Hetero-functional network minimum cost flow optimization: A hydrogen–natural gas network example

Sustainable energy grids and networks are converging. In recent decades, cost, sustainability, and digitization drivers have caused engineering systems to evolve into systems-of-systems that deliver multiple services across multiple application domains. These engineering systems include electrified-transportation systems, the energy–water nexus, and multi-modal energy systems. The rather complex and heterogeneous interdependencies between engineering system services necessitates a precise informatic representation that ultimately supports optimized management of the holistic dynamics and tradeoffs. Consequently, ontologically-robust, quantitative modeling tools are needed to represent the heterogeneity of the modeled system-of-systems while still remaining generic and extensible to a diversity of application domains. Hetero-functional graph theory has demonstrated itself as a such modeling tool. This work now builds upon this foundation to develop a dynamic hetero-functional network minimum cost flow optimization that meets the requirements of these emerging systems-of-systems. It optimizes the supply, demand, transportation, storage, transformation, assembly, and disassembly of multiple operands in distinct locations over time in a systems-of-systems of arbitrary number, function, and topology. First, the paper introduces a general approach to define a dynamic system-of-system model that integrates customizable dynamic device models into a hetero-functional graph theory structural model. To this end, the work leverages Petri net dynamics and the hetero-functional incidence tensor. The Petri net based models are then translated into a quadratic program in canonical form. The hetero-functional network minimum cost flow optimization is demonstrated on a hydrogen–natural gas infrastructure test case. Four distinct scenarios are studied to demonstrate potential synergies and cascading network effects of policy across multiple infrastructures.