*2.2. CHP Plant Control Logic*

The control logic of the CHP plant was defined based on the result of an optimal load allocation procedure, which led to defining the optimal ICE single unit load for each value of the heat demand. The optimal load allocation problem was formulated as follows (Equation (1)): CHP prime movers were managed in order to cover the DH demand ( . *Qth*,*DH*) while keeping equal to zero the heat dissipation to stack ( . *Qth*,*Diss*), with the following constraints: (i) the ICE regulation ranges in between 40% to 100% of the nominal load (according to ICE datasheet); (ii) minimum exhaust gas temperature (*Texhaust*) equal to 110 ◦C [17], as conservative value, to prevent water condensation along the discharge line; (iii) when a potential ICE heat dissipation would occur, the boilers are turned on to cover the heat demand, in place of the ICEs, in order to avoid high-grade enthalpy wasted heat.

$$\dot{Q}\_{lh,\text{Diss}}(\overline{\mathbf{x}}) = 0 \text{ such that} \begin{cases} \dot{Q}\_{lh,PM}(\overline{\mathbf{x}}) = \dot{Q}\_{lh,\text{Dil}} \text{ if } \dot{Q}\_{lh,\text{Dil}} < \dot{Q}\_{lh,\text{Pil},\text{max}}\\ \dot{Q}\_{lh,PM}(\overline{\mathbf{x}}) = \dot{Q}\_{lh,\text{Pil},\text{max}} \text{ if } \dot{Q}\_{lh,\text{Dil}} \ge \dot{Q}\_{lh,\text{Pil},\text{max}}\\ T\_{\text{exhust}}(\overline{\mathbf{x}}) = 110 \text{ } ^\circ \text{C} \\ 0.4 \le \overline{\mathbf{x}} \le 1 \end{cases} \tag{1}$$
