  Considering the intermittency of renewable energy systems, a sizing and
scheduling model is proposed for a finite number of static electric loads. The
model objective is to maximize solar energy utilization with and without
storage. For the application of optimal load size selection, the energy
production of a solar photovoltaic is assumed to be consumed by a finite number
of discrete loads in an off-grid system using mixed-integer linear programming.
Additional constraints are battery charge and discharge limitations and minimum
uptime and downtime for each unit. For a certain solar power profile the model
outputs optimal unit size as well as the optimal scheduling for both units and
battery charge and discharge (if applicable). The impact of different solar
power profiles and minimum up and down time constraints on the optimal unit and
battery sizes are studied. The battery size required to achieve full solar
energy utilization decreases with the number of units and with increased
flexibility of the units (shorter on and off-time). A novel formulation is
introduced to model quasi-dynamic units that gradually start and stop and the
quasi-dynamic units increase solar energy utilization. The model can also be
applied to search for the optimal number of units for a given cost function.
