*2.3. Desalination Model*

The energy required for a desalination plant to generate one volumetric unit of freshwater is defined as the energy intensity (EI). It is divided into electrical energy intensity (EIel) for mechanical processes and a thermal energy intensity (EIth) for heating processes [19]. MVC and RO, which do not have external heating, have zero EIth [19]. Equation (8) relates the EIel to the water generated . *Vde*(*t*) and the electrical power entering the desalination plant *Pde*(*t*) at time *t*. For desalination technologies that require external heating, the mass of coal used . *mcl*(*t*) [kg/h] is given by Equation (9), wherein Δ*H* is the lower heating value of coal (17.89 MJ/kg) [43]:

$$
\dot{V}\_{dc}(t) = \frac{P\_{dc}(t)}{\text{EI}\_{\text{el}}},\tag{8}
$$

$$
\dot{m}\_{cl}(t) = \frac{P\_{dc}(t)}{\Delta H} \times \frac{EI\_{th}}{EI\_{cl}} \,\tag{9}
$$

The generated water is then sent to a storage tank, where the water demanded is simultaneously drawn. This is summarized by Equation (10), wherein *<sup>V</sup>*(*t*) is the volume of water in the tank, . *Vld*(*t*) is the water demand, and Δ*t* is the simulation time step (1 h):

$$V(t + \Delta t) = V(t) + \left[\dot{V}\_{dc}(t) - \dot{V}\_{ld}(t)\right]\Delta t\_\prime \tag{10}$$

The power that enters the desalination plant depends on the water level. If the water level is above 20%, then the minimum power requirement *Pmin de* (*t*) depends on the turndown ratio (TDR). The TDR is the ratio between minimum and rated production, and operation below this point will damage the desalination plant. If the water level is below 20%, the minimum power requirement will be set to restore the water level to at least 20%. This is summarized by Equation (11), wherein *Vtank* is the volume of the storage tank:

$$P\_{dc}^{\text{min}}(t) = \begin{cases} \text{TDR} \cdot S\_{dc} & V(t) \ge 0.2V\_{tank} \\ \frac{\text{EL}\_{\text{el}}}{\Delta t} \Big(0.2 - \frac{V(t)}{V\_{tank}}\Big) & V(t) < 0.2V\_{tank} \end{cases} \tag{11}$$

The EI and TDR of the considered desalination technologies are shown in Table 3.


**Table 3.** Energy intensity (EI) and turndown ratio (TDR) of desalination technologies.
