Sustainability analysis of complex dynamic systems using embodied energy flows: The eco-bond graphs modeling and simulation framework

This article presents a general methodology for modeling complex dynamic systems focusing on sustainability properties that emerge from tracking energy flows. We adopt the embodied energy (emergy) concept that traces all energy transformations required for running a process. Thus, energy at any process within a system is studied in terms of all the energy previously invested to support it (up to the primary sources) and therefore sustainability can be analyzed structurally. These ideas were implemented in the bond graph framework, a modeling paradigm where physical variables are explicitly checked for adherence to energy conservation principles. The results are a novel Ecological Bond Graphs (EcoBG) modeling paradigm and the new EcoBondLib library, a set of practical ready-to-use graphical models based on EcoBG principles and developed under the Modelica model encoding standard. EcoBG represents general systems in a three-faceted fashion, describing dynamics at their mass, energy, and emergy facets. EcoBG offers a scalable graphical formalism for the description of emergy dynamic equations, resolving some mathematical difficulties inherited from the original formulation of the equations. The core elements of EcoBG offer a soundly organized mathematical skeleton upon which new custom variables and indexes can be built to extend the modeling power. This can be done safely, without compromising the correctness of the core energy balance calculations. As an example we show how to implement a custom sustainability index at local submodels, for detecting unsustainable phases that are not automatically discovered when using the emergy technique alone. The fact that we implemented EcoBondLib relying on the Modelica technology opens up powerful possibilities for studying sustainability of systems with interactions between natural and industrial processes. Modelica counts on a vast and reusable knowledge base of industrial-strength models and tools in engineering applications, developed by the Modelica community throughout decades.