Optimal Coordination of Flexible DERs in Local Energy and Flexibility Markets to Ensure Social Equity

Milad Kabirifar; Niloofar Pourghaderi; Payman Dehghanian

REVIEW 5 major objections 5 minor 18 references

Optimal Coordination of Flexible DERs in Local Energy and Flexibility Markets to Ensure Social Equity

T0 review · 5 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper establishes that pricing local energy by consumers' energy burden and clearing DER flexibility under disturbances yields equitable prices and fair curtailment for a 0.75% welfare loss.

desk verdict Useful market-design idea with a definitional equity result; Stage I pricing needs a fixed-point or equilibrium check before the numbers mean much. read the letter →

arxiv 2506.02179 v1 pith:ZXVRT23V submitted 2025-06-02 eess.SY cs.SY

Niloofar Pourghaderi , Milad Kabirifar , Payman Dehghanian This is my paper

classification eess.SYcs.SY

keywords localelectricitymarketssocialequityenergyburdendistributionlocationalmarginalpricedistributedresourcesflexibilitymarketsecond-orderconeprogrammingloadcurtailmentfairness

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

The paper aims to establish that a local electricity market can be cleared for social equity rather than efficiency alone. It does this by pricing energy according to each customer's energy burden, defined as energy cost divided by income, and by using distributed energy resources as flexibility during network disturbances. In the first stage, distribution locational marginal prices are adjusted so low- and medium-income customers pay less; in the second stage, a real-time flexibility market flattens the pro-rated load curtailment across buses. On the IEEE 33-bus test system, the equity adjustment costs only 0.75% of social welfare, and a 25% load disturbance produces 3.55% total pro-rated curtailment with flexibility, versus 5.93% without it.

What carries the argument

The carrying mechanism is the energy burden index, $EB_{n,t}=(\text{energy cost})/(\text{income})$, used as a multiplicative price-adjustment factor in Equations (9)–(11): first the bus DLMP is scaled by the bus-average burden, then each customer's price is scaled by their own burden, and a revenue-neutrality constraint renormalizes the product. The second stage's engine is the pro-rated curtailment objective in Equation (25), which minimizes total curtailment plus the spread between maximum and minimum curtailment ratios across actors. Both stages sit on the SOCP distribution load-flow model of Equations (5)–(8), which convexifies the network constraints so that losses, congestion, and voltage limits enter the DLMP and the flexibility dispatch.

What would settle it

After clearing with Equations (9)–(11), compute the realized energy cost divided by income at each bus and compare it with the fixed $EB_{n,t}$ used as input; if the burden ordering across income groups reverses, or if the total of adjusted payments no longer matches the unadjusted total, the equity result rests on the fixed-weight assumption rather than on a consistent equilibrium.

Watch

Extended reading notes

Core claim

The central claim is that equity can be inserted directly into market clearing without sacrificing technical feasibility. Stage I clears a day-ahead local energy market with an SOCP distribution-network model, then rescales the DLMP at each bus by an energy burden index $EB_{n,t}$ equal to energy cost over income, using Equations (9)–(11) to keep the total payment across customers at each bus revenue-neutral. Stage II clears a real-time local flexibility market whose objective is to minimize total curtailment and the gap between the largest and smallest pro-rated curtailment ratios, while EV, BESS, flexible load, PV, and DG flexibility restore balance after a disturbance. In simulation, adjusted DLMPs are lower at low- and medium-income buses, social welfare falls by 0.75%, and a 25% load increase yields 3.55% total pro-rated curtailment versus 3.38% for efficiency-only clearing and 5.93% with no flexibility.

Load-bearing premise

The energy burden index is fixed when prices are adjusted, even though the adjusted prices change energy costs and therefore change the very burdens the prices are meant to fix.

Editorial extensions

If this is right

Low- and medium-income customers at the designated buses pay lower time-of-day DLMPs than they would under efficiency-only clearing.
Total social welfare falls by only 0.75%, giving a bounded and visible cost for the equity gain.
A 25% load disturbance is handled with 3.55% total pro-rated curtailment when DER flexibility is cleared with the equity objective, versus 5.93% without flexibility.
The curtailment profile is flatter across buses, so no single income group bears the brunt of a disturbance.
Because both stages are SOCP, a distribution system operator can solve day-ahead energy and real-time flexibility clearing in one convex framework.

Reading between the lines

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

The paper leaves open whether the equity result survives if the energy burden weights are updated after prices change; an iterative fixed-point version could shift the price ordering and the revenue-neutrality balance.
The same burden-scaled pricing rule could be applied to wholesale or transactive energy markets wherever customer income data exists, moving the mechanism beyond local distribution networks.
The fairness objective could be generalized to a tunable trade-off between total curtailment and inequality, letting operators choose how much efficiency to sacrifice for flatter outcomes.
Testing on observed feeder-level income and consumption data would show whether the assumed low-, medium-, and high-income bus groupings match real energy-burden patterns.

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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

Colleague,

Short version: this is a plausible two-stage market design that adds energy-burden-adjusted DLMPs and equity-aware pro-rated curtailment to the authors' earlier local flexibility market work. The combination is new relative to [14], [12], and their own [4]/[6], and the SOCP formulation is reasonable. It deserves a serious referee, but only with the expectation of major revision.

What earns credit: the paper is honest about the cost of fairness (0.75% welfare reduction) and spells out both stages with enough detail to be reproduced in principle. The DER flexibility models in Stage II are standard but complete. The comparison with the no-flexibility case (5.93% curtailment) makes the value of flexibility visible, and the Stage II pro-rated objective is a sensible formalization of fairness.

The soft spots are substantial. Stage I's equity adjustment is post-hoc: Equations (9)-(11) rescale DLMPs after the clearing problem is solved, and the rescaled prices feed nothing back into dispatch. More importantly, the energy burden EB is defined as energy cost divided by income, so it depends on the very prices being adjusted. Without a fixed-point/iteration or proof that the adjusted prices are consistent with realized bills, the reported "lower prices for low-income actors" is a property of an ad hoc scaling rule, not of market clearing. Relatedly, with fixed load, Equation (11) can only redistribute surplus among consumers; it cannot change total social welfare. The 0.75% welfare loss has no accounting basis in the model as written. This is not a nitpick: it undermines the main Stage I claim.

The circularity issue is real: lower prices for high-EB customers follow directly from the scaling in (9)-(10), and flatter curtailment follows directly from the max-min objective in (25). What is left are the magnitudes—0.75% welfare loss, 3.55% vs 3.38% curtailment—and those are not backed by a clean welfare accounting.

Validation is also thin: one deterministic 33-bus scenario, hand-assigned income groups, no sensitivity or confidence bounds, no code or data. That alone would be acceptable for a conference paper, but not for a strong journal version.

Who this is for: researchers working on equity-aware distribution market design, especially those who want a concrete starting point for energy-burden pricing. The paper is worth engaging with, not because the numbers are trustworthy as-is, but because the modeling gap is clear and fixable.

Recommendation: send to peer review, but the referee should insist on either a fixed-point/equilibrium formulation for Stage I or a clear statement that the price adjustment is a post-processing redistribution rule, with welfare computed accordingly.

Referee Report

5 major / 5 minor

Summary. The paper proposes a two-stage market-clearing framework for local distribution networks. In Stage I, a day-ahead local energy market is cleared by minimizing operational costs subject to an SOCP distribution-network power-flow model, and the resulting DLMPs are then adjusted using an energy-burden index so that low- and medium-income consumers receive lower prices. In Stage II, a real-time local flexibility market minimizes total load curtailment during a disturbance while also minimizing the spread of pro-rated curtailment across buses, using flexibility from EVs, BESSs, flexible loads, PVs, and conventional DGs. The framework is validated on a modified IEEE 33-bus network with hand-assigned income groups, reporting a 0.75% social-welfare reduction from the equity-based pricing and, under a 25% load disturbance, total curtailment of 3.55% with flatter pro-rated curtailment versus 3.38% in the efficiency-only case and 5.93% without flexibility.

Significance. If the proposed framework were fully consistent, it would be a useful contribution to the emerging literature on social equity in local electricity markets. The paper has several strengths: the use of a convex SOCP formulation that incorporates network losses and voltage constraints, the explicit modeling of multiple DER types in both energy and flexibility markets, and a concrete numerical demonstration that flexibility reduces curtailment during disturbances. However, the paper does not provide reproducible code or data for the energy-burden values, and the validation is limited to one deterministic 33-bus scenario with a single disturbance magnitude. The central quantitative claims about equity pricing currently rest on a post-hoc price adjustment whose weights depend on the prices being set, and the welfare-loss figure is not derived from a well-defined welfare metric. These issues are load-bearing for the paper's main claims.

major comments (5)

[§II-B, Eqs. (9)–(11)] The adjusted prices are not well-defined as a market-equilibrium outcome. The energy burden EB_{a,t} is defined in Section II-A as the ratio of energy cost to income, so it depends on the very DLMPs that Eqs. (9)–(10) adjust. The manuscript provides no fixed-point iteration, no existence/uniqueness argument, and no demonstration that the announced prices are consistent with the realized bills of the agents. Consequently, the adjusted prices may not reflect the realized energy burdens, and the revenue-neutrality condition in Eq. (11) is not guaranteed to hold after the adjustment. The authors should either define EB using a baseline (pre-adjustment) price, solve for a fixed point, or explicitly reframe Eqs. (9)–(11) as an ex-post price-rebalancing rule with fixed exogenous weights, and then state the limitations of that reframing.
[§III, Fig. 2 and text] The claim of a '0.75% reduction in social welfare' has no clear accounting basis. The Stage I objective (1) minimizes operational costs and the loads are fixed or price-inelastic; Eqs. (9)–(11) adjust prices after the optimization and do not enter any agent's objective, any constraint, or the dispatch. With revenue neutrality enforced by Eq. (11), the price adjustment merely redistributes payments among consumers and cannot change total social welfare unless a price-responsive demand model or a separate welfare measure is introduced. Neither appears in the manuscript. The authors should either define the welfare metric used to compute the 0.75% figure, or remove the claim and replace it with a statement about payment redistribution only.
[§III, Fig. 3 and text] The Stage II fairness result is definitional rather than empirical. The objective function (25) explicitly minimizes the difference between maximum and minimum pro-rated curtailment, so the flatter curtailment profile in the proposed model is a direct consequence of the objective. The meaningful quantitative result is the trade-off: the proposed model increases total curtailment from 3.38% to 3.55%, a relative increase of about 5%, not '5% load curtailment' as stated. This trade-off should be reported precisely. In addition, the claim that this single deterministic 25% disturbance demonstrates equity 'under unbalanced operating conditions' is too strong without sensitivity analysis over disturbance magnitudes, locations, and DER availability.
[§II-B, overall two-stage structure] The two-stage decomposition is asserted without justification. Stage II treats the Stage I dispatch as fixed inputs (as stated in the paragraph after Eq. (26)) and only adjusts flexibility within the Stage II bounds, but the manuscript does not discuss whether this sequential clearing leads to a jointly optimal or even feasible-for-both-stages solution. In particular, Stage II flexibility adjustments may violate Stage I constraints or require changes in Stage I decisions that are not modeled. The authors should either prove that the decomposition is valid under the market timing (e.g., day-ahead vs. real-time), or explicitly identify the resulting suboptimality as a limitation.
[§III, setup and data] The numerical validation depends on several hand-assigned inputs that are not given in the paper: the numerical values of EB_{n,t} and EB_{a,t}, the classification of buses into income groups, the DER penetration and flexibility shares, and the 25% disturbance pattern. No sensitivity analysis is reported for any of these choices. The model's conclusions about equity are therefore not yet shown to be robust. The authors should provide the full input data and, at minimum, a sensitivity study over the energy-burden values and disturbance scenarios.

minor comments (5)

[Equations (5)–(8)] The notation in the network constraints is garbled in places (e.g., the index ranges over Ω_N, Ω_N, Ω_T are not consistently written), which makes it hard to verify the SOCP formulation. Please rewrite these equations with clear set notation.
[Eq. (1)] The objective function is typeset with unclear line breaks and missing parentheses; some summation indices appear as subscripts on the cost terms. Please reformat for readability.
[§III, first paragraph] The statement 'DGs and BESSs penetration level is 30%, with 15% of the total loads considered flexible' is ambiguous: 30% of what (capacity, energy, number of buses)? Clarify the definitions of these percentages.
[§III, Fig. 3 and text] The phrase 'additional 5% load curtailment' is misleading; the correct statement is an increase from 3.38% to 3.55% (a relative increase of about 5%, or 0.17 percentage points). Please revise for precision.
[§III, Fig. 3] The legend entry 'Minimizng total load curtailment' contains a typo; it should be 'Minimizing total load curtailment'.

Circularity Check

2 steps flagged · score 6.0 of 10

The equity results in both stages are definitional rather than derived: Stage I prices are rescaled by the energy-burden index by construction, and Stage II explicitly minimizes the spread of pro-rated curtailment; only the quantitative trade-off magnitudes remain nontrivial.

self definitional [Section II-B1, Eqs. (9)-(11); Section II-A energy burden definition]
"To ensure a fair distribution of energy prices among consumers, the energy burden index is used to adjust the DLMP for customers located at each bus in the distribution network. Initially, the DLMP at each bus is adjusted based on the average energy burden of the customers served by that bus. Subsequently, the energy price for each customer is adjusted based on their individual energy burden and the new DLMP of the corresponding bus (Equations (9) - (11))."

The adjusted prices are defined, in Eqs. (9)-(10), to be proportional to the energy burden index EB, and EB is itself defined in Section II-A as energy cost divided by income. Therefore, higher-EB (typically low-income) customers receiving lower per-unit prices is a restatement of the adjustment formula, not an independent market outcome. The reported result that 'the adjusted DLMP is lower for low- and medium-income actors in comparison with high-income actors' follows by construction from these equations. Moreover, since EB depends on energy cost, which depends on price, the weights used in Eqs.
self definitional [Section II-B2, Eq. (25); Section III, Fig. 3 discussion]
"The objective of this stage is to minimize load curtailments during disturbances and to fairly distribute the impact of the disturbances among different consumers by minimizing the difference between maximum and minimum pro-rated load curtailment, as expressed in (25)."

Equation (25) directly contains the maximum-minus-minimum pro-rated curtailment term in the objective, so the qualitative finding that the proposed model produces 'a more distributed load curtailment across all buses' and 'a flatter violation in dispatched load' is exactly what the optimization is constructed to do. The fairness result is therefore the objective function itself, not a consequence of the market design. The only nontrivial numerical outputs are the magnitudes: 3.55% total curtailment versus 3.38% for pure curtailment minimization and 5.93% without flexibility. Those trade-off numbers are genuine, but the claim of equitable distribution is definitional.

full rationale

Most of the paper's derivation chain is a conventional SOCP dispatch; the DLMP from Eq. (4) is an independent output of the optimization, and the network and DER constraints are standard engineering models. The circularity is concentrated in the equity layer. In Stage I, Eqs. (9)-(11) define the customer price as a rescaling of the DLMP by the energy-burden index EB, while EB is itself defined as energy cost divided by income. This makes the lower prices for low- and medium-income actors a direct consequence of the definition of the adjustment rule, not a prediction of the market-clearing model. The paper does not iterate EB against the adjusted prices or check revenue neutrality ex post, so the reported 'adjusted DLMP' is not a fixed point of a well-defined market process. In Stage II, Eq. (25) explicitly minimizes the spread of pro-rated curtailment, so the flatter curtailment profile in Fig. 3 is the objective itself, not an empirical result. What is not circular is the quantitative trade-off: the 0.75% social-welfare reduction, the 3.55% versus 3.38% curtailment comparison, and the 5.93% without flexibility are numerical outputs. However, the 0.75% welfare figure is not backed by a defined welfare metric in the paper, which is a correctness concern rather than a circularity. The paper's self-citations, notably refs. [4] and [6] for DER data and framework, are not load-bearing for the claimed equity novelty. Overall, because the central equity claims reduce by construction to the pricing formula and the Stage II objective, while genuine quantitative trade-offs remain, the score is 6.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central model rests on standard SOCP and network assumptions, a domain assumption that energy burden is a valid equity measure, and several ad hoc-to-paper choices: external EB values, a hand-chosen income-to-bus mapping, and a two-stage decomposition that fixes first-stage dispatch. These assumptions are reasonable for a case study, but they limit the generality of the equity claims.

free parameters (4)

Energy burden values EB_{n,t}, EB_{a,t} = not provided
Inputs to the price adjustment in Eqs. (9)-(11) are not tabulated or sourced; they directly set the magnitude of the price shift.
Income-to-bus mapping = low: 2-5, 14-19, 28-33; medium: 6-10, 19-23; others high
Chosen in Section III, this mapping determines which buses receive discounts, so it largely creates the observed equity result.
DER penetration and flexibility shares = 30% DGs/BESS, 15% flexible loads, 10% EV ownership
Scenario assumptions in Section III with no sensitivity analysis; they set the available flexibility in Stage II.
Disturbance magnitude = 25% random load increase
Single chosen contingency in Fig. 3; the curtailment tradeoff numbers are specific to this scenario.

assumptions (4)

domain assumption SOCP relaxation of the DistFlow equations is exact for the radial IEEE 33-bus network.
Adopted from [17] and used in Eqs. (5)-(8) without verifying exactness for the specific loading and equity cases.
domain assumption Energy burden (energy cost over income) is a valid and sufficient measure of social equity for price adjustment.
Used in Eqs. (9)-(11) and motivated by [16]; the paper does not justify that this single index captures the full equity objective.
ad hoc to paper The EB values are exogenous and fixed even after DLMPs change.
Eqs. (9)-(11) rescale prices using fixed EB weights, creating a potential inconsistency because EB depends on energy cost; no fixed-point update is given.
ad hoc to paper Two-stage decomposition is valid: the stage-I dispatch can be fixed as an input to stage-II flexibility adjustments without a joint optimality guarantee.
Stage II uses first-stage variables as parameters, so the combined solution may be suboptimal relative to a joint market clearing.

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Cite this review

Pith. "Pith review of Optimal Coordination of Flexible DERs in Local Energy and Flexibility Markets to Ensure Social Equity." pith.science (2026). https://pith.science/paper/ZXVRT23V

@misc{pith2026250602179,
  author       = {Pith},
  title        = {Pith review of: Optimal Coordination of Flexible DERs in Local Energy and Flexibility Markets to Ensure Social Equity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZXVRT23V}},
  note         = {Machine review of arXiv:2506.02179}
}

read the original abstract

Local electricity markets offer a promising solution for integrating renewable energy sources and other distributed energy resources (DERs) into distribution networks. These markets enable the effective utilization of flexible resources by facilitating coordination among various agents. Beyond technical and economic considerations, addressing social equity within these local communities is critical and requires dedicated attention in market-clearing frameworks. This paper proposes a social equity-based market-clearing framework for the optimal management of DERs' energy and flexibility within local communities. The proposed framework incorporates consumers' energy burden to ensure fair pricing in energy market clearance. Furthermore, to ensure equity during unbalanced operating conditions, flexible resources are managed in the local flexibility market, ensuring that all participants can trade power fairly under network disturbances. The model is formulated as a second-order cone programming (SOCP) optimization and validated on the IEEE 33-bus test distribution network.

Figures

Figures reproduced from arXiv: 2506.02179 by the authors.

**Figure 2.** Optimal DERs management and DLMP signal in Stage 1. 1.5 3.5 5.5 7.5 9.5 11.5 13.5 15.5 17.5 19.5 21.5 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 Pro-Rated Curtailed Load (%) Bus Numbers Equity-based (proposed model) Minimizng total load curtailment Ignoring DERs' flexibility [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Load curtailment in case of disturbane occurrence. proposed model demonstrates a more distributed load curtailment across all buses. This results in a flatter violation in dispatched load across network buses, whereas in the latter case, significant dispatched load deviations occur at some nodes while other nodes experience no load curtailment. In the equity-based real-time flexibility market clearing framework, the… view at source ↗

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Works this paper leans on

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Pith tools

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

[1] [14]

Securing energy equity with multilayer market clearing,

Q. Zhang and F. Li, “Securing energy equity with multilayer market clearing,” IEEE Transactions on Energy Markets , Policy and Regulation, 2024

work page 2024

[2] [12]

Equity -aware power distribution system restoration,

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work page 2024

[3] [4]

A local flexibility market framework for exploiting DERs’ flexibility capabilities by a technical virtual power plant,

N. Pourghaderi, M. Fotuhi -Firuzabad, M. Moeini -Aghtaie, M. Kabirifar, and P. Dehghanian, “A local flexibility market framework for exploiting DERs’ flexibility capabilities by a technical virtual power plant,” IET Renewable Power Generation , vol. 17, no. 3, pp. 681–695, 2023

work page 2023

[4] [6]

Exploiting DERs’ flexibility provision in distribution and transmission systems interface,

N. Pourghaderi, M. Fotuhi -Firuzabad, M. Moeini -Aghtaie, M. Kabirifar, and M. Lehtonen, “Exploiting DERs’ flexibility provision in distribution and transmission systems interface,” IEEE Transactions on Power Systems, vol. 38, no. 2, pp. 1963–1977, 2022

work page 1963

[5] [1]

Intersectionality and energy transitions: A review of gender, social equity and low -carbon energy,

O. W. Johnson, J. Y.-C. Han, A.-L. Knight, S. Mortensen, M. T. Aung, M. Boyland, and B. P. Resurreccion, “Intersectionality and energy transitions: A review of gender, social equity and low -carbon energy,” Energy Research & Social Science, vol. 70, p. 101774, 2020

work page 2020

[6] [2]

Distribution market-clearing and pricing considering coordination of DSOs and ISO: An epec approach,

H. Chen, L. Fu, L. Bai, T. Jiang, Y. Xue, R. Zhang, B. Chowdhury, J. Stekli, and X. Li, “Distribution market-clearing and pricing considering coordination of DSOs and ISO: An epec approach,” IEEE Transactions on Smart Grid, vol. 12, no. 4, pp. 3150–3162, 2021

work page 2021

[7] [3]

Self -sustainable community of electricity prosumers in the emerging distribution system,

Y. Cai, T. Huang, E. Bompard, Y. Cao, and Y. Li, “Self -sustainable community of electricity prosumers in the emerging distribution system,” IEEE Transactions on Smart Grid , vol. 8, no. 5, pp. 2207 – 2216, 2016

work page 2016

[8] [5]

A multi -block admm based approach for distribution market clearing with distribution locational marginal price,

Y. He, Q. Chen, J. Yang, Y. Cai, and X. Wang, “A multi -block admm based approach for distribution market clearing with distribution locational marginal price,” International Journal of Electrical Power & Energy Systems, vol. 128, p. 106635, 2021

work page 2021