  The variability of solar energy in off-grid systems dictates the sizing of
energy storage systems along with the sizing and scheduling of loads present in
the off-grid system. Unfortunately, energy storage may be costly, while
frequent switching of loads in the absence of an energy storage system causes
wear and tear and should be avoided. Yet, the amount of solar energy utilized
should be maximized and the problem of finding the optimal static load size of
a finite number of discrete electric loads on the basis of a load response
optimization is considered in this paper. The objective of the optimization is
to maximize solar energy utilization without the need for costly energy storage
systems in an off-grid system. Conceptual and real data for solar photovoltaic
power production is provided the input to the off-grid system. Given the number
of units, the following analytical solutions and computational algorithms are
proposed to compute the optimal load size of each unit: mixed-integer linear
programming and constrained least squares. Based on the available solar power
profile, the algorithms select the optimal on/off switch times and maximize
solar energy utilization by computing the optimal static load sizes. The
effectiveness of the algorithms is compared using one year of solar power data
from San Diego, California and Thuwal, Saudi Arabia. It is shown that the
annual system solar energy utilization is optimized to 73% when using two loads
and can be boosted up to 98% using a six load configuration.
