Matrix Modeling of Energy Hub with Variable Energy Efficiencies

The modeling of multi-energy systems (MES) is the basic task of analyzing energy systems integration. The variable energy efficiencies of the energy conversion and storage components in MES introduce nonlinearity to the model and thus complicate the analysis and optimization of MES. In this paper, we propose a standardized matrix modeling approach to automatically model MES with variable energy efficiencies based on the energy hub (EH) modeling framework. We use piecewise linearization to approximate the variable energy efficiencies; as a result, a component with variable efficiency is equivalent to several parallel components with constant efficiencies. The nonlinear energy conversion and storage relationship in EH can thus be further modeled under a linear modeling framework using matrices. Such matrix modeling approach makes the modeling of an arbitrary EH with nonlinear energy components highly automated by computers. The proposed modeling approach can further facilitate the operation and planning optimization of EH with variable efficiencies. Case studies are presented to show how the nonlinear approximation accuracy and calculation efficiency can be balanced using the proposed model in the optimal operation of EH.