## Methodology
### Subsystem Models  
In this subsection, models and features adopted for the components of the simulated energy system are described. The cogeneration unit is a spark ignition reciprocating internal combustion engine fueled by natural gas. Part-load efficiencies have been considered [22] and shown in Figure 2, where the load factor is defined as \(L_{ICE}=E_{ICE}/E_{ICE,nom}\). The heat recovery system recovers heat from the exhaust gas, jacket cooling water system and lube oil of the ICE in the form of hot water at around 90 \({}^{\circ}\)C. The power capacity lower bound has been set to 50% of the nominal power capacity. The reversible heat pump and the non-reversible electric chiller are air-to-water units. The single-effect absorption chiller, fed by the hot water recovered from the ICE, has a cooling tower as heat sink. The heat pump and the chillers have been modelled considering both ambient temperature and part-load condition effects on the coefficient of performance. The so-called \"locally constant exergy efficiency\" (or Carnot efficiency) approach allows to consider how the temperature of the thermal sources affects the performance of the heat pump/chiller. Moreover, part-load behavior can be considered by a correction factor. The coefficient of performance (COP) of the units is expressed as the product of the ideal COP (i.e., the COP of the Reversed Carnot Cycle), the exergy efficiency (defined as the ratio between the actual COP of the unit and the ideal COP at those thermal source temperatures), and a part-load correction factor [18]:  
\[COP=COP_{id}\cdot\eta_{ex}\cdot CF \tag{1}\]  
The ideal COP of the electrically driven heat pumps under the heating and cooling modes are, respectively:  
\[COP_{RHP-H,id}=\ (T_{hot}+273.15)/(T_{hot}-T_{cold}) \tag{2}\]  
\[COP_{RHP-C,id/EC,id}=\ (T_{cold}+273.15)/(T_{hot}-T_{cold}) \tag{3}\]  
The ideal COP of the absorption chiller is:  
\[COP_{AC,id}=\ 1-\frac{(T_{hot}+273.15)}{\left(T_{gen}+273.15\right)}\left/1- \frac{(T_{cold}+273.15)}{(T_{hot}+273.15)}\right. \tag{4}\]  
Moreover, the effect of the ambient temperature on the capacity of the heat pump must be considered, by means of temperature coefficients (\(\kappa\)):  
\[Q_{RHP-H}=Q_{nom,RHP-H}[1+\kappa_{RHP-H}[T_{amb}-T_{nom,RHP-H}]] \tag{5}\]  
\[C_{RHP-C/EC}=C_{nom,RHP-C/EC}[1+\kappa_{RHP-C/EC}[T_{nom,RHP-C/EC}-T_{amb}]] \tag{6}\]  
Figure 2: Part-load efficiencies of the ICE. where \(T_{nom,RHP-H}=7\)\({}^{\circ}\)C, \(T_{nom,RHP-C/EC}=35\)\({}^{\circ}\)C, \(\kappa_{RHP-H}=0.04\) kW/\({}^{\circ}\)C and \(\kappa_{RHP-C/EC}=0.015\) kW/\({}^{\circ}\)C based on a survey on technical specification sheets by [23]. Based on technical specification sheets [24; 25; 26; 27], the following values for the exergy efficiencies have been adopted: \(\eta_{ex,RHP-H}=35\%\), \(\eta_{ex,RHP-C/EC}=29\%\), \(\eta_{EX,AC}=34\%\). The part-load correction factors [28] are shown in Figure 3.  
As mentioned, a cooling tower is included in the system to dissipate the heat from the condenser/absorber of the absorption chiller. The inlet temperature of the condenser water (outlet temperature of the cooling tower) changes as the outdoor weather conditions vary (i.e., as the ambient wet bulb temperature varies). The so called \"fixed approach control\" method has been considered as the control method of the cooling tower. Such a method consists in varying the cooling tower air flow rate to maintain a constant temperature difference between the cooling tower outlet water temperature and the ambient air wet bulb temperature [18]. This temperature difference is commonly known as \"approach\". Therefore, the inlet temperature of the cooling water circuit of the absorption chiller can be evaluated as the sum of the ambient air wet bulb temperature and the approach temperature, set at 6 \({}^{\circ}\)C. The electric power consumption due to cooling tower fans is evaluated as 0.026 kW per kW of heat rejection capacity [29].