Building a Hetero-Functional Graph Model of the American Multi-Modal Energy System

Written by Dakota J. Thompson and Amro M. Farid

As one of the most pressing challenges of the 21st century, global climate change demands a host of changes across at least four critical energy infrastructures: the electric grid, the natural gas system, the oil system, and the coal system. In the context of the United States, this paper refers to this system-of-systems as “the American Multi-Modal Energy System (AMES)." The needs of climate change demand mitigation and adaptation strategies which are far more demanding than the needs of just mitigation alone. Therefore, as policies are developed to drive the sustainable energy transition forward, they must not just aim to mitigate climate change but must also adapt to its effects with resilient architectures. In effect, the need for decarbonization must be harmonized with the need for economic development, national energy security, and equitable energy access. These combined requirements to develop effective policies necessitate an understanding of the AMES interdependencies and how they vary geographically and temporally. Furthermore, this cross-sectoral interdependency can introduce architectural fragility that must be managed as an integral part of the sustainable energy transition.

Holistic multi-energy system models should serve to improve the understanding of these interdependent systems as they evolve into the future. Unfortunately, while there have been many attempts at modeling multi-energy systems and large-scale flows of energy, the field remains relatively nascent. While initial models were developed in response to the oil crisis and then to mitigate climate change with decarbonization, they have also been developed to introduce new energy streams such as hydrogen, synthetic fuels, biofuels, and other renewable energy sources. These works introduce their own weaknesses, including the lack of asset-level granularity, the difficulty of use, and specific one-off, geographically-specific use case models. Additionally, most of the works investigating these energy systems in the past have been performed on individual energy networks. More recently, work has been published analyzing only a couple of systems together such as pairing the electric grid with one of the other fossil fuel systems that compose the AMES. These works, however, do not include all four critical energy infrastructures and do not extend to the entire American geography. As an exception, the EIA developed a comprehensive model called the National Energy Modeling System (NEMS) which it uses to produce the (American) Annual Energy Outlook. Despite serving this important function and being publicly available, this software tool remains opaque and difficult to use. The EIA website itself recognizes that "[the] NEMS is only used by a few organizations outside of the EIA. Most people who have requested NEMS in the past have found out that it was too difficult or rigid to use." Consequently, holistic multi-energy system models of the AMES remain a present need for open-source, citizen-science to inform policies.

With a deficit of spatially and functionally resolved data, and with the current methods for modeling multi-energy systems having their limitations, the National Science Foundation (NSF) put forth a call for “research to develop and make available simulated and synthetic data on interdependent critical infrastructures (ICIs), and thus to improve understanding and performance of these systems". The NSF project entitled "American Multi-Modal Energy System Synthetic & Simulated Data (AMES-3D)" seeks to fill this void with an open-source structural and behavioral model of the AMES. Adhering to a Model-Based Systems Engineering (MBSE) approach, this project develops an interdependent system data set and its associated models on top of a strong theoretical foundation in systems engineering. As a result, it can be used for practical applications in the energy systems field to address not just mitigation of climate change but adaptation and resilience as well. This is made possible by using asset-level, openly-available datasets to infer the AMES' reference architecture to organize and define the interconnections between the four subsystems. The reference architecture uses the Systems Markup Language (SysML) to model the four interdependent energy systems and the flows of mass and energy within and between them. This reference architecture provides a more detailed and self-consistent MBSE foundation for energy models moving forward relative to the “reference energy systems" that have been used in some national energy system optimization models. The datasets used to infer the reference architecture are also used to instantiate the AMES into an instantiated architecture.

Our recent paper [4] uses a data-driven, MBSE-guided approach to develop open-source structural models of the American Multi-Modal Energy System. More specifically, the AMES reference architecture is applied to an asset-level GIS dataset called Platts Map Data Pro to create models of several regions. The instantiated structural models include, for the first time, the electric grid, the natural gas system, the oil system, the coal system, and the interconnections between them as defined by the AMES reference architecture, for the full contiguous United States of America. Initial results are organized into two categories; a formal and hetero-functional graph for each of the regions being studied: New York, California, Texas, and the full contiguous USA. The states were chosen for their size and the diversity of their energy policies. Consequently, the chosen regions have also taken distinct directions to advance the sustainable energy transition. In 2019, California had the most renewable energy generation out of all the states. In the meantime, New York state efforts to expand renewable energy capacity are balanced by its reliance on natural gas and oil to meet space heating energy demands. Alternatively, Texas, while being the nation’s leading crude oil and natural gas producing state, is also the nation’s leading producer of wind-powered electric generation. By using MBSE and HFGT, new open-source data models are presented for these three states and the full USA to aid in advancing and guiding the sustainable energy transition and energy policies [4].


  1. 1.    D. Thompson and A. M. Farid, “A Reference Architecture for the American Multi-Modal Energy System,” 2021. 
  2. D. Thompson, W. C. Schoonenberg, I. Khayal, and A. M. Farid, “The Hetero-functional Graph Theory Toolbox,” 2020.
  3. D. Thompson, W. C. Schoonenberg, and A. M. Farid, “A Hetero-functional Graph Resilience Analysis of the Future American Electric Power System,” IEEE Access, vol. 9, pp. 68837–68848, 2021.
  4. D. Thompson and A. M. Farid, “A Hetero-functional Graph Structural Analysis of the American Multi-modal Energy System,” 2022.


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Dakota J. Thompson graduated from Colby College in 2018 with a B.A.  in Physics and minor in Computer Science. He is now a Ph.D. candidate studying energy systems engineering at the Thayer School of Engineering at Dartmouth. As an undergraduate, Dakota worked on several research projects with the LIINES at the Thayer School of Engineering at Dartmouth and continues his research in power grid resilience, renewable energy integration, and hetero-functional graph theory.
20160404 Amro Farid 2 RG30 Edit CROP
Amro M. Farid is currently a Visiting Associate Professor of Mechanical Engineering at MIT and an Associate Professor of Engineering at the Thayer School of Engineering at Dartmouth. He leads the Laboratory for Intelligent Integrated Networks of Engineering Systems (LIINES) and has authored over 150 peer reviewed publications in Smart Power Grids, Energy-Water Nexus, Electrified Transportation, Industrial Energy Management, and Interdependent Smart City Infrastructures. He received his Sc. B. in 2000 and his Sc. M. 2002 from the MIT Mechanical Engineering Department. He went on to complete his Ph.D. degree at the Institute for Manufacturing within the University of Cambridge (UK) Engineering Department in 2007. He has varied industrial experiences from the electric power, automotive, semiconductor, defense, chemical, and manufacturing sectors. As an Environment and Greenhouse Gases Specialist, he designed and implemented Air Liquide's Worldwide Environmental Management System and was the lead technical advocate for Air Liquide's position on the EU Emissions Trading Scheme. In 2010, he began his academic career as a visiting scholar at the MIT Technology Development Program and the Masdar Institute of Science and Technology (UAE). In 2014, he founded Engineering Systems Analytics LLC as a startup engineering software and consulting company to provide techno-economic insight to energy and infrastructure operators. In 2021, he became a Fulbright Future Scholar to investigate the energy-water-hydrogen nexus in Australia. As an academic, he has made active contributions to the MIT-Masdar Institute Collaborative Initiative, the MIT Future of the Electricity Grid Study, the IEEE Vision for Smart Grid Controls, and the Council of Engineering Systems Universities. He currently serves as Chair of IEEE Smart Cities R&D Technical Activities Committee, and Co-Chair of the IEEE Systems, Man & Cybernetics (SMC) Technical Committee on Intelligent Industrial Systems. He is a senior member of the IEEE and a member of the ASME and INCOSE.

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