*2.7. Stochastic Profile Generation*

Stochastic energy and water demand profiles were generated using Equations (14) and (15). In these equations, *Pld*(*t*) and . *Vld*(*t*) are the deterministic energy and water profiles, δ*hr*(*t*) is a random number that varies every hour, and δ*dy*(*t*) varies every day. Both random numbers are drawn from a normal distribution centered at 0 with 5% variance. Generation of the stochastic hourly solar insolation profiles are discussed by Bendt et al. in [59] and Graham et al. in [60,61].

$$P\_{ld}^{\text{stoc}}(t) = P\_{ld}(t) \left[ 1 + \delta\_{lr}(t) + \delta\_{dy}(t) \right] \tag{14}$$

$$
\dot{V}\_{ld}^{\text{stoc}}(t) = \dot{V}\_{ld}(t) \left[ 1 + \delta\_{\text{lrr}}(t) + \delta\_{dy}(t) \right] \tag{15}
$$

After each set of generation and demand profiles are formed, a Monte-Carlo approach calculated the corresponding optimum sizes and metrics 100 times to determine their distribution. The number of simulation points were chosen to balance computation time and accuracy.
