⚡ electrical engineering

Cleaner energy microgrids under market power and limited regulation in developing countries

This paper proposes a bi-level game-theoretic model for Lebanese microgrids that demonstrates how regulatory price and feed-in-tariff caps can effectively counter the market power of monopolistic diesel generators, thereby maximizing household economic surplus and enabling renewable energy shares to reach up to 100%.

Original authors: Elsa Bou Gebrael (American University of Beirut, Maroun Semaan Faculty of Engineering and Architecture, Industrial Engineering and Management Department Beirut, Lebanon), Majd Olleik (American Univers

Published 2026-03-19

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CC BY 4.0

Original authors: Elsa Bou Gebrael (American University of Beirut, Maroun Semaan Faculty of Engineering and Architecture, Industrial Engineering and Management Department Beirut, Lebanon), Majd Olleik (American University of Beirut, Maroun Semaan Faculty of Engineering and Architecture, Industrial Engineering and Management Department Beirut, Lebanon), Sebastian Zwickl-Bernhard (Vienna University of Technology, Institute of Energy Systems and Electrical Drives, Energy Economics Group)

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a neighborhood in a developing country where the national power grid is like a broken water pipe: it's unreliable, often dry, and sometimes completely gone for days. To survive, the neighbors have built their own "well"—a neighborhood diesel generator run by a single company (let's call them The Generator Boss).

The Generator Boss owns the well, the pipes, and the pump. Because they are the only game in town, they act like a monopolist. They can charge whatever they want, and if they feel like turning off the water for a few hours to save fuel, they do. It's expensive, it's dirty (lots of smoke), and the neighbors have no say in it.

However, the neighbors are getting smart. Many have installed their own solar panels on their roofs. But there's a problem:

At noon: The sun is blazing, and the solar panels are making too much electricity. The neighbors can't use it all, so it goes to waste (like water overflowing a bucket).
At night: The sun is gone, and the solar panels are useless. The neighbors still need to buy expensive diesel power from The Generator Boss.

The Big Question:
How can a government regulator (who is weak and can't just fire The Generator Boss) create a deal that lets neighbors share their extra solar power, lowers the price for everyone, and stops the smoke, without The Generator Boss losing money and walking away?

The Solution: A "Two-Level" Game

The authors of this paper created a mathematical "game" to solve this. Think of it as a negotiation between two players:

Level 1: The Referee (The Regulator)
The Referee can't force The Generator Boss to do anything, but they can set the rules of the game. They set two limits:

The Price Cap: "You, Generator Boss, cannot charge the neighbors more than $X per unit of electricity."
The Buy-Back Floor: "You, Generator Boss, must pay neighbors at least $Y for any extra solar power they want to sell to you."

The Referee's goal is to make the neighbors as happy as possible (maximizing their "economic surplus") while making sure The Generator Boss still makes a profit.

Level 2: The Player (The Generator Boss)
The Generator Boss sees these rules and thinks, "Okay, how do I make the most money under these rules?"

If the neighbors' solar power is cheap to buy, the Boss might buy it instead of burning expensive diesel.
If the Boss has enough money (a big budget), they might buy their own solar panels and batteries to replace the old, smelly diesel generator.
If the rules are too tight, the Boss might just turn off the power for a few hours to save costs.

What Happened in the Real World (The Lebanon Case Study)

The researchers tested this model using real data from a village in Lebanon. Here is what they found, using simple analogies:

1. The "Sweet Spot" Deal
When the Referee set a fair price cap and a fair buy-back rate, magic happened.

Neighbors got cheaper power: The price dropped because the Boss didn't have to burn as much expensive diesel.
Neighbors got paid: They could sell their extra noon-time solar power to the Boss.
The Boss got richer (or at least stayed rich): By buying cheap solar power and eventually switching to their own solar+battery system, the Boss saved money on fuel.
Result: The neighbors' happiness (economic surplus) went up by 18%.

2. The "Budget" Factor
Think of the Generator Boss's budget like a wallet.

Small Wallet: If the Boss is poor, they can't afford to buy new solar panels. They are forced to buy the neighbors' solar power because it's the cheapest option. This is actually good for the neighbors!
Big Wallet: If the Boss has a lot of money, they might buy their own solar panels. This is great for the environment (less diesel), but they might stop buying the neighbors' power as much. However, the overall system still works better than before.

3. The "Solar Neighbor" Factor

If only a few neighbors have solar panels, the system doesn't change much.
But if 90% of the neighbors have solar panels, the whole neighborhood becomes a clean energy hub. The Boss can almost completely stop using diesel. The renewable energy share jumps from 0% to nearly 100%.

4. The Catch (The "Unmet Demand")
There is one downside. Because the Boss is trying to maximize profit, they might occasionally turn off the power for a few hours if it's too expensive to run the system (like when it's cloudy and winter).

In the old days, the Boss turned off the power whenever they wanted.
In the new system, they still do it a little bit, but the Referee can't fully stop it just by setting prices.
However, the paper shows that even with this small risk of power cuts, the neighbors are still much better off financially and environmentally than before.

The Bottom Line

This paper proves that even in places where the government is weak and a single company controls the power, you can still create a win-win-win situation:

Neighbors get cheaper, cleaner electricity and get paid for their solar panels.
The Generator Boss stays profitable and eventually upgrades to cleaner, cheaper technology.
The Planet gets less pollution.

It's like turning a neighborhood where everyone is fighting over a broken well into a community garden where everyone shares the harvest, even if the landlord (the Generator Boss) still keeps the keys to the gate.

1. Problem Statement

In many developing countries facing geopolitical instability, corruption, or economic crises (e.g., Lebanon, Yemen, Nigeria), national electricity grids are unreliable or non-functional. Consequently, communities rely on neighborhood diesel generators operated by private Diesel Generator Companies (DGCs). These DGCs function as natural monopolies, controlling both generation and distribution with weak regulatory oversight.

Simultaneously, households are increasingly adopting off-grid Solar Photovoltaic (PV) systems. However, these systems face two major inefficiencies:

Curtailment: Excess solar generation during peak hours is wasted because it cannot be fed into the local microgrid.
Intermittency: Solar systems cannot meet demand during low-sunlight hours, leading to reliance on expensive and polluting diesel.

The Core Challenge: Existing techno-economic studies optimize microgrids but ignore the market power of incumbent DGCs. A purely technical optimization fails in practice because the DGC, acting as a profit-maximizing monopolist, controls access and supply. The paper asks: How can a regulator with limited oversight design a policy to integrate household PV assets into a DGC-controlled microgrid, reduce diesel reliance, and improve household economic welfare without destroying the DGC's profitability?

2. Methodology

The authors propose a Bi-level Game-Theoretic Model (Stackelberg Game) to simulate the interaction between a regulator and a monopolistic DGC.

A. The Game Structure

Leader (Regulator): Acts first. The regulator's goal is to maximize Household Economic Surplus (HES). The regulator sets two policy instruments:
1. $P_{max}$ : An upper cap on the electricity price charged by the DGC to households.
2. $FiT_{min}$ : A lower cap on the Feed-in Tariff (FiT) paid by the DGC to households for excess PV generation.
- Constraint: The regulator must ensure the DGC's Net Present Value (NPV) under the new policy is at least equal to its NPV under the status quo (ensuring DGC participation).
Follower (DGC): Acts second. The DGC responds to the regulator's caps by optimizing its operations to maximize its own NPV.
- Decision Variables: The DGC chooses the actual selling price ( $P \le P_{max}$ ), the actual FiT ( $FiT \ge FiT_{min}$ ), the dispatch of its diesel generator, the purchase of household PV excess, and investments in new assets (PV and batteries).
- Objective: Maximize NPV while minimizing unmet demand (via a small penalty weight $\epsilon$ ).

B. Mathematical Formulation

Objective Function (Regulator): Maximizes the discounted sum of (Value of Served Demand - Cost of Electricity) + (Value of PV Feed-in).
Objective Function (DGC): Maximizes NPV defined as Total Revenues minus Capital Costs, Variable Operation Costs, Fixed Operation Costs, and Unmet Demand penalties.
Constraints:
- Supply-Demand Balance: Ensures generation + feed-in = demand + battery charging + unmet demand.
- Budget Constraint: The DGC's investment in new capacity is limited by a specific budget ( $\Pi$ ).
- Technical Constraints: Includes piecewise linear approximations of diesel generator heat rates, battery state-of-charge dynamics, and capacity limits.
Solution Approach: The model is solved by iterating over a grid of $(P_{max}, FiT_{min})$ tuples. A lemma proves that the DGC will always set $P = P_{max}$ and $FiT = FiT_{min}$ to maximize profit, allowing the non-linear terms to be treated as fixed parameters during the optimization.

3. Case Study and Data

Location: Deir Qanoun Ennaher, Lebanon.
Context: A microgrid centered around a 400 kW diesel generator serving 650 households (40% are PV owners).
Data Sources:
- Load Profiles: High-resolution hourly data collected via logging devices in 3 households (Aug 2024–Apr 2025), clustered into representative summer, winter, and spring/fall days.
- Solar Data: Capacity factors from renewables.ninja.
- Parameters: Diesel costs, technology lifetimes (PV: 20y, Batteries: 8y, Diesel: 5y), and current market prices.

4. Key Results

The study compares the Status Quo (Diesel-only, no feed-in) against the Proposed Model (Regulated price/FiT caps with DGC optimization).

A. Performance Improvements (Base Case)

Under a budget of $420k (matching current operations):

Household Economic Surplus (HES): Increased by 18% (from \ $6.99M to \$ 8.26M).
Electricity Price: Reduced from \ $0.40/kWh to **\$ 0.36/kWh**.
Feed-in Tariff: Set at $0.12/kWh, incentivizing households to sell excess power.
Renewable Penetration: Rose from 0% to 60.1%.
Waste Reduction: Wasted household PV generation potential dropped from 58.8% to 6.2%.
Trade-off: Unmet demand increased slightly (1.9% to 12.2%) because the DGC, constrained by budget and profit motives, did not invest in enough capacity to cover every peak hour, preferring to rely on cheaper PV/battery mixes.

B. Sensitivity Analysis: Budget Constraints

Higher Budgets: As the DGC's budget increases (e.g., to $1.75M), the HES gains increase further (up to 41% over status quo).
Technology Shift: With sufficient budget, the DGC phases out diesel entirely, replacing it with PV-battery systems.
FiT Dynamics: With tight budgets, the DGC relies heavily on cheap household feed-in (high FiT needed). With loose budgets, the DGC invests in its own PV, allowing the regulator to lower the FiT cap while still maintaining high renewable penetration.

C. Sensitivity Analysis: PV Penetration

Threshold Effect: If PV-owners are less than 10% of households, the proposed model yields lower HES than the status quo (due to lack of feed-in volume).
Optimal Penetration: HES improvements peak when 90% of households own PV. At this level, the DGC focuses almost entirely on battery storage and feed-in management.
Renewable Share: At 75% PV penetration and high budgets, renewable energy share approaches 100%.

D. The Limitation of Limited Regulation

The study highlights a critical finding: Price caps alone cannot guarantee supply reliability.

The proposed model results in higher unmet demand than the status quo in most scenarios because the DGC prioritizes profit over serving every marginal unit of demand.
However, if the regulator had the power to also cap unmet demand (extended regulation), HES would increase by an additional 10% in the base case. The gap between "limited" and "extended" regulation is small (<5-7%) when budgets are sufficient or PV penetration is high.

5. Key Contributions

Theoretical Framework: Development of a bi-level game-theoretic model that explicitly accounts for monopolistic market power and limited regulatory oversight in developing contexts. Unlike previous studies that assume neutral grid operators, this model treats the DGC as a strategic profit-maximizer.
Policy Design: Demonstrates that a simple policy tuple (Price Cap + Minimum FiT) is sufficient to unlock significant renewable integration and economic surplus, even without the regulator having direct control over the DGC's investment decisions.
Empirical Validation: Application of the model to real-world, high-resolution data from Lebanon, moving beyond theoretical assumptions to practical, data-driven insights.

6. Significance

For Developing Nations: Provides a roadmap for transitioning from polluting, expensive diesel microgrids to cleaner, cheaper hybrid systems without waiting for national grid stabilization.
For Policymakers: Shows that regulators do not need full control over the utility to achieve green transitions. By setting the right price boundaries, they can align the monopolist's profit motive with public welfare (renewable integration and lower prices).
Energy Transition: Highlights the critical role of prosumers (households with PV). Integrating their excess generation is more cost-effective than building new generation capacity, provided the regulatory framework allows for fair trading.
Realism: The paper acknowledges the political reality that DGCs are entrenched and profitable; therefore, policies must be designed to be compatible with their profitability to be adopted in practice.

Conclusion

The paper concludes that while limited regulatory oversight leads to some trade-offs in supply reliability (unmet demand), a well-designed price and tariff cap policy can significantly increase household welfare and renewable energy penetration. The transition to cleaner microgrids is feasible even under monopoly conditions, provided the regulator ensures the DGC remains profitable while incentivizing the purchase of household solar power.