The unit commitment problem with uncertainty is considered one of the most challenging power system scheduling problems. Different stochastic models have been proposed to solve the problem, but such approaches have yet to be applied in industry practice because of computational challenges. In practice, the problem is formulated as a deterministic model with reserve requirements to hedge against uncertainty. However, simply requiring a certain level of reserves cannot ensure power system reliability as the procured reserves may be nondispatchable because of transmission limitations. In this paper, we derive a set of feasibility cuts (constraints) for managing the unit commitment problem with uncertainty. These cuts eliminate unreliable scheduling solutions and reallocate reserves in the power system; they are induced by the extreme rays of a polyhedral dual cone. This paper shows that, with the proposed reformulation, the extreme rays of the dual cone can be characterized by combinatorial selections of transmission lines (arcs) and buses (nodes) of the power system. As a result, the cuts can then be characterized using engineering insights. The unit commitment problem with uncertainty is formulated as a deterministic model with the identified extreme ray feasibility cuts. Test results show that, with the proposed extreme ray feasibility cuts, the problem can be solved more efficiently, and the resulting scheduling decision is also more reliable.

Electric power and energy engineering has as a basic tenet the relief of humankind of its burden, and the transmission and processing of information. In this paper, the salient advances of the first century of the electrification of the World is reviewed with special emphasis on the contemporary design and operation of electric power and energy systems. The advancements of power engineering are reviewed from a 2012 perspective, and issues of sustainability and the utilization of renewable resources are discussed.