MILP and MINLP models for the optimal scheduling of multi-energy systems accounting for delivery temperature of units, topology and non-isothermal mixing

Multi-Energy Systems (MES) represent an increasingly important element in the undergoing energy transition, as they can effectively supply different energy vectors to their users through the coordinated local management of a set of different energy sources. This work presents an innovative Mixed Integer Linear Programming (MILP) formulation for the operational planning of MES featuring thermal generators arranged in series and/or parallel with different and/or variable heat delivery temperatures and filled-tank thermal energy storages. The proposed model can approximate the non-isothermal mixing processes occurring in water collectors and storage systems through the definition of a set of virtual headers at constant temperature levels. To assess the accuracy of the MILP model (called water-flow MILP), a detailed MINLP model of the MES is formulated (water-flow MINLP). The two models are compared with the energy-flow MILP model adopted in the literature (neglecting details of the internal MES arrangement and supply temperatures), considering a set of real-world case studies consisting in different possible MES designs designed to serve the District Heating Network of our university. Results indicate how literature energy-flow models tend to underestimate operating costs by as much as 16% and define an operational solution not able to reach the target heat delivery temperature. The proposed linearized water-flow MILP model allows to identify scheduling solutions which are not only feasible but also equal or better than the solutions found by solving the MINLP model. For MES with multiple dispatchable units (e.g., CHP engine, heat pumps and boilers), the MINLP model cannot be solved to global optimality within 1 h while the MILP water flow model can find feasible solutions with 6% lower cost.