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arxiv: 1907.08125 · v1 · pith:K3UEBLSLnew · submitted 2019-07-18 · 📡 eess.SY · cs.SY· math.OC

Centralised and Distributed Optimization for Aggregated Flexibility Services Provision

P. Olivella-Rosell , F. Rullan , P. Lloret-Gallego , E. Prieto-Araujo , R. Ferrer-San-Jos\'e , S. Barja-Martinez , S. Bjarghov , V. Lakshmanan
show 5 more authors
A. Hentunen J. Forsstr\"om S. Ottesen R. Villafafila-Robles A. Sumper
This is my paper

Pith reviewed 2026-05-24 19:44 UTC · model grok-4.3

classification 📡 eess.SY cs.SYmath.OC
keywords distributed optimizationADMMbattery aggregationflexibility servicesprosumer optimizationdecentralized controlenergy storage
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The pith

A modified ADMM solves the centralized battery optimization problem for flexibility services but runs 5 to 12 times faster on 100 sites.

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

The paper formulates a cost-minimization problem for operating distributed batteries to supply aggregated flexibility, where the objective includes both energy costs and battery degradation. It replaces the usual centralized solver with a decomposed approach based on a modified alternating direction method of multipliers that updates all primal variables at once and adds a proximal Jacobian regularization term. In a case study using real data from 100 prosumer sites the distributed version produces exactly the same battery schedules as the centralized version while cutting run time by a factor of five to twelve. A reader would care because the approach removes the main computational barrier that prevents aggregators from scaling flexibility services to large numbers of small battery owners.

Core claim

The modified ADMM with concurrent primal updates and proximal Jacobian term produces a solution that is mathematically equivalent to the centralized optimum for the convex battery-operation problem while requiring only one-fifth to one-twelfth the computation time on a 100-prosumer instance.

What carries the argument

Modified ADMM with concurrent primal-variable updates and a proximal Jacobian regularization term, which decomposes the global optimization across individual prosumers while preserving convergence to the centralized solution.

If this is right

  • Aggregators can manage fleets of hundreds of batteries without the centralized solver becoming the bottleneck.
  • The same schedules that minimize total cost can be computed locally at each site and only aggregated signals need to be exchanged.
  • Re-optimization can be performed more frequently because each iteration is faster.
  • The approach extends directly to other convex resource-allocation problems that share the same structure of local costs plus global service constraints.

Where Pith is reading between the lines

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

  • The speed-up may allow the same framework to be used inside real-time markets that clear every few minutes rather than every hour.
  • If the convexity assumption holds for other storage technologies the method could be reused without re-deriving convergence proofs.
  • Larger test cases with thousands of sites would be needed to confirm that the observed speed-up scales linearly.

Load-bearing premise

The inclusion of battery degradation costs and flexibility-service constraints creates a convex optimization problem to which the modified ADMM is guaranteed to converge.

What would settle it

An instance with 100 or more prosumers in which the distributed schedules differ from the centralized optimum or the run-time advantage disappears.

Figures

Figures reproduced from arXiv: 1907.08125 by A. Hentunen, A. Sumper, E. Prieto-Araujo, F. Rullan, J. Forsstr\"om, P. Lloret-Gallego, P. Olivella-Rosell, R. Ferrer-San-Jos\'e, R. Villafafila-Robles, S. Barja-Martinez, S. Bjarghov, S. Ottesen, V. Lakshmanan.

Figure 1
Figure 1. Figure 1: Centralised algorithm flowchart for attending flexibility requests. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of errors, total prosumers costs and dual variable per [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: ALFM problem results under a FR of 50 kWh of 100 sites. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 6
Figure 6. Figure 6: Primal error comparison of different acceleration algorithms under [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Prosumer total cost over time of centralised and distributed [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
read the original abstract

The recent deployment of distributed battery units in prosumer premises offer new opportunities for providing aggregated flexibility services to both distribution system operators and balance responsible parties. The optimization problem presented in this paper is formulated with an objective of cost minimization which includes energy and battery degradation cost to provide flexibility services. A decomposed solution approach with the alternating direction method of multipliers (ADMM) is used instead of commonly adopted centralised optimization to reduce the computational burden and time, and then reduce scalability limitations. In this work we apply a modified version of ADMM that includes two new features with respect to the original algorithm: first, the primal variables are updated concurrently, which reduces significantly the computational cost when we have a large number of involved prosumers; second, it includes a regularization term named Proximal Jacobian (PJ) that ensures the stability of the solution. A case study is presented for optimal battery operation of 100 prosumer sites with real-life data. The proposed method finds a solution which is equivalent to the centralised optimization problem and is computed between 5 and 12 times faster. Thus, aggregators or large-scale energy communities can use this scalable algorithm to provide flexibility services.

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

2 major / 1 minor

Summary. The paper formulates a convex optimization problem minimizing energy and battery degradation costs for aggregated flexibility services from prosumer batteries. It proposes a modified ADMM solver with concurrent (Jacobi-style) primal updates and a proximal Jacobian regularization term, claiming that the distributed solution is numerically equivalent to the centralized optimum while being 5-12 times faster on a 100-prosumer case study with real data.

Significance. If the convergence claim holds, the work supplies a practical, scalable distributed method for large-scale prosumer aggregation that directly addresses the computational bottleneck of centralized solvers in distribution-system and balancing contexts. The numerical speed-up on real data is a concrete strength.

major comments (2)
  1. [Modified ADMM section] Modified ADMM / algorithm section: no convergence theorem, Lyapunov argument, or reference to conditions under which the concurrent-update PJ-ADMM variant is guaranteed to reach the same global minimizer as the centralized convex program. Standard ADMM guarantees do not automatically extend to Jacobi-style updates plus the added proximal term; this is load-bearing for the headline equivalence claim.
  2. [Case study section] Case-study section: equivalence and timing results are reported for a single 100-prosumer instance. Without additional instances, sensitivity to the proximal regularization parameter, or a demonstration that the reported speed-up is not an artifact of the specific data set, the general claim that the method “finds a solution which is equivalent” remains under-supported.
minor comments (1)
  1. Notation for the proximal Jacobian term and the concurrent-update ordering should be made fully explicit (e.g., which variables are updated in parallel and how the dual update is sequenced) to allow readers to reproduce the exact iteration.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help improve the clarity and support for our claims. We address each major comment below.

read point-by-point responses

  1. Referee: [Modified ADMM section] Modified ADMM / algorithm section: no convergence theorem, Lyapunov argument, or reference to conditions under which the concurrent-update PJ-ADMM variant is guaranteed to reach the same global minimizer as the centralized convex program. Standard ADMM guarantees do not automatically extend to Jacobi-style updates plus the added proximal term; this is load-bearing for the headline equivalence claim.

    Authors: We acknowledge that the manuscript does not contain a self-contained convergence proof or Lyapunov analysis for the specific PJ-ADMM variant with concurrent updates. The proximal Jacobian term is included precisely to restore stability and convergence for the Jacobi-style scheme; this is justified by reference to the existing PJ-ADMM literature (e.g., works establishing convergence under convexity and appropriate step-size conditions). Because the underlying problem remains convex, the cited conditions are satisfied. In revision we will add an explicit paragraph citing the relevant PJ-ADMM convergence results and stating that our formulation meets the required assumptions, thereby supporting the numerical equivalence claim. revision: partial

  2. Referee: [Case study section] Case-study section: equivalence and timing results are reported for a single 100-prosumer instance. Without additional instances, sensitivity to the proximal regularization parameter, or a demonstration that the reported speed-up is not an artifact of the specific data set, the general claim that the method “finds a solution which is equivalent” remains under-supported.

    Authors: The presented case uses real measured data for 100 prosumers and constitutes a realistic large-scale test. To strengthen generality we will add, in the revised manuscript, a sensitivity study varying the proximal regularization parameter over a range that preserves convergence, together with a brief discussion of why the observed speed-up and equivalence are not artifacts of this particular data set (e.g., by noting that the problem structure is representative of typical prosumer aggregation). revision: yes

Circularity Check

0 steps flagged

No circularity: equivalence validated against external centralized benchmark

full rationale

The paper formulates a convex optimization problem for battery operation and flexibility services, then applies a modified ADMM (concurrent primal updates plus proximal Jacobian term) whose output is compared numerically to the solution of the same centralized convex program on a 100-prosumer instance with real data. This comparison is an external benchmark, not a self-referential fit. No equation reduces the reported equivalence or speed-up to a parameter defined inside the paper, no self-citation chain supplies a uniqueness theorem, and no ansatz is smuggled via prior work by the same authors. The derivation chain therefore remains self-contained against the stated external solver benchmark.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper relies on standard convexity and convergence properties of ADMM plus the modeling choice that battery degradation can be expressed as a convex cost; no new entities are postulated and no parameters are reported as fitted inside the abstract.

axioms (2)
  • domain assumption The joint optimization problem is convex.
    Required for ADMM convergence guarantees invoked by the equivalence claim.
  • domain assumption Battery degradation cost is a convex function of charge/discharge power.
    Part of the objective function that enables the distributed formulation.

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discussion (0)

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