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, a standardized matrix modeling approach is proposed to automatically model MES with variable energy efficiencies based on the energy hub (EH) modeling framework. Piecewise linearization is used to approximate the variable energy efficiencies; as a result, a component with variable efficiency is equivalent to several parallel components with constant efficiencies. Splitters and concentrators are proposed as standardized components to facilitate the split and merge of energy flows imposed by piecewise linearization. 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 executed in MATLAB and presented to show how the nonlinear approximation accuracy and calculation efficiency can be balanced using the proposed model in the optimal operation of EH. For the optimal operation of a five-component EH with energy storage, the proposed approach reduces the approximation error from 13.7% to 0.1% with only 0.2 s computation time increase compared to the exiting constant efficiency model.