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arxiv: 2507.02636 · v2 · submitted 2025-07-03 · 🧮 math.OC · cs.SY· eess.SY

Online Convex Optimization for Coordinated Long-Term and Short-Term Isolated Microgrid Dispatch

Ning Qi , Yousuf Baker , Bolun Xu This is my paper

Pith reviewed 2026-05-19 06:28 UTC · model grok-4.3

classification 🧮 math.OC cs.SYeess.SY
keywords microgrid dispatchonline convex optimizationlong-duration energy storagestate-of-charge trackingregret boundsconvex hull approximationisolated microgridhybrid energy storage
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The pith

A non-anticipatory framework coordinates long-term and short-term dispatch in isolated microgrids by approximating long-duration storage dynamics with a convex hull, using kernel regression for state-of-charge targets, and applying adaptive

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

The paper establishes a dispatch method for isolated microgrids that pairs long-duration and short-duration energy storage without requiring forecasts of future conditions. It replaces the nonconvex electrochemical model of long-duration storage with a convex hull approximation to keep the optimization tractable, then generates hindsight-optimal state-of-charge trajectories offline and uses kernel regression to produce dynamic reference trajectories online. An adaptive online convex optimization routine with explicit state-of-charge tracking and expert tracking is shown to produce policies whose cumulative cost exceeds the best fixed policy in hindsight by an amount that grows sublinearly in time. Simulations indicate that the resulting schedule lowers total cost by 73.4 percent relative to prior methods and removes load loss entirely. A reader would care because the approach turns an otherwise intractable long-horizon planning problem into a sequence of online convex problems whose performance guarantees improve with longer storage duration and more training data.

Core claim

By replacing the nonconvex LDES dynamics with a convex hull approximation, training kernel regression on hindsight-optimal SoC and net-load trajectories, and running an adaptive OCO algorithm that penalizes deviation from the dynamic SoC reference while tracking expert advice, both the long-term contract and short-term power decisions achieve sublinear regret; the combined policy reduces operating cost by 73.4 percent and eliminates load shedding compared with state-of-the-art baselines, with further gains as LDES duration increases.

What carries the argument

Adaptive online convex optimization algorithm that augments the standard regret-minimizing update with an SoC-reference tracking term and an expert-tracking term, allowing the step-size to adapt while enforcing consistency with the long-term SoC target generated by kernel regression.

If this is right

  • Long-term and short-term decisions can be computed sequentially without future information while still guaranteeing sublinear regret for both horizons.
  • Cost savings and reliability improve as the physical duration of the long-duration storage increases.
  • The framework tolerates forecast errors and sudden component failures without inducing load loss.
  • Stronger penalties on SoC deviation and more regression training scenarios tighten the regret bounds.

Where Pith is reading between the lines

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

  • The same convex-hull-plus-tracking structure could be tested on other nonconvex storage technologies whose dynamics admit a tight convex outer approximation.
  • Regret bounds that improve with finer convex approximations suggest a practical trade-off between model fidelity and computational speed that could be quantified on larger networks.
  • Because the method is non-anticipatory, it may integrate directly with real-time market signals or fault-detection systems without requiring separate forecast modules.

Load-bearing premise

The convex hull approximation of the nonconvex LDES electrochemical dynamics is accurate enough that decisions computed on the approximate model remain near-optimal when executed on the true dynamics.

What would settle it

Apply the online decisions produced by the approximated model to a high-fidelity nonconvex simulation of the LDES and check whether the realized cost and load-loss statistics remain within a few percent of the values reported under the convex model.

Figures

Figures reproduced from arXiv: 2507.02636 by Bolun Xu, Ning Qi, Yousuf Baker.

Figure 1
Figure 1. Figure 1: Illustration of Convex Hull Approximation for the LDES Model. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Non-anticipatory long-short-term coordinated dispatch framework. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Diagram of the test microgrid system. respectively. The initial SoC and final SoC target of LDES are set to 0.2 and 0.5, respectively. The nonconvex model of LDES is adopted from the semi-empirical model [5]. The ground-truth data for renewable generation and load power from 1984 to 2024 are publicly available [31]. The optimization is performed hourly over an entire year and implemented in MATLAB with Gur… view at source ↗
Figure 4
Figure 4. Figure 4: Training process and testing performance of kernel regression. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Performance of the proposed method: (a) varying with penalty [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of operational performance across different methods: [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
read the original abstract

This paper proposes a novel non-anticipatory long-short-term coordinated dispatch framework for isolated microgrid with hybrid short-long-duration energy storages (LDES). We introduce a convex hull approximation model for nonconvex LDES electrochemical dynamics, facilitating computational tractability and accuracy. To address temporal coupling in SoC dynamics and long-term contracts, we generate hindsight-optimal state-of-charge (SoC) trajectories of LDES and netloads for offline training. In the online stage, we employ kernel regression to dynamically update the SoC reference and propose an adaptive online convex optimization (OCO) algorithm with SoC reference tracking and expert tracking to mitigate myopia and enable adaptive step-size optimization. We rigorously prove that both long-term and short-term policies achieve sublinear regret bounds over time, which improves with more regression scenarios, stronger tracking penalties, and finer convex approximations. Simulation results show that the proposed method outperforms state-of-the-art methods, reducing costs by 73.4%, eliminating load loss via reference tracking, and achieving an additional 2.4% cost saving via the OCO algorithm. These benefits scale up with longer LDES durations, and the method demonstrates resilience to poor forecasts and unexpected system faults.

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 / 2 minor

Summary. The paper proposes a non-anticipatory long-short-term coordinated dispatch framework for isolated microgrids with hybrid short- and long-duration energy storage. It introduces a convex hull approximation for nonconvex LDES electrochemical dynamics to enable tractability, generates hindsight-optimal SoC trajectories offline for kernel regression-based dynamic references, and develops an adaptive OCO algorithm incorporating SoC reference tracking and expert tracking. The authors prove sublinear regret bounds for the long-term and short-term policies (improving with more regression scenarios, stronger tracking penalties, and finer approximations) and report simulation results showing 73.4% cost reduction versus state-of-the-art methods, elimination of load loss, and an additional 2.4% saving from the OCO component.

Significance. If the convex approximation accuracy is sufficient for the regret guarantees to translate to the true nonconvex dynamics, the framework provides a practical, theoretically grounded online method for microgrid dispatch that addresses temporal coupling and myopia in long-duration storage planning. The rigorous sublinear regret analysis, the scaling of benefits with LDES duration, and the resilience claims to forecast errors are strengths that could advance reliable operation of isolated systems with high renewable penetration.

major comments (1)
  1. The sublinear regret bounds are derived for the convexified problem (see the long-term and short-term policy analyses). No quantitative bound is supplied on the approximation error (e.g., Hausdorff distance between the convex hull and true nonconvex LDES feasible set, or the resulting optimality gap when the convex decisions are applied to the actual electrochemical dynamics). This is load-bearing for the central claims of 73.4% cost reduction and zero load loss, as the simulations demonstrate performance on the approximated model but do not include a direct comparison against a nonconvex reference solver on identical instances.
minor comments (2)
  1. Clarify in the simulation section the precise data exclusion rules, forecast error models, and parameter tuning procedure for the tracking penalties and convex approximation granularity to support reproducibility of the 73.4% figure.
  2. Add a short discussion of how the kernel regression scenario count and approximation fineness were selected in the numerical experiments.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed and constructive review. The major comment correctly identifies that our regret analysis applies to the convexified problem and that a quantitative characterization of the convex hull approximation error is not provided in the current manuscript. We address this point directly below and commit to revisions that strengthen the connection between the theoretical guarantees and the nonconvex dynamics.

read point-by-point responses

  1. Referee: The sublinear regret bounds are derived for the convexified problem (see the long-term and short-term policy analyses). No quantitative bound is supplied on the approximation error (e.g., Hausdorff distance between the convex hull and true nonconvex LDES feasible set, or the resulting optimality gap when the convex decisions are applied to the actual electrochemical dynamics). This is load-bearing for the central claims of 73.4% cost reduction and zero load loss, as the simulations demonstrate performance on the approximated model but do not include a direct comparison against a nonconvex reference solver on identical instances.

    Authors: We agree that the sublinear regret bounds hold for the convexified formulation, which is necessary for tractable online optimization and for applying standard OCO analysis tools. The convex hull is constructed as a tight outer approximation of the nonconvex LDES electrochemical feasible set, ensuring that every convex-feasible decision remains feasible (though possibly conservative) when applied to the true dynamics. We acknowledge that the manuscript does not supply an explicit quantitative bound such as the Hausdorff distance or a derived optimality gap. In the revision we will add a dedicated subsection that (i) computes the Hausdorff distance numerically for the LDES parameters used in the case studies, (ii) provides an a-posteriori bound on the optimality gap incurred by projecting convex decisions onto the nonconvex set, and (iii) reports offline comparisons against a nonconvex solver on representative small-scale instances where exact solution is feasible. These additions will clarify the conditions under which the reported cost reductions and zero load-loss results translate to the original nonconvex system. The 73.4 % figure and load-loss elimination are obtained by running the full proposed pipeline (including the convex model) against benchmark methods that themselves rely on approximations or heuristics; we will make this comparison basis explicit. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper derives sublinear regret bounds mathematically for the adaptive OCO algorithm applied to the convexified long-term and short-term problems. The dependence of the bound on hyperparameters (number of regression scenarios, tracking penalties, approximation fineness) is a standard analytic feature and does not constitute a reduction to fitted values or self-definition. The convex-hull approximation is introduced as an explicit modeling step for tractability; performance on the original nonconvex dynamics is evaluated via simulation rather than claimed by construction from the regret proof. No self-citations, ansatz smuggling, or renaming of known results appear as load-bearing steps in the abstract or described framework. The derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete and limited to elements explicitly named in the summary.

free parameters (2)
  • tracking penalty weights
    Used to balance SoC reference tracking against cost minimization in the OCO stage; their specific values affect both regret and reported savings.
  • convex approximation granularity
    Fineness of the hull model is stated to improve regret; chosen to trade accuracy for tractability.
axioms (2)
  • domain assumption Hindsight-optimal SoC trajectories generated offline are representative enough to train a kernel regressor that produces useful online references.
    Invoked to justify the offline-to-online transfer; location: abstract description of training stage.
  • domain assumption The convex hull approximation preserves the essential feasible region and cost behavior of the true nonconvex LDES dynamics.
    Central modeling choice enabling tractability; location: abstract introduction of the model.

pith-pipeline@v0.9.0 · 5750 in / 1641 out tokens · 58811 ms · 2026-05-19T06:28:55.207348+00:00 · methodology

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Reference graph

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