Modelling of Non-linear CHP Efficiency Curves in Distributed Energy Systems

Distributed energy resources gain an increased importance in commercial and industrial building design. Combined heat and power (CHP) units are considered as one of the key technologies for cost and emission reduction in buildings. In order to make optimal decisions on investment and operation for these technologies, detailed system models are needed. These models are often formulated as linear programming problems to keep computational costs and complexity in a reasonable range. However, CHP systems involve variations of the efficiency for large nameplate capacity ranges and in case of part load operation, which can be even of non-linear nature. Since considering these characteristics would turn the models into non-linear problems, in most cases only constant efficiencies are assumed. This paper proposes possible solutions to address this issue. For a mixed integer linear programming problem two approaches are formulated using binary and Special-Ordered-Set (SOS) variables. Both suggestions have been implemented into the optimization model DER-CAM to simulate investment decisions of CHP micro-turbines and CHP fuel cells with variable efficiencies. The approaches have further been applied successfully in a case study with four different commercial buildings. Comparison of the results between the standard version and the new approaches indicate that total annual system costs remain almost unchanged. System performance is subject to change and storage technologies become more important. Part load operation has mainly been found important for fuel cell units. The micro-turbine is found almost exclusively in full load, thus rendering the application of the new approaches for this technology unnecessary for the considered unit sizes and building types. The approach using binary variables was the most promising method to model variable efficiencies in terms of computational costs and results. It should especially be considered for specific fuel cell technologies. Further investigation on the impacts of this approach on the prediction of fuel cell and micro-turbine performance is suggested.