Interval quadratic programming for day-ahead dispatch of uncertain predicted demand

In this paper, we propose an interval quadratic programming method for the day-ahead scheduling of power generation and battery charge cycles, where the prediction uncertainty of power consumption and photovoltaic power generation is described as a parameter vector lying in an interval box. The interval quadratic programming is formulated as the problem of finding the tightest box, i.e., interval hull, that encloses the image of a function of the minimizer in parametric quadratic programming. To solve this problem in a computationally efficient manner, we take a novel approach based on a monotonicity analysis of the minimizer in the parametric quadratic programming. In particular, giving a tractable parameterization of the minimizer on the basis of the Karush-Kuhn-Tucker condition, we show that the monotonicity analysis with respect to the parameter vector can be relaxed to the sign pattern analysis of an oblique projection matrix. The monotonicity of the minimizer is found to be essential in the day-ahead dispatch problem, where uncertain predicted demand, described by a parameter vector, is dispatched to power generation and battery charge cycles while the economic cost is minimized. Finally, we verify the efficiency of the proposed method numerically, using experimental and predicted data for power consumption and photovoltaic power generation.