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arxiv: 2605.26901 · v1 · pith:LD63JIHYnew · submitted 2026-05-26 · 📡 eess.SY · cs.SY

Load Management of Distribution Systems via Online Dynamic Pricing

Jiarui Yu , Zhiyu He , Wenbin Wang , Colin N. Jones , Florian D\"orfler , Hanmin Cai This is my paper

Pith reviewed 2026-06-29 15:43 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords dynamic pricingonline feedback optimizationpeak demand managementdistribution systemselectric vehiclesaggregate loadday-ahead pricing
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The pith

An online feedback optimization algorithm designs day-ahead electricity prices to cut distribution peaks using only aggregate load measurements.

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

The paper proposes an Online Feedback Optimization algorithm that iteratively adjusts day-ahead electricity prices based solely on observed total load to reduce peaks caused by electric vehicle charging. Prices are updated without any individual user consumption data or behavioral models, and a cost-deviation penalty term is included relative to a reference tariff. The updates converge to the optimal price despite limited observability, and finite-horizon simulations show peak reductions close to those of a full-information Stackelberg benchmark while using far less computation. Additional tests confirm robustness to different starting points and charging-window mismatches.

Core claim

The OFO algorithm updates prices iteratively from aggregate load measurements alone and converges to the optimal day-ahead price vector, delivering peak reduction performance comparable to a Stackelberg benchmark that requires full model information while incurring substantially lower computational cost.

What carries the argument

The Online Feedback Optimization (OFO) algorithm, which performs iterative price updates via feedback from aggregate load measurements.

If this is right

  • Peak-demand management becomes feasible in grids where only feeder-level measurements are available.
  • Privacy concerns from collecting individual user data can be avoided while still achieving near-optimal load shifting.
  • Day-ahead price setting requires far lower online computation than model-based game-theoretic methods.
  • The approach remains effective under realistic mismatches in charging windows.

Where Pith is reading between the lines

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

  • The same aggregate-feedback loop could be tested on real-time pricing rather than day-ahead tariffs.
  • If the convergence holds under network constraints, OFO might extend to voltage or congestion management.
  • Scaling the method to larger networks would require checking whether the number of iterations stays practical.

Load-bearing premise

Iterative price updates driven only by total load measurements are enough to reach the optimal price without knowing individual user behavior or consumption patterns.

What would settle it

Run the OFO price updates on a distribution system where the resulting peak demand remains substantially higher than the Stackelberg benchmark across multiple initial conditions and charging schedules.

Figures

Figures reproduced from arXiv: 2605.26901 by Colin N. Jones, Florian D\"orfler, Hanmin Cai, Jiarui Yu, Wenbin Wang, Zhiyu He.

Figure 1
Figure 1. Figure 1: Interaction between the Distribution System Operator and the Distribution Grid via Online Feedback Optimization. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Reference price profile for a single day (observed on 26 May 2025). [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Estimated Sensitivity Matrix for Warm Initialization of Online Sensi [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of Original OFO and Smoothened OFO Performances. [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of Online Daily Peaks Loads of Three Methods in Four Months. [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of daily load and price profiles of the initial day and the last day. [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of Online Objectives of Three Methods in Four Months. [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Comparison of Online Daily Peaks Loads of Three Methods in Four Months under Model Mismatch. [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
read the original abstract

The growing adoption of electric vehicles (EVs) is increasing peak demand in distribution systems, which can threaten grid stability and reduce operational efficiency. Dynamic electricity pricing is a promising means of mitigating these peaks by shifting flexible demand. However, most existing approaches rely on detailed user-level consumption data and behavioral models, which are often difficult to obtain in practice and may raise privacy concerns. This paper proposes an Online Feedback Optimization (OFO) algorithm for day-ahead price design with limited data, where only aggregate loads are observed. OFO updates prices iteratively using aggregate load measurements, enabling effective peak reduction without access to individual user data. The formulation also includes a term that penalizes deviations in total electricity cost relative to a reference tariff. Although relying only on aggregate load measurements, the OFO price updates efficiently converge to the optimal price. In finite-horizon simulations, OFO achieves peak reduction close to that of the Stackelberg benchmark with full model information. Meanwhile, its computational effort is substantially lower. Additional tests under multiple initial conditions and delayed charging-window mismatch further confirm the robustness of the proposed method. Overall, these results show that OFO is a scalable and computationally efficient approach for peak-demand management in distribution systems with limited observability.

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 introduces an Online Feedback Optimization (OFO) algorithm for designing day-ahead dynamic electricity prices to manage peak demand from electric vehicles in distribution systems. The method relies solely on aggregate load measurements to iteratively update prices, incorporates a penalty term for deviations in total electricity cost from a reference tariff, and is claimed to converge to the optimal price. Simulations show it achieves peak reduction close to a full-information Stackelberg benchmark with significantly lower computational effort and demonstrates robustness to different initial conditions and charging window mismatches.

Significance. Should the convergence properties hold, this work would offer a scalable, privacy-preserving approach to load management that does not require individual user consumption data or behavioral models, addressing practical challenges in distribution system operation amid rising EV adoption. The comparison to the benchmark and robustness tests provide evidence of its potential effectiveness and efficiency.

major comments (1)
  1. [Abstract] Abstract: The assertion that 'the OFO price updates efficiently converge to the optimal price' using only aggregate load measurements lacks any supporting convergence theorem, sufficient conditions (e.g., strong monotonicity of the aggregate price-to-load map or step-size rules), or analysis of the penalized cost function, with all evidence limited to finite-horizon simulations under specific EV scenarios.
minor comments (1)
  1. The abstract would benefit from including at least one key equation for the OFO update rule or the penalized objective to allow initial assessment of the claimed properties.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for this constructive comment on the abstract. We agree that the current wording overstates the theoretical support for convergence and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The assertion that 'the OFO price updates efficiently converge to the optimal price' using only aggregate load measurements lacks any supporting convergence theorem, sufficient conditions (e.g., strong monotonicity of the aggregate price-to-load map or step-size rules), or analysis of the penalized cost function, with all evidence limited to finite-horizon simulations under specific EV scenarios.

    Authors: We agree with the referee. The manuscript contains no convergence theorem, no sufficient conditions such as strong monotonicity or step-size rules, and no analysis of the penalized cost function; all supporting evidence is from the finite-horizon simulations. We will revise the abstract to replace the claim of convergence with the statement that the OFO updates 'numerically achieve peak reduction close to the Stackelberg benchmark in simulations.' We will also add a clarifying sentence in Section IV or the conclusion noting that formal convergence analysis is beyond the scope of the present work. These changes will appear in the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No significant circularity; claims rest on external simulations

full rationale

The abstract and skeptic summary describe OFO convergence and peak-reduction performance as demonstrated via finite-horizon simulations under specific EV scenarios, without any quoted equations, fitted parameters renamed as predictions, or self-citation chains that reduce the central claim to its own inputs by construction. No self-definitional steps, ansatz smuggling, or uniqueness theorems imported from the authors appear in the provided text. The derivation is therefore treated as self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are identifiable beyond the general mention of a cost-deviation penalty term whose weight is unspecified.

free parameters (1)
  • weight on total electricity cost deviation penalty
    Formulation includes this term but its specific value or selection method is not stated in the abstract.

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Reference graph

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