A systematic approach for the selection of the typical and extreme days for the optimal design of multi energy systems

A critical result of the analysis of multi energy systems (MES) is that, when optimizing their design, the operation strategy and the part load behaviour of the units must be considered in the optimization model. This way, the model is to be formulated as a two stage problem, where the design and the operation variables are optimized, respectively, in the first and in the second stage. In order to guarantee the computational tractability, the scheduling/operation problem is solved for a limited set of typical and extreme periods. The selection of these periods is an important aspect of the design methodology, as the selection and sizing of the generation units and storages is carried out on the basis of their optimal operation in the selected periods. This work proposes a novel Mixed Integer Linear Program (MILP) clustering model, devised to find at the same time the most representative days of the year and the extreme days. The clustering MILP model allows controlling the features of the selected typical and extreme days and setting a maximum deviation tolerance between the integral of the load duration curves of the typical days and the historical data. The novel approach is tested on the design of a district energy system for the University of Parma Campus in Northern Italy and compared with the two well-known clustering techniques “k-means” and “k-medoids” (typically used to select the typical days), using two approaches to select the extreme days.