Variables and parameters Sample Clauses

Variables and parameters. The main optimization variables are: ▪ The installation of equipment ( ∈ {0,1}); ▪ The capacity of equipment ( ∈ ℝ≥0); ▪ Energy flows ( ∈ ℝ≥0); ▪ Storage energy contents ( ∈ ℝ≥0); ▪ Online status of energy conversion units ( ∈ {0,1}). The above mentioned variables are used in the following equations. Furthermore, the index () indicates the particular technology, the index () identifies the input or output in multiple input- output units,the index () is the discrete time step, and the index () the energy form. For energy system components, the following groups are proposed: ▪ Conversion units (CU); ▪ Energy storages (ST); ▪ Renewables (RE); ▪ Inlet and outlet grid connections (GCin and GCout), respectively; ▪ Energy demands (Dem); ▪ Couplings of similar energy forms (Cplg), e.g., the flow of high to medium temperature heat; ▪ Waste of energy (Waste), i.e., energy that is not used for satisfying any demands. Each conversion unit (CU) is described by its first output (e.g., the electric power output for combined heat and power plants). Hence, also the capacity determines the maximum allowed first output. Climatic conditions can be described by the ambient dry-bulb temperature (amb), ambient pressure (amb), relative humidity (amb), global horizontal irradiance (), and wind speed (w). Table 2.1: Energy conversion units and storages model parameters [2]. Parameter Variable Units Function of Energy conversion units and storages Minimum and maximum capacity min, max [kW] [m3/h] - [kWh] [m3] Fixed and variable invest (including transportation and installation) [$] [$/kWh] [$] [$/m3] [$] [$/kWh] [$] [$/m3] Fixed and variable operation and maintenance costs [$/a] [$/kW/a] [$/a] [$/(m3/h)/a] - [$/a] [$/kWh/a] [$/a] [$/m3/a] Asset depreciation range (economical life time) [a] - Negative and positive ramping constraint −, + [%/h] - Energy conversion units Start-up costs [$/kW] [$/(m3/h)] - Minimum and maximum part-load ratio min, max [-] amb, amb, amb, Efficiencies (electrical, thermal, …) [-] amb, amb, amb, , Energy storages Charge and discharge efficiency ch, dch [-] - Self-discharge rate [%/h] - Energy conversion and storage technologies were modeled by the parameters summarized in Table 2.1. The functional relationships of the parameters are also shown in this table.