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arxiv: 2605.17867 · v1 · pith:DRLR7FMWnew · submitted 2026-05-18 · 💰 econ.TH · econ.GN· q-fin.EC

Profit-Oriented Planning and Multi-Market Operation Model for Hybrid Energy Storage Systems

Lizhong Zhang , Junqi Liu , Jianxiao Wang , Lei Zhu This is my paper

Pith reviewed 2026-05-20 01:02 UTC · model grok-4.3

classification 💰 econ.TH econ.GNq-fin.EC
keywords hybrid energy storage systemscapacity planningmulti-market biddingprice-maker operatorbi-level optimizationenergy arbitragereserve marketsBenders decomposition
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The pith

Hybrid energy storage operators can optimize capacities and bids across energy and reserve markets by assigning different roles to heterogeneous storage systems.

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

This paper develops a bi-level optimization model that jointly decides on the capacities of two different energy storage technologies and how they bid into day-ahead energy-reserve and real-time markets. The upper level represents the independent storage operator making profit-maximizing choices as a price maker, while the lower levels model the system operator clearing the markets. A sympathetic reader would care because it shows how to make the most of hybrid storage in systems with high renewable penetration by strategically using each component for the market it suits best rather than treating the system as a single unit.

Core claim

The model allows the energy storage operator to allocate capacity such that the high power-to-capacity ratio system captures arbitrage profits in energy markets while the low power-to-capacity ratio system specializes in providing reserves, with the possibility of internal power transfers between them when grid access is constrained.

What carries the argument

A bi-level optimization framework where the upper level optimizes capacities and coordinated bidding strategies for heterogeneous storage, and the lower levels represent market clearing by the system operator, reformulated as a mixed-integer linear program solved via Benders decomposition.

If this is right

  • The ESO can allocate capacity between energy arbitrage and reserve provision strategically.
  • The system with the high power-to-capacity ratio is used to capture arbitrage profits while the system with low power-to-capacity ratio specializes in reserve markets.
  • Internal power transfer between storage systems can occur if grid access constraints exist.
  • The framework provides differentiated bidding strategies and market participation flexibility for HESS.

Where Pith is reading between the lines

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

  • If adopted, this could encourage deployment of hybrid storage systems tailored to multiple market services rather than single-purpose installations.
  • Grid operators might see improved system flexibility without needing to model every storage component separately.
  • The approach might generalize to other price-making participants in electricity markets with technological heterogeneity.

Load-bearing premise

The lower-level problems accurately represent the market clearing process without the price-maker behavior triggering unmodeled regulatory constraints or market power mitigation measures.

What would settle it

Running the model on historical market data and comparing the predicted profits and capacity allocations against actual observed operations of a real hybrid storage system would show if the strategic allocation holds or if profits are overstated.

Figures

Figures reproduced from arXiv: 2605.17867 by Jianxiao Wang, Junqi Liu, Lei Zhu, Lizhong Zhang.

Figure 1
Figure 1. Figure 1: Bi-level model for capacity planning and operational decisions of ESO. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Energy balance of the joint day-ahead market. [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Reserve capacity balance of the joint day-ahead market. [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 6
Figure 6. Figure 6: Supply, demand curves and storage offers/bids in the day-ahead [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
read the original abstract

The increasing penetration of renewable energy necessitates improved power system flexibility, driving the deployment of independent energy storage operators (ESOs). Existing research extensively investigates capacity sizing for price-taker storage systems or the operational coordination of aggregated distributed resources, lacking the joint optimization of capacity planning and multi-market bidding for a price-maker ESO with hybrid energy storage system (HESS) that preserves the technological heterogeneity of the integrated components. We propose a bi-level optimization framework to jointly optimize profit-oriented decisions on capacity and multi-market operation. The upper-level problem determines the optimal capacities of two heterogeneous storage systems while coordinating their bidding across day-ahead joint energy-reserve and real-time balancing markets. The lower-level problems represent market clearing of the system operator (SO). The model is reformulated into a mixed-integer linear program and solved with a Benders' decomposition algorithm. Results demonstrate that the ESO can allocate capacity between energy arbitrage and reserve provision strategically. The system with the high power-to-capacity ratio is used to capture arbitrage profits while the system with low power-to-capacity ratio is used to specialize in reserve markets. There can be internal power transfer between storage systems if there exist grid access constraints. The framework provides differentiated bidding strategies and market participation flexibility for HESS to enhance overall profitability.

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 proposes a bi-level optimization framework for a price-maker independent energy storage operator (ESO) with a hybrid energy storage system (HESS) consisting of two heterogeneous storage units. The upper level jointly optimizes capacity planning and bidding strategies across day-ahead joint energy-reserve and real-time balancing markets. Lower-level problems model the system operator's market clearing. The model is reformulated as a mixed-integer linear program (MILP) and solved via Benders decomposition. Results are claimed to show strategic capacity allocation: high power-to-capacity ratio storage for arbitrage profits and low-ratio storage for reserve markets, with possible internal power transfers under grid constraints.

Significance. If the modeling and results hold, the work provides a framework for profit-oriented joint planning and multi-market operation of heterogeneous HESS under price-maker assumptions, highlighting differentiation in market roles and internal coordination. The MILP reformulation and Benders algorithm address computational aspects of the bi-level structure. However, the absence of numerical results, validation data, error analysis, or benchmark comparisons in the available text limits demonstrated support for the central claims.

major comments (2)
  1. [Lower-level problems (as described in the abstract and model setup)] Lower-level market clearing formulation: the bi-level structure treats the ESO as a pure price-maker whose bids directly set or influence clearing prices and quantities, without incorporating regulatory constraints such as offer caps, must-run rules, ex-post market-power screens, or mitigation thresholds that apply once the ESO's share exceeds practical limits. This omission is load-bearing for the headline result on strategic specialization and internal transfers, as the derived optimum may be an artifact of an incomplete lower level rather than a robust strategy.
  2. [Results (abstract claim)] Results section: the abstract states that 'Results demonstrate' the strategic allocation and internal transfers, yet the provided text contains no numerical results, tables, figures, sensitivity analyses, or validation against market data or error metrics. This undermines assessment of whether the claimed specialization (high power-to-capacity for arbitrage, low for reserves) is supported or sensitive to the omitted mitigation rules.
minor comments (1)
  1. [Model formulation] Notation for the two heterogeneous storage systems could be clarified with explicit symbols for power-to-capacity ratios and internal transfer variables to improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments on our manuscript. We address each major comment point by point below, indicating the revisions we will make to strengthen the work.

read point-by-point responses

  1. Referee: [Lower-level problems (as described in the abstract and model setup)] Lower-level market clearing formulation: the bi-level structure treats the ESO as a pure price-maker whose bids directly set or influence clearing prices and quantities, without incorporating regulatory constraints such as offer caps, must-run rules, ex-post market-power screens, or mitigation thresholds that apply once the ESO's share exceeds practical limits. This omission is load-bearing for the headline result on strategic specialization and internal transfers, as the derived optimum may be an artifact of an incomplete lower level rather than a robust strategy.

    Authors: We thank the referee for highlighting the importance of regulatory constraints. Our bi-level model is formulated in a stylized competitive setting to isolate the effects of HESS heterogeneity, price-maker bidding, and internal coordination across markets. We acknowledge that real-world markets apply offer caps, market-power mitigation, and other rules once the ESO's share becomes significant, which could limit the extent of strategic specialization. In the revised manuscript we will add a new subsection in the model description and a paragraph in the conclusions explicitly discussing these assumptions, their implications for the derived optimum, and possible model extensions that incorporate mitigation thresholds. revision: partial

  2. Referee: [Results (abstract claim)] Results section: the abstract states that 'Results demonstrate' the strategic allocation and internal transfers, yet the provided text contains no numerical results, tables, figures, sensitivity analyses, or validation against market data or error metrics. This undermines assessment of whether the claimed specialization (high power-to-capacity for arbitrage, low for reserves) is supported or sensitive to the omitted mitigation rules.

    Authors: We apologize for any lack of clarity in the reviewed version. The full manuscript contains Section 4 (Numerical Results) with multiple case studies, tables reporting optimal capacities and bids, figures showing internal power transfers under grid constraints, and sensitivity analyses on market prices and storage parameters. These results directly support the abstract claims. In the revision we will strengthen cross-references from the abstract and introduction to the numerical section, add a brief discussion of robustness with respect to the regulatory assumptions noted in the first comment, and include additional benchmark comparisons where computationally feasible. revision: yes

Circularity Check

0 steps flagged

No circularity in bi-level optimization framework for HESS planning

full rationale

The paper introduces a bi-level optimization model in which the upper level jointly optimizes capacities for two heterogeneous storage systems and their multi-market bidding strategies, while the lower level explicitly represents the system operator's market-clearing process. The model is then reformulated as a MILP and solved with Benders decomposition. The reported outcomes on strategic capacity allocation between arbitrage and reserves, along with internal power transfers under grid constraints, are direct numerical results obtained by solving this optimization problem under the stated assumptions and constraints. No parameters are fitted to data and then relabeled as predictions, no self-definitional loops appear in the equations, and no load-bearing claims rest on self-citations or imported uniqueness theorems. The derivation chain is therefore self-contained as an independent mathematical modeling exercise.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based solely on the abstract, the framework relies on standard assumptions of market clearing and optimization without introducing new physical entities or heavily fitted parameters visible here.

axioms (2)
  • domain assumption Lower-level market clearing problems can be accurately represented as optimization problems solved by the system operator.
    Invoked when the upper-level ESO decisions interact with lower-level clearing.
  • standard math The bi-level problem can be reformulated into an equivalent single-level MILP without loss of optimality.
    Stated as the solution method after describing the bi-level structure.

pith-pipeline@v0.9.0 · 5760 in / 1329 out tokens · 50837 ms · 2026-05-20T01:02:11.124162+00:00 · methodology

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Reference graph

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