Graph/Game Theory-Based Energy Routing Methods in the Energy Internet
Authors: Amani Fawaz; Imad Mougahrbel; Kamal Al-Haddad; Hadi Y. Kanaan
Extended Abstract:
The rapid transition of modern power systems toward decentralization and intelligence has led to the emergence of the Energy Internet (EI), an architecture interconnecting distributed energy resources, storage systems, and consumers through Energy Routers (ERs) with bidirectional power and information flows. Within this infrastructure, energy routing is critical for optimal energy transfer, subscriber matching, power transmission scheduling, and congestion management in dynamic networks.
The complexity of multi-source, multi-load environments needs real-time routing protocols applied to distributed resources and intelligent decision-making. A thorough review of existing methods is therefore essential to highlight their strengths, limitations, and applicability to emerging EI architectures.
This paper presents a comprehensive review of energy routing methods based on Graph Theory and Game Theory, two foundational frameworks for routing and decision-making in energy systems. In graph-theoretic approaches, the energy network is modeled as a directed, weighted graph with ERs as nodes and power links as edges. Algorithms such as graph traversal and shortest-path methods are employed to identify energy-efficient paths that minimize losses and mitigate congestion. While effective for path selection and network optimization, these approaches may exhibit reduced performance in rapidly changing EI topologies.
In game-theoretic approaches, interactions among prosumers, microgrids, and ERs are modeled as strategic games, through auctions, Stackelberg games, and coalition formation, to achieve subscriber matching, pricing, and distributed energy trading with fairness and incentive compatibility. However, many studies retain partial centralization or simplifying assumptions, leaving real-time dynamics and cybersecurity aspects only partially addressed.
A comparative evaluation across routing functionality (subscriber matching, energy-efficient path selection, transmission scheduling), computational complexity, scalability, security, power constraints, and fault tolerance shows that graph-based models excel at optimizing physical flows and minimizing losses, while game-theoretic models are more effective in market design and resource allocation. Nonetheless, no single method fully satisfies all requirements in dynamic, large-scale, self-organizing EI contexts.
Finally, the paper outlines future research directions, including Multi-Agent Systems (MAS), AI-based learning, and Metaheuristic Optimization, to hybridize the structural rigor of graph theory with the strategic intelligence of game theory, ultimately moving toward self-learning, autonomous, and resilient energy routing.
Additional information
This review paper is the result of a collaborative research effort written by Dr. Amani Fawaz, Prof. Imad Mougharbel, Prof. Kamal Al-Haddad, and Prof. Hadi Y. Kanaan, all of whom have significantly contributed to advancing research in the field of the Energy Internet. Their collective work focuses on developing intelligent power routing protocols, Energy Router (ER) architecture, and AI-driven control strategies to enhance the efficiency, resilience, and sustainability of future smart energy networks. This publication is part of ongoing research activities at École Supérieure d’Ingénieurs de Beyrouth (ESIB-USJ) and École de Technologie Supérieure de Montréal (ÉTS Montréal). This work is supported by the Agence Universitaire de la Francophonie (AUF), the research council at Saint-Joseph University of Beirut (USJ) and the National Council for Scientific Research in Lebanon (CNRS-L). The authors continue to explore decentralized, packetized, and adaptive energy routing frameworks that will shape the next generation of intelligent energy networks.