## 2 Case Study and System Model
### Thermal and Electrical Energy Demands during the Cruise  
On the basis of the documentation made available by the manufacturer [53], the electrical and thermal demand curves have been identified for the two type of cruises (summer and winter).  
The electrical demand (Pelect) is the sum of the following contributions:  
* PPOD--power for the pod propulsion system and for the maneuvering propellers;
* P technical--absorbed power for non-propulsive technical uses;
* P pumps--galley--lights, power absorbed for the hotel functions and for the relative systems, excluding that for air conditioning (HVAC);
* P HVAC, absorbed power for air conditioning (during the summer cruise only);  
The P HVAC is the required cooling capacity to be satisfied by absorption and compression refrigeration machines. The demand curves are shown in the diagrams of Figures 1 and 2 respectively for winter and summer cruise.  
Currently, on cruise ships most of the thermal users are satisfied first of all by the thermal carrier consisting of saturated steam at 10 bar and 180 \({}^{\circ}\)C, produced by thermal recovery on the exhaust gases of the engines and by integration boilers powered by liquid fuel. In addition, the heat recovered from the Hight Temperature (HT) cooling circuit of the ICEs (approx. 90 \({}^{\circ}\)C) can be partially used, while the heat of the Low Temperature (LT) cooling circuit (approx. 50 \({}^{\circ}\)C) remains unused and has to be dissipated. To achieve an optimal exploitation of the heat recovered from the engines, the production of mechanical energy by means of bottom cycles, fed by the highest temperature heat source, must be  
Figure 1: Electrical demand during the winter cruise.  
considered as a priority. It is, therefore, recommended to use as much high temperature heat as possible for the mechanical energy production, feeding the different thermal users at a temperature level close (slightly higher) to the temperature of the user itself.  
The following users are mandatory satisfied by the steam vector (\"steam user loads\" in Figures 3 and 4):  
* Thermal request for air conditioning heating;
* Thermal request for galley users, excluding the galley hot water use;
* Laundry steam. The other on-board thermal users have been grouped into the following terms (Figures 3 and 4):
* Hotel only--hot water, for sanitary use, at about 60 \({}^{\circ}\)C;
* Hotel not hot water, at about 90 \({}^{\circ}\)C (swimming pool heaters and laundry);
* ER users (thermal consumption in the engine rooms) at about 90 \({}^{\circ}\)C;
* Tank heating (thermal treatment of fuel, sludge, etc.) at about 50 \({}^{\circ}\)C;
* Evaporat. \"A\" + \"B\" (thermal consumption of the evaporation desalinators for producing pure water to be used in engines type \"A\" and \"B\").  
In the optimization procedure, the input data of the electrical and thermal hourly requests will be organized in the following matrices (day of the cruise--time of day):  
* Electric power, RICEL,
* Heat as saturated steam at 10 bar and 180 \({}^{\circ}\)C, RICTER_St,
* Hot water at 60-90 \({}^{\circ}\)C, RICTER_HTW,
* Chilled water at 8 \({}^{\circ}\)C, RICOOL.  
The last three matrices correspond to the thermal energy carriers STEAM, H\({}_{2}\)O HT and H\({}_{2}\)O LT in Figure 5. The thermal demands classified as low temperature (40-45 \({}^{\circ}\)C) are considered to be certainly satisfied by the low temperature hot water produced by the ICE, without the need for integrations.  
Figure 2: Electrical demand during the summer cruise.  
Figure 4: Thermal demand during the summer cruise.  
Figure 3: Thermal demand during the winter cruise.