sharing.
  • The auctioneer and RUs interact until reaching a Stackelberg equilibrium, where neither side has an incentive to change strategy.The auctioneer acts as leader and RUs as followers in the single-leader-multiple-follower game.
  • A unique Stackelberg equilibrium always exists for the proposed game between the auctioneer and participating RUs.The proof uses the auctioneer’s nonempty continuous strategy set, bounded RU strategies, and strict concavity of RU utility.
  • The equilibrium price is unique because it maximizes average SFC cost savings after substituting the RU best-response storage quantities.The uniqueness follows from the exclusive parameters associated with SFC bids and RU reluctance values.

C. Algorithm for payment

The distributed algorithm lets the auctioneer and RUs iteratively select the auction price and shared ES amounts, while tracking the average cost savings for SFCs. The algorithm is guaranteed to reach the unique Stackelberg equilibrium.

  • C. Algorithm for payment: The auctioneer and RUs interact in a distributed iterative algorithm to reach the unique Stackelberg equilibrium.The auctioneer proposes prices, and each RU responds with its ES-sharing strategy.
  • C. Algorithm for payment: Theorem 2 states that Algorithm 1 is always guaranteed to reach the proposed SLMFSG’s SE.The guarantee follows from bounded strategy sets and continuity of the RUs’ utility functions, which ensure fixed points for their responses.
  • C. Algorithm for payment: Algorithm 1 scans auction prices from pmin_t to pmax_t and has each RU adjust its shared ES amount.The procedure evaluates RU responses for each candidate auction price.
  • C. Algorithm for payment: The auctioneer computes average cost savings to SFCs and records the price yielding the maximum observed savings.The algorithm updates the desirable price when the current savings meet or exceed the recorded value.
  • C. Algorithm for payment: The algorithm returns the SE consisting of the RUs’ shared ES strategies and the auctioneer’s auction price.The final SE is represented by (x∗, p∗_t).

D. Allocation Rule

After the equilibrium shared ES amounts are determined, the auctioneer allocates jointly shared quantities between RUs and SFCs according to an oversupply-burden rule. The rule distinguishes demand exceeding available ES from available ES exceeding SFC demand.

  • D. Allocation Rule: At equilibrium, each RU’s shared amount x∗_i is determined in response to the auction price p∗_t.These equilibrium amounts are then used for allocation between the RUs and SFCs.
  • D. Allocation Rule: The auctioneer allocates each RU’s jointly shared quantity Q_i according to the specified allocation rule.The rule uses the equilibrium shared ES amounts and an excess-ES allotment term η_i.
  • D. Allocation Rule: When SFC requirements exceed available ES space, each RU allows SFCs to share all ES x_i placed into the market.No oversupply burden arises in this case.
  • D. Allocation Rule: When available ES exceeds total SFC demand, each RU bears a fraction of the oversupply.The total burden can be distributed proportionally or equally among participating RUs.
  • D. Allocation Rule: Oversupply can be allocated in proportion to each RU’s shared ES or reservation price, or shared equally.These alternatives determine how the excess-ES burden η_i is assigned.

1) Proportional allocation:

Proportional allocation assigns each RU a fraction of the total oversupply burden according to a specified RU attribute. The passage identifies reservation price and shared ES as proportional allocation bases.

  • 1) Proportional allocation:: Replacing r_i with x∗_i makes the burden allocation proportional to the ES shared by each RU.This provides a shared-ES-based implementation of the proportional rule.
  • 1) Proportional allocation:: The proportional allocation basis can therefore reflect either reservation prices or the RUs’ shared ES amounts.Both alternatives are presented as ways to distribute the total burden.

2) Equal allocation:

Equal allocation distributes oversupply evenly among participating RUs. The paper presents this approach as more suitable for making the auction strategy-proof.

  • 2) Equal allocation:: Equal allocation makes each RU bear an equal burden from oversupply.This contrasts with proportional allocation based on RU properties.
  • 2) Equal allocation:: Equal allocation is more suitable for making the auction scheme strategy-proof than proportional allocation.The passage links strategy-proofness to truthful reporting of private information such as reservation price.

E. Properties of the Auction Process

The proposed auction is individually rational and incentive compatible: participants maximize their utilities, and truthful behavior is the best strategy at the unique Stackelberg equilibrium.

  • All participants are individually rational because RUs maximize their utilities while the auctioneer selects a price that maximizes SFC savings.The resulting participation provides higher utility for rational owners and customers.
  • Reservation prices represent how much each RU wants to be paid for sharing its energy storage with SFCs and affect the total payment and burden.
  • Truthful auction is the best strategy for every participating RU and SFC, establishing incentive compatibility.The mechanism converges to a unique Stackelberg equilibrium, which stabilizes the RUs’ strategy selections.
  • The mechanism’s incentive compatibility means neither RUs nor SFCs have an incentive to falsify their allocated storage after adopting the specified allocation rules.This conclusion follows from convergence to a stable equilibrium and strategy-proof allocation.

F. Adaptation to Time-Varying Case

The auction extends to time-varying operation by running the storage-sharing mechanism in time slots, with participation, offered capacity, and requirements updated over time. Each time slot retains the mechanism’s incentive compatibility and individual rationality properties.

  • Time-slotted operation: The time-varying scheme runs the modified auction independently in application-dependent time slots, such as one-hour intervals.Auction price and shared storage amount are determined for each slot.
  • Participation: Participation in each time slot depends on reservation prices, bidding prices, available RU storage, and SFC storage requirements.The determination rule selects participating RUs and SFCs using these time-specific conditions.
  • Intertemporal effects: An RU’s offered storage at time t is influenced by its previous-slot burden when excess shared storage occurred.The time-varying formulation accounts for prior contributions and available capacity when determining current offers.
  • SFC requirements: SFC storage requirements depend on shared-facility demand, prior available shared storage, and renewable-energy generation.When prior shared storage is negligible, requirements can be modeled as random across time slots.
  • Properties: The time-varying auction preserves incentive compatibility and individual rationality in every time slot.The payment and allocation rules follow the static mechanism’s rules for each respective slot.

V. CASE STUDY

The case studies evaluate convergence, reluctance effects, changing SFC storage requirements, comparative utility, computational complexity, and time-varying operation of the proposed auction scheme.

  • Convergence: 20 iterations are required for the proposed SLMFG to reach the SE, where average cost savings per SFC reaches its maximum.The reported convergence speed is a few seconds in the considered case study.
  • Convergence: RU1, RU2, and RU3 reach the SE faster, while RU4, RU5, and RU6 show no interest in sharing ES.RU1–RU3 place ES in the market after the second iteration because the updated auction price exceeds their reservation prices.
  • Reluctance effects: 16.73%, 67.6%, and 95.3% reductions in average RU utility occur as reluctance increases, while SFC utility reductions are 38.9%, 77.7%, and 96%.The reductions are reported relative to the average RU utility at α_i = 0.001 and for corresponding reluctance settings.
  • Storage requirements: Average RU utility initially increases with SFC storage requirements, and the proposed scheme improves performance over ED and FIT across the studied cases.The considered SFC requirements range from 100 to 600 ES units; the supplied passage reports the general trend and comparison.
  • Computational complexity: The determination rule reduces computational complexity by selecting participating RUs and SFCs before iterative price updates by the auctioneer.The auctioneer then interacts iteratively with participating RUs to set the price while increasing average SFC savings.
  • Comparative utility: 34.76% average improvement over ED and 34.34% over FIT are reported for the proposed scheme.The ED comparison is attributed to the auction methodology, while the FIT comparison is attributed to the difference between auction and FIT prices.
  • Time-varying operation: The modified auction captures time variation by updating reservation prices and available sharing according to prior time-slot sharing and changing SFC requirements.In the four-slot case, oversupply in time slot 3 contributes to the ES shared in time slot 4.

VI. CONCLUSION

The paper proposes a modified auction-based scheme for joint energy-storage ownership between residential units and shared facility controllers. Its Stackelberg formulation establishes auction properties and an algorithm for jointly determining price and shared storage, while identifying extensions for broader practical settings.

  • Scheme and mechanism: The modified auction allocates jointly owned energy storage between residential units and shared facility controllers through specified determination, payment, and allocation rules.The payment rule is facilitated by a Single-leader-multiple-follower Stackelberg game between the auctioneer and residential units.
  • Theoretical properties: The proposed auction possesses individual rationality and incentive compatibility through the unique Stackelberg equilibrium of the game.
  • Algorithm: The proposed algorithm is guaranteed to reach the Stackelberg equilibrium and determines the auction price and the amount of energy storage offered for joint ownership.
  • Future directions: Future work includes scheduling shared-space loads, scaling participation to many controllers or residential units, cooperative game-theoretic bidding, and quantifying residential-unit reluctance to share storage.
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