## 2 Case Study and System Model
### Model Super-Structure  
To allow optimal exploitation of fuel energy, various components dedicated to energy recovery from the main engines can be considered, such as ORC and Stirling bottom units, thermal storage systems, absorption refrigeration chillers, etc.  
Once the super-structure of the energy system has been defined including all possible components, the optimization process will have to identify which components will be actually installed and the time scheduling of the load of each of them.  
Figure 5: Super-structure of the on board energy system.  
The whole super-structure is schematized in Figure 5, where each component is represented as a box, connected to the other components of the system and to the end users by means of the flows that will appear in the MILP model.  
The seven energy vectors connecting the system with the users, highlighted in Figure 5, are the following:  
* Exhaust gases (EG), which directly feed the Stirling engine and the recovery boilers (EGRS), without any connection with other on-board users.
* Electric power (EE) for propulsion, hotel services and all auxiliaries of the on-board energy system; it must meet the electrical energy demand (EEd).
* Steam (STEAM); it must meet the steam demand (Sd).
* Hot water at 85-90 \({}^{\circ}\)C (H\({}_{2}\)O HT); it must meet the hot water demand (HTWd).
* Hot water at about 50 \({}^{\circ}\)C (H\({}_{2}\)O LT); it must meet the low temperature water demand (LTWd), or must be dissipated.
* Chilled water at 8-10 \({}^{\circ}\)C (CHILLED WATER); it must meet the for chilled water demand (CWd).
* Fresh water; it must meet the demand for fresh water (FWd); the latter is considered constant for simplicity, regardless of the ship's operating conditions, and its effect on the whole energy consumption of the ship is limited to the electric energy demand of the reverse osmosis desalinator.  
The components possibly adopted inside the on board energy system, shown in Figure 5, are the following:  
* DD. GG. Main diesel engines. This block is modeled considering the actual individual ICE, allowing the definition of the optimal management of the engines within the solution of the overall system optimization problem. In the case study the block is made up of 5 ICE--2 units of 14,400 kWmecc/600 rpm each (12V) and 3 units of 9600 kWmecc/600 rpm (8L) [53]. This block contains also the required auxiliaries for the engine operation, such as the exhaust gas recovery system (EGRS) and the exhaust gas treatment unit (exhaust gas treatment--EGT).
* Stirl. Stirling units directly powered by the exhaust gases engine [54].
* SB. Steam Boiler. It integrates the heat recovery from the ICE if necessary.
* SS. Steam storage.
* HTW. Boilers, identified accordingly to 3 different types of feeding energy considered--liquid fuel (B), steam taken from the on-board steam carrier (S) and thermal solar panels (ST). The HTW S boilers also possibly has a thermal storage function, at a temperature of 90 \({}^{\circ}\)C.
* ORC. Organic Rankine cycle units for the electrical conversion of the heat recovered by the engines.
* TD. Thermal dissipater. It has to dissipate the excess thermal power in the H\({}_{2}\)O LT line into the seawater.
* AC. Absorption chillers. They can be powered by H\({}_{2}\)O HT line and, indirectly, also by way of the steam line.
* CC. Compression chillers traditionally present on board the ship, whose size is determined in relation with the introduction of the absorption chillers.
* CWS. Chilled water storage.
* ODFW. Reverse osmosis desalinator.
* FWS. Fresh water storage.
* PV. Photovoltaic solar panels, the overall surface of which is optimized.