## 3 Case Study
These sizes have been chosen consistently with the peak demand expected for each units (Table 1) taking into account that up to six elements of the same kind can be adopted in parallel. The technical characteristics of all pieces of equipment are described in File S1, jointly with their investment costs. The latter have been obtained by a market survey and also include transportation, installation, connection, engineering costs, etc. The amortization factors which multiply the investment costs are a function of the interest rate and of the life span of each component. The interest rate is assumed equal to 6% and is a sum of the real economic interest rate (4%) and a risk rate, assumed in this case equal to 2%. The life span of DHCN has been fixed equal to 30 years, for PV and ST panels and TS equal to 20 years, for ICE, MGT, ABS and HP equal to 15 years, and for BOI and CC equal to 10 years. Maintenance costs are reported in File S1 and they are proportional to the energy produced by each component. Operation costs are related to the costs of fuels and electricity. The Italian gas and electricity market has been liberalized since 2007, after a process which began in the 1999 with the \"Bersani Decree\" [35] and lasted eight years. Since 2007 all consumers can freely choose a supplier and leave the regulated-rate system or can remain connected to the old regulated market. Herein, the regulated-rate system has been considered as reference for the electricity and gas prices. The natural gas cost has been considered constant all year long, as well as the price of the bought electricity, while the price of the sold electricity has been assumed variable in each time interval, based on the hourly market prices. In particular, the bought electricity price has been considered equal to 0.17 \(\upepsilon\)/kWh, while electricity sold price variable between 0.05-0.12 \(\upepsilon\)/kWh, and natural gas price equal to 0.06 \(\upepsilon\)/kWh. The prices considered include the pure cost of energy (about 40%) and taxes (about 60%). The CO\({}_{2}\) emissions related to the consumption of electricity and natural gas have been assumed from literature [33]. The natural gas CO\({}_{2}\) emissions depend on the chemical composition of the gas and then on its provenience. However, the slight difference can be ignored considering the same value for the natural gas CO\({}_{2}\) emissions. The same approximation cannot be made for electricity. In fact, electricity carbon intensity depends heavily on the national electricity system. The reference case study has been optimized assuming the average electricity carbon intensity of the European Union in 2007-2009 (0.356 kgCO\({}_{2}\)/kWh), while a second set of optimizations has been performed assuming the average electricity carbon intensity of the OECD Americas (Canada, United States, Mexico, Chile) in 2007-2009 (0.485 kgCO\({}_{2}\)/kWh). The natural gas carbon intensive has been assumed equal to 0.202 kgCO\({}_{2}\)/kWh. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Equipment** & **Unit 1** & **Unit 2** & **Unit 3** & **Unit 4** & **Unit 5** & **Unit 6** & **Unit 7** & **Unit 8** & **Unit 9** \\ \hline MGT & 65 & 100 & 30 & 30 & 30 & 30 & 200 & 65 & 100 \\ ICE & 70 & 140 & 50 & 50 & 50 & 50 & 200 & 70 & 140 \\ ABS & 70 & 105 & 35 & 35 & 35 & 35 & 105 & 70 & 105 \\ HP & 70 & 105 & 35 & 35 & 35 & 35 & 105 & 70 & 105 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Component sizes (kW). To take into account the incentives that many European countries have adopted to promote the development of new energy technologies, two different incentives have been considered for the reference case study:  
* natural gas detaxation for cogeneration use; and
* renewable energy production incentives. Cogeneration systems complying with restrictions defined by the DIgs 20/07 [36] are classified in Italy as \"high efficiency cogeneration systems\" and can operate with natural gas detaxation.