*A.1.2. Diesel*

Diesel generators can output any power below its rated size *Sds*. A minimum power ratio *r* (0.1) is implemented and the minimum power output of a diesel generator is given by Equation (A2):

$$P\_{ds}^{\text{min}}(t) = rS\_{ds} \tag{A2}$$

The amount of fuel consumed by the plant is directly proportional to the rated size and the power output *Pds*(*t*) as given by Equation (A3). Both *C*<sup>0</sup> and *C*<sup>1</sup> are arbitrary constants [65].

$$
\dot{V}\_{fl}(t) = \mathcal{C}\_0 \mathcal{S}\_{ds} + \mathcal{C}\_1 P\_{ds}(t), \tag{A3}
$$

The fuel efficiency is given by Equation (A4), wherein ρ is the density of diesel (820 kg/m3) and Δ*HLHV* is the lower heating value of diesel (43.2 MJ/kg). The efficiency is specified as 0.3 and 0.4 at the minimum and maximum loading, respectively. This allows the coefficients in Equation (A3) to be determined.

$$
\eta\_{ds}(t) = \frac{P\_{ds}(t)}{\rho \dot{V}\_{ds}(t) \Delta H\_{LHV}},
\tag{A4}
$$
