⚡ electrical engineering

Coalition Formation with Limited Information Sharing for Local Energy Management

This paper proposes a privacy-preserving, computationally efficient coalition formation algorithm for local energy management that utilizes aggregate information bounds and ADMM-based optimization to reduce costs without requiring full information sharing among prosumers.

Original authors: Luke Rickard, Paola Falugi, Eric C. Kerrigan

Published 2026-03-31

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Luke Rickard, Paola Falugi, Eric C. Kerrigan

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 where every house has its own solar panels and a battery in the garage. Some days, a house produces more electricity than it needs; other days, it needs to buy more from the main power grid.

Currently, every house acts alone. If House A has extra power, it sells it back to the grid for a low price. If House B needs power, it buys it from the grid for a high price. They are essentially ignoring their neighbors, even though House A could sell directly to House B for a price in between, saving everyone money.

This is the problem of Local Energy Management. The paper proposes a solution called Coalition Formation, but with a twist: it solves the problem without forcing neighbors to reveal their private secrets.

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

1. The Problem: The "Open Book" Policy

In traditional methods, to figure out if House A and House B should team up, they have to share everything. They have to show their bank statements, their daily schedules, their battery health, and their exact energy usage to everyone else.

The Analogy: It's like trying to find a roommate by handing your entire diary, tax returns, and medical history to every stranger on the street. It's efficient for finding the perfect match, but terrible for privacy. Plus, doing all that math for every possible pair of houses takes a supercomputer's worth of time.

2. The Solution: The "Blind Date" Approach

The authors propose a new algorithm that acts like a smart blind date.

How it works: Instead of sharing their whole lives, the houses only share a single, vague hint: "Right now, I plan to buy 5 units from the grid," or "I plan to sell 5 units."
The Magic Trick: The algorithm uses a mathematical "safety net" (an upper bound). It asks: "If we team up based only on these buying/selling plans, could we possibly save money?"
- If the answer is a definite "No," they don't bother teaming up.
- If the answer is "Maybe, or yes," they form a team (a Coalition).
The Benefit: They never have to reveal their private data (like exactly how much they use or when) just to see if a partnership is worth it. It's like checking if two puzzle pieces fit by looking at the edge shape, rather than trying to assemble the whole picture first.

3. The "Group Chat" Optimization (ADMM)

Once a group of houses decides to form a coalition, they need to decide who buys from whom and how to charge their batteries.

The Old Way: One house acts as the "Boss," collects everyone's data, solves a giant math problem, and tells everyone what to do. This is slow and risky (if the Boss gets hacked, everyone's data is gone).
The New Way (ADMM): The houses use a distributed method called ADMM. Imagine a group of friends trying to agree on a dinner menu. Instead of one person dictating the menu, everyone writes down their preference, passes it to a neutral moderator, and the moderator suggests a compromise. They repeat this until everyone agrees.
The Result: They reach a consensus on how to trade energy without ever sending their full private data to a central server. They only share "tentative plans" back and forth.

4. The "Weather Forecast" (Model Predictive Control)

Energy needs change constantly. The sun might go behind a cloud, or a family might decide to cook dinner early.

The system doesn't just plan for today; it looks ahead (like a weather forecast). Every hour, it re-evaluates the situation.
The Safety Net: If the forecast changes and a coalition suddenly looks like it will cost more money than acting alone, the system instantly dissolves the coalition. The houses go back to acting alone. This guarantees that the new system never performs worse than the old, lonely way.

5. The Results: Faster, Cheaper, and Safer

The authors tested this with real data from 70 buildings.

Privacy: They shared very little information.
Speed: It was much faster than the "brute force" method (which tried to calculate every possible combination). In fact, the "brute force" method crashed the computer when trying to solve for 70 buildings, while this new method solved it in minutes.
Money: The coalitions saved money compared to everyone acting alone, almost reaching the savings of the "perfect" (but privacy-invasive) method.

Summary

Think of this paper as inventing a secure, efficient neighborhood energy club.

Before: You had to show your whole life to join the club, and the club took days to organize.
Now: You just whisper your "buy/sell" intention to the group. If the math says "Yes, we can save money," you join forces. You keep your secrets, the math happens fast, and everyone pays less for electricity.

It's a win for privacy, a win for speed, and a win for your wallet.

1. Problem Statement

The paper addresses the challenge of coordinating energy exchange among "prosumers" (entities that both consume and produce electricity) in distributed energy systems. While coalitional control offers a framework where agents group together to reduce costs through internal trading, existing bottom-up coalition formation methods suffer from two critical drawbacks:

Privacy Concerns: Current methods require agents to share full local information (detailed demand, generation, storage constraints, and optimization variables) to evaluate potential coalition merges. This exposes sensitive household data to potential attackers or competitors.
Computational Overhead: Evaluating every potential coalition merge requires solving a complete optimization problem for each candidate pair. As the number of agents increases, the combinatorial search space becomes intractable, creating a significant computational bottleneck.

The authors aim to develop a limited information sharing scheme that allows agents to form beneficial coalitions without revealing private local models, while significantly reducing computational complexity.

2. Methodology

The proposed framework integrates Model Predictive Control (MPC), Coalition Formation, and Distributed Optimization (ADMM).

A. System Modeling

Agents: A set of $N$ buildings, each with fixed demand ( $d_i$ ), generation ( $g_i$ ), and a battery with charge/discharge dynamics.
Trading: Agents can trade with the main grid (buying/selling at prices $P_{buy}$ and $P_{sell}$ ) or with other agents within a coalition.
Cost Function: A linear cost function based on grid trading prices. The goal is to minimize the cumulative cost of all agents.

B. Limited Information Coalition Formation Algorithm

Instead of solving the full optimization problem for every potential merge (as done in standard bottom-up approaches), the authors propose an algorithm that uses an efficiently computable upper bound on the value of a candidate coalition.

The Bound: The algorithm calculates a potential cost reduction based solely on aggregate net grid trade plans ( $Q_i(t)$ ) from the decentralized solution.
Logic: If two agents (or coalitions) have opposite grid trade directions at the same time step (one buying, one selling), they can potentially trade internally. The algorithm estimates the savings by assuming they swap the minimum of their opposing trade volumes at the price difference ( $P_{buy} - P_{sell}$ ).
Process:
1. Agents calculate their decentralized grid trade plans.
2. They share only these aggregate trade plans (not internal constraints or variables).
3. The algorithm iteratively merges coalitions if the estimated upper bound of the merged cost is lower than the sum of individual costs.
4. Guarantee: The method proves that the final coalition structure will never result in a total cost higher than the fully decentralized operation.

C. Within-Coalition Optimization (ADMM)

Once coalitions are formed, the agents must optimize their joint strategy. To avoid centralizing data:

Distributed Approach: The authors use the Alternating Direction Method of Multipliers (ADMM).
Mechanism: Agents solve local subproblems and exchange only tentative coalition trade schedules ( $z_i$ ) and dual variables ( $\lambda_i$ ) with a coordinator.
Privacy: Individual consumption, generation, and battery constraints remain private; only the net trade schedule is shared.
Feasibility: Since ADMM converges asymptotically, the final solution takes the consensus variable $z_i$ (which satisfies the coalition balance constraint $\sum C_{tot} = 0$ ) and recomputes local grid trades to ensure power balance is strictly maintained.

D. Model Predictive Control (MPC) Integration

The framework operates in a receding horizon manner:

At each time step, agents use forecasted demand and generation to solve the coalition formation problem.
Coalitions are dynamically re-evaluated and reformed at every time step to adapt to changing conditions.
Stability Check: If a formed coalition violates the condition that its realized cost is lower than the sum of its members' decentralized costs, the coalition is dissolved immediately, ensuring the system never performs worse than the decentralized baseline.

3. Key Contributions

Limited Information Algorithm: A novel coalition formation algorithm that replaces full optimization with a computationally cheap upper bound based on aggregate grid trades, eliminating the need to share private local data.
Privacy Preservation: The method ensures agents only share tentative grid trade plans, protecting sensitive usage and generation data.
Performance Guarantee: Theoretical proof that the resulting coalition structure guarantees a total cost no greater than that of decentralized operation.
Integrated Framework: The combination of limited-information formation, ADMM-based distributed optimization, and MPC for dynamic, real-time adaptation.
Scalability: Demonstration that the approach scales significantly better than full-information or brute-force optimal methods.

4. Numerical Results

The authors evaluated the framework using real-world data (15-minute intervals) for building energy usage, generation, and prices.

Open-Loop Optimization (70 Buildings):
- Decentralized Cost: €239.
- Limited Information Cost: €232 (Improved over decentralized).
- Optimal Coalition (Brute Force): Timed out (TO) after 24 hours, proving intractability for large $N$ .
- Bottom-Up (Full Info): €157 (Best cost), but required full data sharing and high computation.
MPC Implementation (10 Buildings):
- Limited Information: Achieved a cost of €489 (vs. €496 for decentralized) with a runtime of 4,067 seconds.
- Centralized/Full Info: Achieved €475 but required 50,700 seconds runtime and 14,986 ADMM iterations.
- Bottom-Up (Full Info): Required 63,432 seconds.
Scalability: As the number of buildings increased, the limited information approach maintained relatively low ADMM iterations and runtime, whereas full-information methods became computationally prohibitive.
Trade-off: Increasing coalition size reduced costs but increased computational load, suggesting an optimal coalition size (e.g., 6 buildings) exists for balancing performance and efficiency.

5. Significance

This work bridges the gap between the theoretical benefits of coalitional control and the practical constraints of privacy and computation in smart grids.

Privacy: It offers a viable path for prosumers to collaborate economically without fear of data leakage, a major barrier to adoption in smart grid technologies.
Efficiency: It demonstrates that near-optimal economic performance can be achieved with a fraction of the computational cost and information exchange required by existing methods.
Applicability: While focused on energy, the "limited information" bounding technique is applicable to general trading games where agents must balance optimality with privacy and communication constraints.

In conclusion, the paper provides a robust, scalable, and privacy-preserving framework for local energy management, proving that strategic cooperation is possible even when agents are unwilling or unable to share their full internal models.