## 5 Conclusions and Future Work
**Abbreviations**  
MES & Multi-Energy System  
LPG & Liquid Propane Gas  
DHW & Domestic Hot Water  
TPES & Total Primary Energy Supply  
TFC & Total Final (energy) Consumption  
NPC & Net Present Cost  
LCOE & Levelized Cost of Energy  
LP & Linear Programming  
MILP & Mixed-Integer Linear Programming  
BESS & Battery Energy Storage System  
**Nomenclature**  
\(T_{gw}\) & Groundwater temperature & K  
\(n_{day}\) & Progressive number of the considered day of the year  
\(T_{amb}\) & Yearly average ambient temperature  
\(n_{day}^{min}\) & Progressive number of the day with the lowest temperature of the year  
\(P_{task}\) & Power required to heat the water for the operation of the task  
\(m_{iv}\) & Water mass flow required by the task  
\(\varphi_{w}\) & Water isobaric specific heat  
\(E_{Th,\ class\ demand}(k,t)\) & Thermal energy demand  
\(E_{bolar}(k,t)\) & Energy supplied by the boiler  
\(E_{Tank_{out}}(k,t)\) & Energy exiting the hot-water tank  
\(E_{Curt}(k,t)\) & Fraction of the excess energy produced by solar collectors that cannot be stored in the tank  
\(E_{lost\ load\_th}(k,t)\) & Allowed fraction of unmet thermal load  
\(E_{El,demand}(t)\) & Electricity demand of the study area  
\(E_{PV}(t)\) & Energy produced by the PV panels  
\(E_{Gen}(t)\) & Energy produced by the generator  
\(E_{bat,th}(t)\) & Flow of energy into the battery  
\(E_{bat,dis}(t)\) & Flow of energy out of the battery  
\(E_{Curt}(t)\) & Electric energy that is curtailed  
\(E_{Res,class}(k,t)\) & Energy supplied to the thermal storage through electric resistance  
\(E_{Res,lat}(t)\) & Cumulative energy absorbed by the electric resistance heating elements of  
\(n\) thermal classes  
\(E_{lost\ load}(t)\) & Allowed fraction of unmet electric load  
\(E_{SC_{in}}(k,t)\) & Total thermal energy provided by the solar collectors  
\(E_{SC}(k,t)\) & Energy generated by a single solar collector  
\(N_{SC}(k)\) & Number of solar collectors in the class  
\(E_{SOC_{Tank}}(k,t)\) & Thermal energy stored in the tank at the time step \(t\)  
\(E_{SOC_{Tank}}(k,t-1)\) & Thermal energy stored in the tank at the timestep \(t\)-1  
\(\eta_{tank}\) & Coefficient accounting for energy losses due to the heat transfer between  
\(\eta_{tank}\) & thermal storage and environment  
\(\eta_{Res}\) & Thermal efficiency of the electric resistances  
\(-\)  
\(D_{SOC}\) & Depth of discharge\(P_{out,max}(k)\) & Tank maximum power of discharge & W \(LPG_{cons}\) & LPG consumption & 1 \(T_{bailer}\) & Boiler efficiency & - \(LHV_{LPG}\) & Lower heating value of the LPG & kJ/kg \(Inv\) & Total investment cost & $ \(YCC\) & Yearly constant cost of the project & $ \(e\) & Discount rate & - \(r\) & Interest rate & - \(Cost_{RP}\) & Cost of components replacement & $ \(N_{PV}\) & Number of installed PV panels & - \(C_{PV}\) & Capacity of a PV unit & kW \(U_{PV}\) & Specific cost of PV unit & $/kW \(C_{bat}\) & Capacity of installed battery bank & kWh \(U_{bat}\) & Specific cost of battery bank & $/kWh \(C_{gen}\) & Capacity of installed generator & kW \(U_{gen}\) & Specific cost of generator & $/kW \(N_{SC}(k)\) & Number of solar collectors installed & - \(C_{SC}\) & Capacity of a solar collector & kW \(U_{SC}\) & Specific cost of solar collector & $/kW \(C_{SOC,tank}(k)\) & Capacity of the installed hot-water tank & kWh \(U_{Tank}\) & Specific cost of the hot-water tank & $/kWh \(C_{Bolac}(k)\) & Capacity of the installed boiler & kW \(U_{Bolac}\) & Specific cost of the boiler & $/kW \(C_{Res}(k)\) & Capacity of the installed electric resistance & kW \(U_{Res}\) & Specific cost of the electric resistance & $/kW \(fun\) & Percentage of the investment financed by a bank & - \(Cost_{QkM}\) & Cost of operation and maintenance of the system & $ \(Cost_{finam}\) & Fixed-rate loan payment & $ \(Cost_{Diesel}(t)\) & Cost of the used diesel & $ \(Cost_{\text{gas}}(t)\) & Cost of the used LPG & $ \(LL_{\text{cost}}(t)\) & Cost of the actually unmet load & $ \(E_{dmanuel}\) & Total energy demand (electric and thermal) of the system & kWh \(E_{dmanuel,net}\) & Net (i.e., after subtracting the lost load) total energy demand & kWh \(E_{supply}\) & Total energy supplied by each _j-th_ energy supply technology & kWh \(\eta_{overall}\) & Overall system efficiency & -