In this paper a model is developed to solve the on/off scheduling of (non-linear) dynamic electric loads based on predictions of the power delivery of a (standalone) solar power source. Knowledge of variations in the solar power output is used to optimally select the timing and the combinations of a set of given electric loads, where each load has a desired dynamic power profile. The optimization exploits the desired power profiles of the electric loads in terms of dynamic power ramp up/down and minimum time on/off of each load to track a finite number of load switching combinations over a moving finite prediction horizon. Subsequently, a userspecified optimization function with possible power constraints is evaluated over the finite number of combinations to allow for real-time computation of the optimal timing and switching of loads. A case study for scheduling electric on/off loads with switching dynamics and solar forecast data at UC San Diego is carried out.

A robust power scheduling algorithm is proposed to schedule power flow between the main electricity grid and a microgird with solar energy generation and battery energy storage subject to uncertainty in solar energy production. To avoid over-conservatism in power scheduling while guaranteeing robustness against uncertainties, time-varying "soft" constraints on the State of Charge (SoC) of the battery are proposed. These soft constraints allow SoC limit violation at steps far from the current step but aim to minimize such violations in a controlled manner. The model predictive formulation of the problem over a receding time horizon ensures that the resulting solution eventually conforms to the hard SoC limits of the system at every step. The optimization problem for each step is formulated as a quadratic programming problem that is solved iteratively to find the soft constraints that are closest to the hard ones and still yield a feasible solution. Optimization results demonstrate the effectiveness of the approach.

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.

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