## 2 Case Study and System Model
### Linearized Model of the Components
A constant efficiency of 70% for HTW B and 90% for HTW S will be used in the model, accordingly to the indications by the shipbuilder [53], while for the thermal solar panels, the data of a typical vacuum tube collector, like Sunwood SW15 by Sunwood energy solutions (viale del lavoro 18, 37067 Villafranca di Verona, VR, Italy) have been used, for which the optical efficiency and the heat transmission coefficients a1 and a2 are known (Table 1). * The HTW S has also a thermal storage function, for users at temperature lower than 90 \({}^{\circ}\)C. In addition, for this component, heat loss has been neglected as an acceptable approximation. * TD. Thermal dissipater. It has to dissipate the excess thermal power in the H\({}_{2}\)O LT line into the seawater. The auxiliary consumptions of the TD are accounted for in the non-propulsive electrical loads, according to the operating data collected for the reference ship. Therefore, the model of this component is not explicitly considered in the balance of energy flows. * AC. Absorption chiller. They can be powered by the H\({}_{2}\)O HT network and, indirectly, by the steam network, too. The linearized model of the absorption chiller calculates the thermal consumption and the cooling power produced at different loads, following the performance of a typical water-lithium bromide absorption machine, presented by [PERSON] and [PERSON], in [57]. Their simulations show that the COP remains approximatively constant, if the activation temperature is in the range 85-95 \({}^{\circ}\)C. Considering to fed the machine with the hot water carrier at 85-90 \({}^{\circ}\)C (H\({}_{2}\)O HT) a constant prudential value of the COP = 0.6 has been assumed. * CC. Compression chillers. They are traditionally present on board the ship, whose size will be reduced in relation to the introduction of the absorption chillers. Referring to the data available from the manufacturers [58], a COP = 5.0 has been adopted. * CWS. Chilled water storage. Considering that all the on board storages are characterized by a short operating cycle (a few hours) the losses due to heat dispersion will be considered null, simply taking into account the maximum accumulated volume. * ODFW. Reverse osmosis desalinator. The linearized model of the electrical consumption and of the fresh water flow produced refers to the components currently installed on board the ship, whose productivity and electrical consumption are known [53]. * FWS. Fresh water storage. Given that the accumulation of fresh water is currently present on board, its auxiliary consumption is accounted for in the non-propulsive electrical loads. Therefore, the model of this component will not be explicitly considered in the super-structure. The cooling flows produced by the absorption and compression chillers are expressed by the following variables:  
* _Cool_abs (g,i)_, cooling power produced by the absorption chillers [kW];
* _Cool_com (g,i)_, cooling power produced by the compression chillers [kW]. Relations 17-20, similar to Equations (13)-(16), relate the cooling powers produced by the chillers to the energy vectors consumed, i.e., the thermal power _HTh_abs (g,i)_, derived from the HTW line, and the electric power _Pel_com (g,i)_, respectively. Figure 7:8  
Figure 7:9  
\[y1\ (g\),\(i\),\(j)\times MCRinf\leq MCR1\ (g\),\(i\),\(j)\leq y1\ (g\),\(i\),\(j)\times MCRm \tag{1}\]0  
\[y1\ (g\),\(i\),\(j)\times MCRinf\leq MCR1\ (g\),\(i\),\(j)\leq y1\ (g\),\(i\),\(j)\times MCRm \tag{1}\]1  
\[y1\ (g\),\(i\),\(j)\times MCRinf\leq MCR1\ (g\),\(i\),\(j)\leq y1\ (g\),\(i\),\(j)\times MCRm \tag{1}\]2  
\[y1\ (g\),\(i\),\(j)\times MCRinf\leq MCR1\ (g\),\(i\),\(j)\leq y1\ (g\),\(i\),\(j)\times MCRm \tag{1}\]3 \begin{table}
\begin{tabular}{c c c} \hline \hline
**Optical Efficiency** & **[\%]** & **67.9** \\ \hline Characteristic Parameter a\({}_{1}\) & [W/m\({}^{2}\) K] & 1.696 \\ Characteristic Parameter a\({}_{2}\) & [W/m\({}^{2}\) K\({}^{2}\)] & 0.0099 \\ \hline \hline \end{tabular}
\end{table}