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arxiv: 2502.18598 · v3 · submitted 2025-02-25 · 💰 econ.TH · math.OC

Locational Energy Storage Bid Bounds for Facilitating Social Welfare Convergence

Ning Qi , Bolun Xu This is my paper

Pith reviewed 2026-05-23 02:22 UTC · model grok-4.3

classification 💰 econ.TH math.OC
keywords energy storagebid boundselectricity marketschance-constrained optimizationsocial welfaremarket powereconomic dispatchuncertainty
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The pith

Energy storage bid bounds derived from chance-constrained dispatch cap offers across uncertainty scenarios and align bids with social welfare.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a method to set locational bid bounds for energy storage in electricity markets. These bounds come from a multi-period economic dispatch model formulated as a chance-constrained problem that includes uncertainty in netload and the system operator's risk preference. Analytical results establish that the bounds limit storage bids in every scenario at a chosen confidence level. Numerical tests on an 8-bus system with agent-based bidding show the bounds reduce total system cost while raising storage profits relative to deterministic alternatives.

Core claim

The paper derives locational energy storage bid bounds from a tractable multi-period economic dispatch chance-constrained formulation that incorporates uncertainty and risk preference. The analytical results verify that the bounds cap storage bids across all uncertainty scenarios with a guaranteed confidence level. Bid bounds decrease with higher state of charge and increase with greater netload uncertainty or risk preference. On the 8-bus ISO-NE test system the bounds align storage bids with the social welfare objective, producing an average 0.17 percent system-cost reduction and 10.16 percent storage-profit increase under 30 percent renewable and 20 percent storage capacity.

What carries the argument

The chance-constrained multi-period economic dispatch formulation that generates the locational bid bounds by enforcing a confidence-level guarantee on bid caps under uncertainty.

If this is right

  • Bid bounds decrease as state of charge increases.
  • Bounds increase with higher netload uncertainty and stronger risk preference.
  • The bounds reduce average system cost by 0.17 percent under the tested renewable and storage penetrations.
  • Storage profit rises by an average of 10.16 percent across uncertainty scenarios and bidding strategies.
  • Both cost and profit effects grow larger as storage economic withholding and total storage capacity increase.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same bounding technique could be applied to other flexible resources whose offers affect system cost under uncertainty.
  • Market rules that embed operator risk preference directly into bid caps may reduce the need for after-the-fact market-power mitigation.
  • Scaling the method to larger networks would test whether locational differences in bounds remain computationally tractable.
  • The observed profit increase for storage suggests the bounds may encourage rather than deter investment when withholding is possible.

Load-bearing premise

The derived bid bounds will align storage bids with the social welfare objective when used inside agent-based storage bidding models on the 8-bus test system.

What would settle it

A simulation run in which storage bids exceed the computed bounds in more than the allowed fraction of scenarios or in which total system cost rises rather than falls after the bounds are imposed.

Figures

Figures reproduced from arXiv: 2502.18598 by Bolun Xu, Ning Qi.

Figure 1
Figure 1. Figure 1: Comparison of hourly weighted average bids and optimal hindsight [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Storage discharge and charge bid bounds variations with SoC under [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Storage bid bounds: (a) variations with netload uncertainty and (b) [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Difference after adding storage bounds under 20% storage capacity and 30% renewable capacity: (a) system cost reduction and (b) storage profit increase. [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Difference after adding storage bounds 35% storage capacity and 30% renewable capacity: (a) system cost reduction and (b) storage profit increase. [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
read the original abstract

This paper proposes a novel method to generate bid bounds that can serve as offer caps for energy storage in electricity markets to help reduce system costs and regulate potential market power exercises. We derive the bid bounds based on a tractable multi-period economic dispatch chance-constrained formulation that systematically incorporates the uncertainty and risk preference of the system operator. The key analytical results verify that the bounds effectively cap storage bids across all uncertainty scenarios with a guaranteed confidence level. We show that bid bounds decrease as the state of charge increases but rise with greater netload uncertainty and risk preference. We test the effectiveness of the proposed pricing mechanism based on the 8-bus ISO-NE test system, including agent-based storage bidding models. Simulation results demonstrate that the proposed bid bounds effectively align storage bids with the social welfare objective and outperform existing deterministic bid bounds. Under 30% renewable capacity and 20% storage capacity, the bid bounds contribute to an average reduction of 0.17% in system cost, while increasing storage profit by an average of 10.16% across various system uncertainty scenarios and bidding strategies. These benefits scale up with increased storage economic withholding and storage capacity.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper derives locational bid bounds for energy storage from a tractable multi-period economic dispatch chance-constrained formulation that incorporates system operator uncertainty and risk preference. It analytically verifies that these bounds cap storage bids across uncertainty scenarios at a guaranteed confidence level, shows how bounds vary with state of charge, netload uncertainty, and risk preference, and tests the mechanism on the 8-bus ISO-NE system using agent-based storage bidding models. Simulations report that the bounds align storage bids with social welfare, outperform deterministic bounds, reduce system costs by an average 0.17%, and increase storage profits by 10.16% under 30% renewables and 20% storage, with benefits scaling under withholding and higher storage capacity.

Significance. If the simulation results hold under properly specified agent optimization, the work offers a systematic, risk-aware method for setting storage offer caps that could improve market efficiency and limit market power in systems with growing storage and renewables. The chance-constrained grounding provides an independent analytical basis for the bounds rather than ad-hoc fitting, which is a strength relative to purely deterministic approaches.

major comments (1)
  1. [Numerical experiments / agent-based simulation results] The agent-based storage bidding models used in the 8-bus ISO-NE simulations are not explicitly formulated. No objective function, information set, or decision rule is given for how storage agents optimize or respond to the locational bounds under uncertainty. Without this, the reported 0.17% average cost reduction and 10.16% profit increase cannot be taken as evidence that the bounds produce social-welfare alignment rather than an artifact of the chosen simulation rules.
minor comments (1)
  1. The abstract and main text should specify the number of uncertainty scenarios, the exact confidence level used in the bounds, and the range of risk preferences tested to allow replication of the reported averages.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comments and the recommendation for major revision. We address the single major comment below.

read point-by-point responses

  1. Referee: [Numerical experiments / agent-based simulation results] The agent-based storage bidding models used in the 8-bus ISO-NE simulations are not explicitly formulated. No objective function, information set, or decision rule is given for how storage agents optimize or respond to the locational bounds under uncertainty. Without this, the reported 0.17% average cost reduction and 10.16% profit increase cannot be taken as evidence that the bounds produce social-welfare alignment rather than an artifact of the chosen simulation rules.

    Authors: We agree that the manuscript does not explicitly formulate the agent-based storage bidding models, including their objective function, information set, and decision rules. This omission limits the interpretability of the simulation results. In the revised manuscript we will add a dedicated subsection (likely in Section 4) that specifies: (i) the agents' objective of maximizing expected profit subject to the locational bid bounds, (ii) the information set consisting of day-ahead netload forecasts, realized state-of-charge, and the system operator's risk parameter, and (iii) the decision rule that selects bids within the derived bounds while respecting storage operational constraints. With these details provided, the reported cost and profit improvements can be directly linked to the bounds rather than to unspecified simulation choices. revision: yes

Circularity Check

0 steps flagged

Derivation of bid bounds from chance-constrained formulation is self-contained

full rationale

The paper derives the bid bounds from a tractable multi-period economic dispatch chance-constrained formulation that incorporates uncertainty and risk preference of the system operator. This analytical step is presented as independent of the later 8-bus ISO-NE simulations, which are used only for validation of effectiveness (including the reported cost and profit changes). No equations reduce by construction to fitted parameters renamed as predictions, no self-citations are invoked as load-bearing uniqueness theorems, and no ansatz is smuggled in. The central claim of guaranteed confidence-level capping follows directly from the chance-constrained model rather than from simulation outcomes or prior self-work.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The paper relies on standard assumptions in optimization and market modeling; no new entities introduced. Based on abstract only.

free parameters (2)
  • risk preference
    Incorporated in the chance-constrained formulation to reflect system operator's risk attitude.
  • confidence level
    Used to guarantee the bounds cap bids across uncertainty scenarios.
axioms (1)
  • domain assumption A multi-period economic dispatch problem can be formulated as a chance-constrained optimization problem.
    Central to deriving the bid bounds from the model.

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    SoC-dependent storage bid bounds: Proof. By substituting (1b) and (13a) into (7), we have: ∂As,t ∂es,t−1 = ∂2Ci(gi,t) ∂2gi,t ∂gi,t ∂ps,t ∂ps,t ∂es,t−1 (15) = −ηs∂2Ci(gi,t)/∂2gi,t ≤0 ∂Bs,t ∂es,t−1 = ∂2Ci(gi,t(ξt)) ∂2gi,t ∂gi,t ∂bs,t ∂bs,t ∂es,t−1 (16) = −∂2Ci(gi,t(ξt))/ηs∂2gi,t ≤0 Hence, we have finished the proof

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    Storage bid bounds scaling with system uncertainty: Proof. From (13a) and quadratic or super-quadratic function Ci, we have: ∂ ˆLMPm,t ∂σn,t = ∂2Ci(gi,t) ∂gi,t∂σn,t = ∂2Ci(gi,t) ∂2gi,t F −1(1−ϵ) ≥0 (17) By substituting (17) into (7), we have finished the proof

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    Storage bid bounds scaling with risk preference: Proof. From (13a) and quadratic or super-quadratic function Ci, we have: ∂ ˆLMPm,t ∂ϵ = ∂2Ci(gi,t) ∂gi,t∂ϵ = − ∂2Ci(gi,t) ∂2gi,t ∂F −1(1−ϵ)σn,t ∂ϵ ≤0 (18) By substituting (18) into (7), we have finished the proof. C. Formulation of Storage Economic Withholding Bids (1) Opportunity Value Function. The storag...

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