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arxiv: 2603.16893 · v2 · submitted 2026-03-02 · 📡 eess.SY · cs.SY· econ.GN· q-fin.EC

Market Power and Distributed Solar Integration in Microgrids under Limited Regulation

Elsa Bou Gebrael (1) , Majd Olleik (1) , Sebastian Zwickl-Bernhard (2) ((1) American University of Beirut , Maroun Semaan Faculty of Engineering , Architecture , Industrial Engineering , Management Department Beirut , Lebanon
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(2) Vienna University of Technology Institute of Energy Systems Electrical Drives Energy Economics Group (EEG) Austria Norwegian University of Science Technology Norway)
This is my paper

Pith reviewed 2026-05-15 18:16 UTC · model grok-4.3

classification 📡 eess.SY cs.SYecon.GNq-fin.EC
keywords microgridsdistributed solarmarket powerfeed-in tariffsrenewable integrationdiesel generatorsLebanon case study
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The pith

Regulator-set price and feed-in-tariff caps in diesel microgrids can raise household economic surplus while enabling up to 100 percent renewable energy through household solar integration.

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 game-theoretic model of neighborhood microgrids where a diesel generator company holds market power. The regulator sets caps on electricity prices and feed-in tariffs to maximize household economic surplus, while the company decides on supply and access. Using data from Lebanon, the model shows that these caps consistently induce significant household photovoltaic feed-in, leading to renewable energy shares of 60 percent under base conditions and approaching 100 percent with higher budgets or more PV owners, compared to zero percent without intervention.

Core claim

The central discovery is that price and feed-in-tariff caps substantially increase household economic surplus and induce household PV feed-in to the microgrid, with the renewable energy share reaching 60% under base conditions and approaching 100% at high DGC budgets or PV-owner penetration levels, in contrast to the status quo of 0% renewables.

What carries the argument

A bi-level game-theoretic model where the upper level is the regulator maximizing household economic surplus via price and feed-in-tariff caps, and the lower level is the profit-maximizing diesel generator company controlling access and supply.

Load-bearing premise

The diesel generator company acts purely as a profit-maximizing monopolist with full control over access and supply, and the regulator can perfectly set and enforce caps without strategic responses or costs.

What would settle it

Empirical data from a microgrid where price and feed-in-tariff caps are implemented showing no significant increase in household PV feed-in or renewable energy share would falsify the central claim.

Figures

Figures reproduced from arXiv: 2603.16893 by (2) Vienna University of Technology, Architecture, Austria, Electrical Drives, Elsa Bou Gebrael (1), Energy Economics Group (EEG), Industrial Engineering, Institute of Energy Systems, Lebanon, Majd Olleik (1), Management Department Beirut, Maroun Semaan Faculty of Engineering, Norway), Norwegian University of Science, Sebastian Zwickl-Bernhard (2) ((1) American University of Beirut, Technology.

Figure 1
Figure 1. Figure 1: Diagram of the bi-level game (a) Status-quo microgrid (b) Proposed microgrid [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Representative diagram of the microgrid before and after change with PV systems at a price 𝐹 𝑖𝑇 of its choice as long as 𝐹 𝑖𝑇 ≥ 𝐹 𝑖𝑇 𝑚𝑖𝑛. The DGC is also free to choose to invest in its own PV and battery storage assets if such an investment is economically attractive (Figure 2b). Formally speaking, in this Stackelberg game, the leader sets a policy affecting the feasible set of the follower, and evaluates… view at source ↗
Figure 3
Figure 3. Figure 3: Representative microgrid demand profiles [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Representative profiles of solar capacity factors 5. Results and discussion We first look at the status-quo microgrid, where the DGC only operates a diesel generator without fed-in electricity from household PV-owners’ excess, nor installing PV nor batteries. This case constitutes the benchmark against which our proposed model is compared. We compute the current NPV of the DGC’s profits (𝑁𝑃 𝑉 𝐷𝐺𝐶 0 ), whic… view at source ↗
Figure 5
Figure 5. Figure 5: Feasible region and HES for every (𝑃 , 𝐹 𝑖𝑇 ) tuple in the proposed model (a) Installed capacities (b) Yearly generation profile [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Capacity and generation portfolio in the proposed model 5.2. Sensitivity analysis on the budget constraint Financing generation capacity expansion is a key concern when determining the optimal size of a microgrid, particularly in lower-income countries. As investment budgets often constitute a barrier to achieving grid reliability, the literature commonly acknowledges this constraint [49]. As long as the D… view at source ↗
Figure 7
Figure 7. Figure 7: Feasible regions of regulatory entity policies [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: HES of feasible policies, with red boxes indicating the maximum [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Optimal HES at different budgets capacity upon retirement of the diesel generator lowers operating costs and increases the DGC’s NPV, even though unmet demand rises ( [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Optimal price and feed-in-tariff at different budgets (a) Total added/retired capacity (b) Total energy generation [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Total added capacities and total energy for different budgets demand on the microgrid, and the increase in the total generation capacity of households (Figure 13b). It is also worth noting that, as the PV-owner share reaches 75% or higher, the DGC’s operations are almost completely focused on battery storage. 5.4. Constraining the unmet demand As shown in previous sections, the proposed microgrid model re… view at source ↗
Figure 12
Figure 12. Figure 12: Difference in HES between the proposed model and status-quo (a) Total added/retired capacity (b) Total energy generation [PITH_FULL_IMAGE:figures/full_fig_p015_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Added capacities and energy for different shares of PV-owners To quantify the effects of the limited regulatory oversight over the quality of supply, and therefore the HES, we introduce a theoretical regulator with the extended power to impose, in addition to (𝑃 𝑚𝑎𝑥, 𝐹 𝑖𝑇 𝑚𝑖𝑛), the status-quo unmet demand levels. Let 𝜒0 represent the unmet demand in the status-quo microgrid. The following constraint guara… view at source ↗
Figure 14
Figure 14. Figure 14: Unmet demand for proposed model and status quo (a) HES under different budgets (b) HES under different PV-owner shares [PITH_FULL_IMAGE:figures/full_fig_p016_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: HES for different microgrid cases 6. Conclusion In many grid-constrained countries affected by political and economic instability, central governments often fail to meet society’s electricity needs. In response, neighborhood diesel generators have emerged to fill this gap by forming informal, diesel-based microgrids that supply power to nearby households and institutions. With the increasing adoption of h… view at source ↗
read the original abstract

Decentralized electricity systems increasingly emerge where centralized grids fail to provide reliable supply. In such settings, privately operated neighborhood microgrids, often based on diesel generators, exhibit significant market power, limited regulatory oversight, and high environmental externalities. In parallel, households increasingly deploy off-grid solar photovoltaic (PV) systems to gain control over electricity supply. However, these systems suffer from curtailed excess generation during peak solar hours and unreliable access at other times. While prior studies have optimized microgrids in low-reliability grid contexts from a techno-economic perspective, they largely neglect the market power exerted by monopolistic private generators. This paper addresses this gap by developing a bi-level game-theoretic model that enables household-generated electricity to be fed into the microgrid while explicitly accounting for the market power of a neighborhood diesel generator company (DGC). The regulator sets price and feed-in-tariff caps to maximize household economic surplus (HES), while the DGC acts as a profit-maximizing agent controlling access and supply. The model is illustrated using high-resolution empirical data from Lebanon. Results show that: (i) price and feed-in-tariff caps substantially increase HES and consistently induce significant household PV feed-in to the microgrid; (ii) higher DGC budgets or greater PV-owner penetration lead to pronounced gains in HES; and (iii) the renewable energy share reaches 60% under base conditions and approaches 100% at sufficiently high budgets or PV-owner penetration levels, compared to 0% under the status quo.

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 / 2 minor

Summary. The paper develops a bi-level game-theoretic optimization model in which a regulator chooses price and feed-in-tariff caps to maximize household economic surplus (HES) while a profit-maximizing diesel generator company (DGC) controls access and supply in a neighborhood microgrid. Household PV owners can feed excess generation into the microgrid. The model is calibrated on high-resolution empirical data from Lebanon. Numerical results indicate that binding caps raise HES, induce substantial PV feed-in, and increase the renewable share from 0 % (status quo) to 60 % under base parameters and near 100 % at higher DGC budgets or PV-owner penetration rates.

Significance. If the quantitative results are robust, the work supplies concrete policy guidance on using limited regulatory instruments to integrate distributed solar into monopolistic microgrids. The bi-level formulation, empirical Lebanon calibration, and explicit comparison against the unregulated benchmark constitute the main strengths; the paper thereby fills a gap between purely techno-economic microgrid studies and analyses that ignore generator market power.

major comments (2)
  1. [Model Formulation and Assumptions] The central quantitative claims (60 % base renewable share, near-100 % at high budgets/PV penetration, and large HES gains) rest on the maintained assumption that the regulator can costlessly and perfectly enforce price/FIT caps with no DGC strategic responses (quality degradation, side payments, or reduced reliability). This assumption is load-bearing for the equilibrium feed-in quantities and renewable-share predictions reported from the Lebanon data; the manuscript provides no sensitivity analysis or enforcement-cost parameterization to test its necessity.
  2. [Results] The abstract and results sections state that the renewable share reaches 60 % under base conditions, yet the manuscript supplies insufficient detail on the functional form of household demand, the existence proof for the lower-level Nash equilibrium, or systematic robustness checks (e.g., alternative demand elasticities or data subsamples). These omissions leave the headline numerical magnitudes only moderately supported.
minor comments (2)
  1. [Notation] A consolidated notation table listing all decision variables, parameters, and duals used in the bi-level program would improve readability.
  2. [Figures] Figure captions should explicitly state the base-case parameter values (DGC budget, PV penetration) used to generate the reported 60 % renewable-share result.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which highlight important aspects of robustness and transparency. We address each major comment below and indicate the revisions planned for the next version of the manuscript.

read point-by-point responses

  1. Referee: [Model Formulation and Assumptions] The central quantitative claims (60 % base renewable share, near-100 % at high budgets/PV penetration, and large HES gains) rest on the maintained assumption that the regulator can costlessly and perfectly enforce price/FIT caps with no DGC strategic responses (quality degradation, side payments, or reduced reliability). This assumption is load-bearing for the equilibrium feed-in quantities and renewable-share predictions reported from the Lebanon data; the manuscript provides no sensitivity analysis or enforcement-cost parameterization to test its necessity.

    Authors: We agree that the perfect-enforcement assumption is central to the baseline equilibria. This is a deliberate modeling choice to isolate the impact of the regulatory caps under limited oversight, consistent with standard bi-level regulatory models. In the revised manuscript we will add a dedicated sensitivity subsection that introduces an enforcement-cost parameter (as a fraction of DGC profit) that effectively relaxes cap stringency. We will report how the renewable share and HES change across a range of enforcement costs and discuss qualitatively the implications of possible DGC responses such as quality degradation. revision: yes

  2. Referee: [Results] The abstract and results sections state that the renewable share reaches 60 % under base conditions, yet the manuscript supplies insufficient detail on the functional form of household demand, the existence proof for the lower-level Nash equilibrium, or systematic robustness checks (e.g., alternative demand elasticities or data subsamples). These omissions leave the headline numerical magnitudes only moderately supported.

    Authors: We accept that additional detail is warranted. Household demand is specified as a linear inverse-demand function Q_h = a_h - b_h P calibrated directly to the high-resolution Lebanon load data; parameters a_h and b_h are estimated per household type to match observed average consumption and price sensitivity. Existence of the lower-level Nash equilibrium follows from the strict concavity of the DGC profit function in its quantity and access decisions together with the compactness of the feasible strategy set. In the revision we will state these elements explicitly in Section 3, add a short proof sketch, and include a new appendix containing robustness tables for demand elasticities between -0.3 and -2.0 as well as results on regional subsamples of the Lebanon dataset. These additions will better substantiate the reported 60 % base-case renewable share. revision: yes

Circularity Check

0 steps flagged

No circularity; bi-level model derived from first principles with external data

full rationale

The paper formulates a bi-level optimization model from first principles: the upper level maximizes household economic surplus by choosing price and feed-in-tariff caps, while the lower level has the diesel generator company maximizing profit subject to those caps and access control. All equations are defined mathematically without reducing reported outcomes (HES gains, renewable shares) to fitted parameters or self-citations by construction. Results are generated by solving the model on independent high-resolution empirical data from Lebanon, making the derivation chain self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard game-theoretic rationality assumptions plus scenario-specific parameters varied in the Lebanon case study; no new physical entities are postulated.

free parameters (2)
  • DGC budget
    Higher values are shown to produce larger HES gains; treated as an exogenous scenario parameter.
  • PV-owner penetration level
    Varied to show impact on renewable share and HES; chosen as input rather than derived.
axioms (2)
  • domain assumption DGC acts as a profit-maximizing monopolist controlling access and supply
    Invoked to define the lower-level optimization problem.
  • domain assumption Regulator can set and enforce price and feed-in-tariff caps to maximize household economic surplus
    Defines the upper-level objective.

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