Microgrids Coalitions for Energy Market Balancing

Cristina Bianca Pop; Ionut Anghel; Tudor Cioara; Viorica Chifu

REVIEW 4 major objections 7 minor 11 references

Microgrids Coalitions for Energy Market Balancing

T0 review · 4 major / 7 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper claims that a memetic algorithm paired with Shapley-value payouts can identify the microgrid coalition that best absorbs market surplus or covers a deficit and distribute the resulting gain fairly.

desk verdict Plausible idea, broken core: the sign error in the objective flips the optimization, and the evaluation is too circular to support the optimal-coalition claim. read the letter →

arxiv 2506.06058 v1 pith:435QHJJS submitted 2025-06-06 cs.GT cs.AI

Viorica Chifu , Cristina Bianca Pop , Tudor Cioara , Ionut Anghel This is my paper

classification cs.GTcs.AI MSC 91A1290C59

keywords microgridcoalitionformationenergymarketbalancingShapleyvaluememeticalgorithmcooperativegametheoryrenewablestoragesimulatedannealing

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to show that choosing which microgrids should trade with the energy market can be treated as a coalition-formation optimization. It claims that a memetic algorithm, a genetic search refined by simulated annealing, can find the coalition that best absorbs a market surplus or covers a deficit, and that the Shapley value then splits the resulting profit fairly among the members. The authors care because renewable-driven imbalances can cause outages, losses, or grid instability, so automatically assembling the right group of batteries matters. On the paper's evidence, the method selects microgrids with medium or large storage capacity and more remaining charge cycles, distributing value in proportion to contribution.

What carries the argument

The load-bearing mechanism is the memetic algorithm whose individuals are coalitions: each microgrid has an activation flag, and the chromosome length equals the community size. Its fitness function is $\nu_{\mathrm{normalized}}(C) - \mathrm{penalty}$, where $\nu_{\mathrm{normalized}}$ is the characteristic function $\nu(C)$ from cooperative game theory (profit or savings from trading with the market minus battery and operating costs, normalized by the population mean and standard deviation) and the penalty is $\rho |E_{EM}-E_C|$ whenever the coalition's tradable energy $E_C$ misses the market imbalance $E_{EM}$. The characteristic function being superadditive motivates cooperation. The Shapley value $\phi_{MG_i}$ then allocates the coalition's value to each member based on marginal contributions. The simulated-annealing step refines the best individuals and is what makes the algorithm memetic.

What would settle it

Enumerate every coalition for a small community (e.g., 15 microgrids), compute $\nu(C)$ exactly for each, and check whether the memetic algorithm returns the coalition with the maximal value across repeated runs; any run that returns a coalition below the exhaustive maximum would refute the optimality claim. Alternatively, run the method on a surplus scenario and check whether the selected coalition actually absorbs the full $E_{EM}$ without penalty.

Watch

Extended reading notes

Core claim

The paper's central claim is that optimal coalitions for energy-market balancing can be identified by encoding each candidate coalition as a binary-flag individual, scoring it with a normalized characteristic function that subtracts a penalty for mismatching the market's energy imbalance $E_{EM}$, and evolving a population with rank-based selection, two-point crossover, one-point mutation, and a simulated-annealing refinement step. The value generated by a coalition is the revenue from selling at deficit prices or the savings from buying at surplus prices, minus battery-degradation and operating costs. The Shapley value distributes that value to each microgrid according to its marginal contribution. The authors assert, based on the Zenodo dataset scenario, that this algorithm identifies the optimal coalition capable of absorbing the market surplus, selecting microgrids with large or medium battery capacity and many remaining charge cycles.

Load-bearing premise

The load-bearing premise is that the market's energy imbalance is a known, fixed quantity that one coalition can fully cover, with a linear trading price that does not change as the coalition trades; if the imbalance is uncertain, the price moves with quantity, or multiple coalitions compete, the optimization the algorithm solves is not the real decision.

Editorial extensions

If this is right

If the claim holds, a distributor can feed in the current market imbalance and price and get back a concrete list of microgrids to activate for that trading interval.
The Shapley payout gives each selected microgrid a share that rewards stored energy and available capacity while penalizing battery degradation, so high-cost batteries are less attractive.
The method favors microgrids with medium or large storage and more remaining charge cycles, meaning the coalition naturally protects battery lifetime.
The parameter study suggests the cooling factor of simulated annealing is the strongest lever on solution quality, so tuning it first is a sensible strategy.
The best configuration runs in about 1.87 seconds in the evaluated scenario, which fits near-real-time balancing decisions.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial inference: the method's optimality claim is conditional on the market imbalance being a known, fixed target; if the price responds to how much energy the coalition sells or buys, the linear characteristic function would need a price-elasticity term.
Editorial inference: the Shapley value is defined over all coalitions, but the memetic search never enumerates them; a direct test would be to compare the algorithm's answer to an exhaustive maximization of $\nu(C)$ on a small community.
Editorial inference: the same coalition machinery could be run repeatedly over consecutive time slots, effectively producing a schedule of which microgrids trade when, rather than a single one-shot coalition.
Editorial inference: because the penalty formulation can be applied symmetrically to surplus and deficit cases, the method is testable as-is on a surplus scenario even though the paper's experiments only demonstrate a deficit.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The paper has a good instinct and a broken center. The problem—microgrids forming coalitions to trade with the grid under surplus and deficit—is relevant, and using a memetic algorithm with Shapley value is a sensible heuristic. But the main objective function has a sign error that flips what the algorithm optimizes. Eq. (11) uses min(ΣEstore, EEM) in the deficit branch, yet Eq. (6) defines deficit as EEM<0, making that term negative and constant for any coalition holding at least |EEM| stored energy. So the algorithm maximizes (negative revenue) minus costs—i.e., it just minimizes battery and operating costs. Eq. (9) is worse: it demands ΣEstore ≅ EEM, equating a positive quantity with a negative one. This isn't a typo; it's a load-bearing inconsistency in the definition of the optimization problem. The Shapley formula in Eq. (15) is also garbled (missing parenthesis, stray minus sign), so the fairness analysis isn't verifiable as written.

What's worth keeping? The related work is solid, and the penalty in Eq. (20) is a reasonable way to enforce balance. Modeling battery degradation through remaining cycles is a nice touch. But the evaluation doesn't back the 'optimal coalition' claim. The parameters are tuned on the same deficit scenario used for testing, so the fitness gains in Section 5 are circular. There's no baseline—no greedy, no plain genetic algorithm, no existing coalition-game method. The evidence is qualitative figures and a modest correlation of 0.46.

Bottom line: the paper deserves a serious rewrite, not a serious referee as-is. Fix the sign conventions, repair the Shapley formula, add a real baseline, and test on both surplus and deficit scenarios with quantitative comparisons. If that happens, it could be a modest but useful contribution to the microgrid-trading literature. As it stands, I'd desk reject, but tell the authors to resubmit after major revision.

Referee Report

4 major / 7 minor

Summary. The paper proposes a method for forming an optimal coalition of microgrids that trades with the energy market during surplus or deficit periods, combining a Shapley-value-based cooperative game approach with a memetic algorithm. The method represents candidate coalitions as binary strings, evaluates them with a fitness function derived from a characteristic function, and refines the population via genetic operators and simulated annealing. The experimental section uses a Zenodo dataset of 50 prosumers in a market-deficit scenario, reporting the coalition composition, battery state evolution, and correlations between storage capacity/cost and Shapley value. The stated central claim is that the algorithm identifies the optimal coalition that maximizes collective trading profit and distributes it fairly among members.

Significance. If the proposed model were correct, the paper would contribute a practical heuristic for microgrid coalition formation in energy markets, with a transparent Shapley-based benefit-sharing rule. The algorithmic machinery (memetic search with simulated annealing) is standard but reasonably engineered, and the parameter-sensitivity analysis is thorough. However, the central mathematical formulation contains a sign inconsistency that invalidates the objective for the deficit scenario actually evaluated, the Shapley formula is misprinted, and the experimental methodology tunes parameters on the very scenario used for performance assessment. As a result, the paper's main claim—that the memetic algorithm identifies the profit-maximizing coalition—is not supported by the evidence presented.

major comments (4)

[Eqs. (6), (9), (11)] The sign conventions are internally inconsistent. Eq. (6) defines a market deficit as EEM < 0, but Eq. (9) then requires sum of positive stored energy to be approximately equal to a negative EEM, which is impossible. In the deficit branch of Eq. (11), the term Price * min(ΣEstore, EEM(t)) is negative for EEM < 0 and constant across all coalitions with ΣEstore ≥ |EEM|. Consequently, maximizing ν(C) in the deficit scenario reduces to minimizing battery-degradation and operating costs, not maximizing trading profit. Since Section 4 evaluates only a deficit scenario, the reported 'optimal coalition' is an artifact of this misspecified objective, and the conclusion that the algorithm maximizes collective profit is unsupported.
[Eq. (15)] The Shapley value formula is misprinted. As written, φ_MGi = Σ_{C⊆MGC\{MGi}} |C|!(|N|−|C|−1)!/|N|! − (ν(C∪MGi)−ν(C)), which subtracts the marginal contribution instead of weighting and adding it. Additionally, the symbol |N| is not defined in the text. Because the Shapley-based distribution is a core contribution and is used in the experimental analysis (e.g., Figure 5), this error makes the reported fairness results unverifiable.
[§5.1–5.2] The adjustable parameters (population size, generation number, cooling factor) are tuned on the single deficit scenario that is later used for the final performance evaluation in Section 5.2 and for the results in Section 4. The manuscript acknowledges this: 'The optimal configuration was identified by applying the methodology on the scenario, in which there was a deficit in the market.' This is an overfitting risk: the reported optimal configuration and fitness evolution may not generalize to surplus periods or to other market conditions, yet the paper claims general ability to identify optimal coalitions for both surplus and deficit. A separate validation scenario or cross-validation is needed.
[§4] The experimental evaluation does not compare the proposed method against any baseline, such as individual trading, random coalition formation, or alternative coalition game formulations, nor does it establish a ground-truth optimal coalition for the test instance. The moderate correlation (≈0.46) between storage capacity and Shapley value is interpreted as validation, but it only describes a tendency within the found coalition and does not demonstrate optimality. Since the fitness function is the same objective that the memetic algorithm maximizes, the reported convergence and stability results characterize the optimizer's behavior, not the economic quality of the solution relative to external criteria.

minor comments (7)

[Abstract] The sentence '...supply energy to the market during periods of is a key aspect...' is incomplete; 'periods of' is missing the noun.
[Eq. (4)] The condition 'ΔE(t) < Estore(t) < Emax' is not a well-formed inequality for a range; likely a typo for a constraint on Estore.
[Eq. (11)] Parentheses are misplaced in the surplus branch: the min should apply to (Emax−Estore) and EEM as a sum over the coalition, but the current notation places the summation inside the min in an unclear way.
[Algorithm 1] The title reads 'Mnemonic Algorithm' instead of 'Memetic Algorithm'; Tmin is used in the while condition but never initialized; line 28 compares a function of two fitness values with a random number without spelling out the acceptance condition.
[Figure 6] The figure captions and the text are mismatched: text says (a) shows fitness vs population size, but caption (a) says 'Fitness vs GenNumber'; (b) caption says 'Fitness vs PopSize' while text says generation number.
[§5.1] There is a typographical error in 'CoolingFactor)the range of variation' and the cooling-factor step is reported as 0 instead of a positive number.
[Conclusion] The sentence 'maximize the profit from purchasing energy during periods of energy shortage' should read 'selling energy' because the deficit scenario involves selling to the market.

Circularity Check

2 steps flagged · score 6.0 of 10

The optimal-coalition claim is defined by the same characteristic function the algorithm optimizes, and the cost-Shapley correlation used as validation is forced by the definition of the Shapley value.

self definitional [Section 3, Eq. (16) and Eq. (18); Conclusion]
"Eq. (16): '𝐶 = max_{𝐶⊆𝐶𝑆} 𝜈(𝐶), ∀𝑀𝐺𝑖 ∈ 𝐶, 𝑣𝑎𝑙𝑢𝑒(𝑀𝐺𝑖, 𝜈(𝐶)) = 𝜙𝑀𝐺𝑖'; Eq. (18): '𝑓𝑖𝑡𝑛𝑒𝑠𝑠(𝑖𝑛𝑑𝑖𝑣) = 𝜈_{𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑}(𝐶) − 𝑝𝑒𝑛𝑎𝑙𝑡𝑦'; Conclusion: 'the algorithm is able to identify the optimal coalition capable of absorbing the market surplus.'"

The paper defines the optimal coalition as the maximizer of ν(C) in Eq. (16), then defines the algorithm's fitness in Eq. (18) as a normalized and penalized version of the same ν(C). Since the algorithm returns the highest-fitness individual, the claim that it 'identifies the optimal coalition' is true by construction relative to the paper's own objective. No independent optimum, external benchmark, or exact comparison is computed; the evaluation reports only fitness values and correlations derived from the same characteristic function. The optimality claim thus reduces to the definition, rather than being an empirically established result.
self definitional [Section 3, Eq. (11) and Eq. (15); Section 4, Figure 5 discussion]
"Eq. (11): '𝜈(𝐶,𝑡) = { ... − ∑ 𝑐𝑜𝑠𝑡𝐸𝑆𝐵^{𝑀𝐺𝑖}_{𝑀𝐺𝑖∈𝐶}(𝑡) − 𝑐𝑜𝑠𝑡𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔(𝐶) ... }'; Eq. (15): '𝜙𝑀𝐺𝑖 = ∑ ... (𝜈(𝐶 ∪ 𝑀𝐺𝑖) − 𝜈(𝐶))'; Section 4: 'the perfectly negative correlation (≃-1.0) between cost and Shapley value ... demonstrates that microgrids with higher costs receive a lower value ... These results validate that our algorithm ensures an equitable distribution of benefits.'"

The Shapley value in Eq. (15) is computed from ν(C), and ν(C) in Eq. (11) subtracts each microgrid's battery cost and operating cost. For an additive cost term −Σ cost_i, the Shapley contribution is exactly −cost_i, so a negative correlation between cost and Shapley value is forced by the definitions. The reported correlation of about −1.0 is therefore an identity implied by the construction of ν(C) and the Shapley formula, not an empirical validation of fair distribution. Using it as evidence of equitable sharing is circular.

full rationale

The paper contains no load-bearing self-citation chain and does not import a uniqueness theorem from the authors' prior work; all cited background is independent. However, two key success claims reduce by construction. First, the 'optimal coalition' is defined in Eq. (16) as the maximizer of ν(C), and the algorithm's fitness in Eq. (18) is a normalized, penalized version of the same ν(C); hence the concluding claim that the algorithm identifies the optimal coalition is an artifact of the definition rather than a validated result against an external optimum. Second, the Section 4 validation of 'equitable distribution' relies on the near-perfect negative correlation between microgrid cost and Shapley value, but because ν(C) in Eq. (11) explicitly subtracts costs and the Shapley value in Eq. (15) is computed from ν(C), that negative correlation is structurally forced. These are genuine reductions of claimed results to the paper's own definitions, so the analysis is partially circular. The deficit-branch sign issue in Eq. (11) is a correctness concern, not a circularity, and does not affect this score; the memetic optimization and Shapley machinery retain independent algorithmic content, which is why the score is 6 rather than higher.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The method depends on several hand-chosen parameters (rho, p, k, cooling factor, population size) and on an assumed market model with a known imbalance and fixed price. The cost model relies on an unspecified degradation coefficient delta and a Weibull assumption with 6000 cycles. No external benchmark or sensitivity analysis is provided. The Shapley formula in Eq. (15) is misprinted, so the exact distribution rule used is unclear.

free parameters (6)

rho (penalty factor) = 0.5
Set in Section 5.1 to penalize deviations between coalition energy and market imbalance; used in fitness Eq. (20). Tuned on the same scenario as the evaluation, making the fitness in-sample.
p (initial active microgrid percentage) = 0.1
Set in Section 3 and 5.1 for initial population generation (Eq. 21). Arbitrary choice with no sensitivity analysis.
k (subpopulation size for simulated annealing) = 20%
Set in Section 5.1; fraction of best individuals chosen for local search. Not justified beyond empirical tuning.
delta (battery degradation coefficient) = unspecified
Used in Eq. (12) to compute battery degradation cost. The paper does not state its value, though it is central to the cost term in the characteristic function.
Cooling factor and SA temperature schedule = 0.7-0.8 (best)
Tuned in Sections 5.1 and 5.2. Cooling factor has the largest influence on fitness, and the chosen value is selected based on fitness on the same evaluation scenario.
Population size and generation count = popSize 50, generations 150 (best)
Tuned in Section 5.2 using the deficit scenario; these parameters affect convergence and diversity and are not validated out-of-sample.

assumptions (5)

standard math Shapley value is a fair and appropriate distribution rule for coalition profit
Invoked in Eq. (15) and throughout, standard cooperative game theory concept. However, the formula is misprinted.
domain assumption Battery dynamics in Eq. (4) correctly describe storage behavior
Taken from reference [8] with charging/discharging efficiencies; no validation on this dataset.
domain assumption Market state is fully described by a known, fixed imbalance EEM and a single price
Eqs. (5)-(6) define the market by deficit/surplus and price, and Eqs. (9)-(11) assume the coalition can trade exactly the market imbalance without affecting price.
ad hoc to paper The characteristic function is superadditive
Eq. (14) asserts non-negative value and superadditivity without proof, but the fitness and Shapley computations rely on these properties.
ad hoc to paper Penalty function in Eq. (20) with rho=0.5 is a valid economic penalty
The linear penalty is an arbitrary modeling choice; no derivation from market rules or cost data.

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Cite this review

Pith. "Pith review of Microgrids Coalitions for Energy Market Balancing." pith.science (2026). https://pith.science/paper/435QHJJS

@misc{pith2026250606058,
  author       = {Pith},
  title        = {Pith review of: Microgrids Coalitions for Energy Market Balancing},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/435QHJJS}},
  note         = {Machine review of arXiv:2506.06058}
}

read the original abstract

With the integration of renewable sources in electricity distribution networks, the need to develop intelligent mechanisms for balancing the energy market has arisen. In the absence of such mechanisms, the energy market may face imbalances that can lead to power outages, financial losses or instability at the grid level. In this context, the grouping of microgrids into optimal coalitions that can absorb energy from the market during periods of surplus or supply energy to the market during periods of is a key aspect in the efficient management of distribution networks. In this article, we propose a method that identify an optimal microgrids coalition capable of addressing the dynamics of the energy market. The proposed method models the problem of identifying the optimal coalition as an optimization problem that it solves by combining a strategy inspired by cooperative game theory with a memetic algorithm. An individual is represented as a coalition of microgrids and the evolution of population of individuals over generations is assured by recombination and mutation. The fitness function is defined as the difference between the total value generated by the coalition and a penalty applied to the coalition when the energy traded by coalition exceeds the energy available/demanded on/by the energy market. The value generated by the coalition is calculated based on the profit obtained by the collation if it sells energy on the market during periods of deficit or the savings obtained by the coalition if it buys energy on the market during periods of surplus and the costs associated with the trading process. This value is divided equitably among the coalition members, according to the Shapley value, which considers the contribution of each one to the formation of collective value.

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Reference graph

Works this paper leans on

11 extracted references · 7 canonical work pages

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Imran Azim, Thomas Morstyn, H

Wayes Tushar, Tapan Kumar Saha, Chau Yuen, M. Imran Azim, Thomas Morstyn, H. Vincent Poor, Dustin Niyato, Richard Bean, A coalition formation game framework for peer-to-peer energy trading, Applied Energy, Volume 261, 2020, 114436, ISSN 0306-2619,

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

Imran Azim, Thomas Morstyn, H

Wayes Tushar, Tapan Kumar Saha, Chau Yuen, M. Imran Azim, Thomas Morstyn, H. Vincent Poor, Dustin Niyato, Richard Bean, A coalition formation game framework for peer-to-peer energy trading, Applied Energy, Volume 261, 2020, 114436, ISSN 0306-2619,

work page 2020

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McCulloch, H

Wayes Tushar, Tapan Kumar Saha, Chau Yuen, Thomas Morstyn, Malcolm D. McCulloch, H. Vincent Poor, Kristin L. Wood, A motivational game-theoretic approach for peer-to-peer energy trading in the smart grid, Applied Energy, Volume 243, 2019, Pages 10-20, ISSN 0306-2619, https://doi.org/10.1016/j.apenergy.2019.03.111

doi:10.1016/j.apenergy.2019.03.111 2019

[3] [3]

Liaqat Ali, S.M. Muyeen, Hamed Bizhani, Arindam Ghosh, A peer-to-peer energy trading for a clustered microgrid – Game theoretical approach, International Journal of Electrical Power & Energy Systems, Volume 133, 2021, 107307, ISSN 0142-0615, https://doi.org/10.1016/j.ijepes.2021.107307

work page arXiv 2021

[4] [4]

Laayati, H

O. Laayati, H. E. Hadraoui, M. Bouzi, A. Elmaghraoui, I. Mousaid și A. Chebak, „A Game Theory Approach (VCG-PSO) for Optimal P2P Energy Trading in Blockchain-Enabled Microgrids,” în 20th International Conference on Smart Technologies, 2023

work page 2023

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Krayem, A

A. Krayem, A. Ahmad și S. Najem, „A game theoretic approach to assess peer to peer rooftop solar PV electricity trading under constrained power supply,” 2021, Energy Systems https://doi.org/10.1007/s12667- 021-00483-3

work page doi:10.1007/s12667- 2021

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K. Anoh, S. Mahatjan, A. Ikpehai, Y. Zhang și B. Adebisi, „Energy Peer-to-Peer Trading in Virtual Microgrids in Smart Grids: A Game-Theoretic Approach,” IEEE Transanction on Smart grid, vol. 11, 2020

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Guerrero, Microgrids: A review, outstanding issues and future trends, Energy Strategy Reviews, Volume 49, 2023, 101127, ISSN 2211-467X, https://doi.org/10.1016/j.esr.2023.101127

Moslem Uddin, Huadong Mo, Daoyi Dong, Sondoss Elsawah, Jianguo Zhu, Josep M. Guerrero, Microgrids: A review, outstanding issues and future trends, Energy Strategy Reviews, Volume 49, 2023, 101127, ISSN 2211-467X, https://doi.org/10.1016/j.esr.2023.101127

arXiv 2023

[8] [8]

Shayan Mohseni, Mir Saman Pishvaee, Energy trading and scheduling in networked microgrids using fuzzy bargaining game theory and distributionally robust optimization, Applied Energy, Volume 350, 2023, https://doi.org/10.1016/j.apenergy.2023.121748

arXiv 2023