Sharp fluctuations in photovoltaic (PV) power generation and idiosyncratic power consumption make the exact net-demand prediction difficult. As a relatively new approach to reliable renewable power prediction, there can be found interval-valued prediction methods that determine confidence intervals with a certain probability, e.g., 95%. Such interval-valued net-demand prediction can be depicted as the red region in the figure below. To comply with this type of prediction, we have formulated an interval-valued economic dispatch problem in terms of parametric optimization, which is described as a problem of finding the tightest box, i.e., interval hull, that encloses the image of an output function consisting of the minimizer of parametric optimization. The resultant interval hulls of the optimal generation and battery charge/discharge schedules are depicted as the blue and green regions in the figure, regarded as necessary regulating capacities to absorb the fluctuation of the net-demand.

Conventional thermal generators generally require several hours for warm-up and cool-down. Therefore, it is crucial to conduct the day-ahead scheduling of startup and shutdown of thermal generators to keep supply-demand balancing for volatile demand and renewable power generation, the amounts of which are also predicted the day before. Such a scheduling problem of conventional generators under uncertainty of demand and renewable power prediction is called a robust unit commitment problem, which is commonly described as two-stage robust optimization.

For robust unit commitment, we have proposed a novel approach that can realize stable power supply with explicit consideration of the feasibility of realtime economic dispatch in realtime operation. In the proposed robust unit commitment problem, we aim at deciding not only the startup and shutdown schedules of thermal generators, but also the admissible operation ranges of generators and batteries that are sufficient for realtime adaptation to the volatility of demand and renewable power generation. Such an ability to realize realtime adaptation is mathematically described as box-based temporal decomposition of feasible regions of multiperiod generator and battery operation.