Raymond A. de Callafon

Abdulelah H Habib, Zachary K Pecena, Vahid R Disfani et al.

This paper presents and evaluates the performance of an optimal scheduling algorithm that selects the on/off combinations and timing of a finite set of dynamic electric loads on the basis of short term predictions of the power delivery from a photovoltaic source. In the algorithm for optimal scheduling, each load is modeled with a dynamic power profile that may be different for on and off switching. Optimal scheduling is achieved by the evaluation of a user-specified criterion function with possible power constraints. The scheduling algorithm exploits the use of a moving finite time horizon and the resulting finite number of scheduling combinations to achieve real-time computation of the optimal timing and switching of loads. The moving time horizon in the proposed optimal scheduling algorithm provides an opportunity to use short term (time moving) predictions of solar power based on advection of clouds detected in sky images. Advection, persistence, and perfect forecast scenarios are used as input to the load scheduling algorithm to elucidate the effect of forecast errors on mis-scheduling. The advection forecast creates less events where the load demand is greater than the available solar energy, as compared to persistence. Increasing the decision horizon leads to increasing error and decreased efficiency of the system, measured as the amount of power consumed by the aggregate loads normalized by total solar power. For a standalone system with a real forecast, energy reserves are necessary to provide the excess energy required by mis-scheduled loads. A method for battery sizing is proposed for future work.

Amir Valibeygi, Abdulelah H. Habib, Raymond A. de Callafon

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.