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Fairness for distribution network operations and planning

This paper reviews various fairness notions and metrics in distribution network planning and operation, analyzing their mathematical complexities and impacts on stakeholders to support transparent and consistent decision-making while addressing the trade-off between efficiency and social cohesion known as the price of fairness.

Original authors: Pedro F. C. de Carvalho, Zijie Liu, Md Umar Hashmi, Dirk Van Hertem

Published 2026-05-01

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Pedro F. C. de Carvalho, Zijie Liu, Md Umar Hashmi, Dirk Van Hertem

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 power grid as a giant, shared water pipe system. In the past, water (electricity) flowed one way: from a big reservoir (the power plant) to everyone's house. But now, many houses have their own small pumps (solar panels and batteries) pushing water back into the pipes. This changes everything.

This paper is about how to manage this new, two-way flow of water without letting the system break, while making sure no one gets treated unfairly.

Here is the breakdown of the paper's main ideas using simple analogies:

1. The Problem: The "Long Pipe" Disadvantage

Think of the power grid like a long line of houses connected to a main water main.

The Old Way (Efficiency): If the pipe gets clogged, the system naturally cuts off the water to the houses at the very end of the line first because they are furthest away. This is "efficient" for the pipe, but it's unfair to the people at the end. They have solar panels just like everyone else, but they get less power because of where they live.
The New Goal (Fairness): The paper argues that we can't just look at what's most efficient for the pipes; we have to make sure the "playing field" is level. Everyone should have a fair chance to use their solar power, regardless of whether they live near the substation or at the end of the street.

2. The Cost of Fairness: The "Price of Fairness" (PoF)

You can't get something for nothing. If you force the system to treat everyone equally, the whole system might become slightly less efficient.

The Analogy: Imagine a bus that is full. To let a few more people on (fairness), you might have to ask some people to stand up or squeeze in tighter, making the ride slightly less comfortable for everyone (efficiency).
The Paper's Point: The authors call this the Price of Fairness (PoF). It's the amount of "efficiency" or "total power" the grid has to give up to ensure everyone gets a fair share. The paper notes that while regulators want fairness, the power companies (DSOs) often end up paying this price through higher costs or less total renewable energy being used.

3. Different Ways to Define "Fair"

The paper explains that "fair" is a tricky word. Different people have different ideas of what it means, and the authors categorize them like different rules for a game:

Egalitarian (The "Equal Slice" Rule): Everyone gets the exact same amount, no matter what. If you have a huge solar panel or a tiny one, you get the same cut.
Proportional (The "Pay-As-You-Go" Rule): You get a share based on what you put in. If you have a bigger solar panel, you get a bigger slice of the pie.
Meritocratic (The "Best Performer" Rule): You get rewarded based on how much value you bring to the group. If your solar panel helps the grid the most, you get the biggest reward.
Bargaining (The "Compromise" Rule): This is a middle ground. It tries to balance getting the most power (efficiency) with making sure no one is left out (fairness). You can tweak a dial to decide how much efficiency you are willing to lose to gain fairness.
Threshold (The "Safety Net" Rule): The system acts normally (efficiently) until someone falls below a certain level of comfort or income. Once they hit that "danger line," the system switches to a fairness mode to help them out.

4. Who is Involved?

The paper looks at who is playing this game:

Consumers (The Households): People with solar panels or batteries. They want to save money and use their own power.
The DSO (The Grid Manager): The company that owns the pipes. Their job is to keep the pressure right so the pipes don't burst. They have to decide who gets cut off when things get crowded.
Aggregators (The Team Captains): People who group many small solar panels together to act like one big power plant.
Regulators (The Referees): The government officials who make the rules to ensure the game is fair and no one gets ripped off.

5. Measuring the Score: The Math Tools

To make sure the game is actually fair, the authors review different "scorecards" (mathematical formulas) used to measure fairness.

Some scorecards look at the average (Social Welfare).
Some look at the gap between the richest and poorest (Gini Coefficient).
Some look at the worst-off person (Min-Max).
The paper points out that some of these scorecards are easy to calculate (like a simple linear equation), while others are very complex and hard for computers to solve quickly (non-linear).

The Bottom Line

The paper doesn't invent a new machine; it's a guidebook. It collects all the different ways researchers have tried to make power grids fair. It warns us that:

We need to be clear about what kind of fairness we want (equal shares? proportional shares?).
We need to be honest about the Price of Fairness—how much efficiency we are losing to get it.
We need to pick the right math tools so the grid can run smoothly without crashing the computer.

The ultimate goal is to help grid planners make decisions that are transparent, so everyone knows why they got the power they did, and to ensure that living at the end of the street doesn't mean getting the short end of the stick.

1. Problem Statement

The rapid integration of Distributed Energy Resources (DERs), particularly Photovoltaic (PV) systems, has transformed distribution networks (DNs) from unidirectional grids to bidirectional systems. This shift necessitates active management of congestion, voltage regulation, and Hosting Capacity (HC). However, traditional efficiency-centric optimization (Utilitarianism) often leads to locational disparity: consumers located farther from substations suffer from lower HC allocation and higher curtailment due to grid physics.

Current literature addresses this through bespoke fairness indicators, but suffers from three critical gaps:

Inconsistency: Lack of common definitions for "fairness" across studies and stakeholders.
Opacity: Limited quantification of the Price of Fairness (PoF), making it unclear how much system efficiency is sacrificed to achieve equity.
Complexity: A proliferation of metrics with varying mathematical complexities (linear vs. non-linear) without a systematic rationale for selection.

2. Methodology

The authors conducted a comprehensive literature review and systematic analysis of fairness integration in DN optimization. The methodology involves:

Categorization of Applications: Grouping existing studies into four domains: Congestion Management (CM), Hosting Capacity (HC), Local Energy Systems (LES), and Voltage Regulation (VR).
Taxonomy of Fairness Notions: Mapping specific fairness concepts to the five overarching notions:
- Egalitarian (E): Equal share of goods/burdens regardless of location.
- Proportional (P): Allocation based on demand or installed capacity.
- Meritocratic (M): Allocation based on contribution (e.g., Shapley Value).
- Bargaining (B): A weighted trade-off between efficiency and equity.
- Threshold (T): Hybrid approaches switching priorities based on utility levels.
Stakeholder Analysis: Identifying how Consumers (C), Distribution System Operators (DSO), Aggregators (A), and Regulators (R) are represented in current frameworks.
Mathematical Review: Analyzing the computational tractability of various fairness metrics (e.g., Jain's Index, Gini Coefficient, $\alpha$ -fairness) and their suitability for Linear Programming (LP) or Mixed-Integer Linear Programming (MILP).

3. Key Contributions

The paper makes several distinct technical contributions:

Unified Framework: It provides a structured overview connecting fairness notions (E, P, M, B, T) to specific DN applications and stakeholders, clarifying the "who" and "how" of fairness in grid planning.
Price of Fairness (PoF) Quantification: It explicitly defines PoF as the efficiency sacrificed ( $PoF = \frac{U - F}{U}$ , where $U$ is the utilitarian optimum and $F$ is the fairness-aware outcome). It highlights that while DSOs often bear the operational cost of PoF, consumers at resilient nodes also pay via reduced output to ensure equity for those at the feeder's end.
Metric Comparison and Linearization: The authors compile a table of fairness metrics (Table II) detailing their formulas, ranges, and "fair values." Crucially, they analyze the mathematical complexity of these metrics, demonstrating how non-linear indices (like Gini or McLoone) can be linearized for use in standard optimization solvers (LP/MILP).
Stakeholder Representation Gap: The review reveals that while Consumers are universally represented, Aggregators and Regulators are often underrepresented in fairness-aware schemes, despite their critical roles in market clearing and tariff design.

4. Key Results and Findings

Fairness Notions in Practice:
- Egalitarian and Proportional notions are the most common in CM and HC studies.
- Meritocratic notions (often using Shapley Value) dominate LES and Energy Community studies.
- Bargaining and Threshold approaches are emerging as hybrid solutions to balance efficiency and equity, often using weighting parameters ( $\mu$ or $K$ ).
Mathematical Tractability:
- $\alpha$ -fairness and $\epsilon$ -fairness are tunable but can be non-convex or difficult to parameterize.
- Jain's Index and Gini Coefficient are widely used but require linearization (e.g., via Taylor series or variable changes) to fit into MILP frameworks.
- Meritocratic Index (MI) is computationally superior to the Shapley Value for large-scale systems, as it reduces to a Root Mean Square Error (RMSE) minimization (convex quadratic programming), whereas Shapley Value calculations become computationally prohibitive as the number of agents increases.
Locational Disparity: The study confirms that without fairness constraints, nodes at the end of feeders are systematically disadvantaged. Fairness-aware controls (like fair curtailment) mitigate this but increase the PoF, manifesting as higher operational costs for DSOs or lower total renewable integration.

5. Significance and Future Outlook

This paper serves as a foundational guide for researchers and practitioners aiming to integrate fairness into grid operations. Its significance lies in:

Transparency: By defining PoF, it allows stakeholders to explicitly weigh the cost of equity against system efficiency.
Standardization: It moves the field away from ad-hoc metrics toward a standardized set of notions and mathematical formulations.
Decision Support: It aids DSOs and regulators in selecting the appropriate fairness metric based on the specific application (e.g., using Meritocratic for communities vs. Proportional for general curtailment) and the available computational resources.

Future Work: The authors recommend that future research must focus on making the PoF explicit in all fairness-aware frameworks and developing strategies to actively tackle locational disparities to ensure transparent and equitable decision-making in the transition to smart grids.