Multistage Adaptive Robust Optimization for the Unit Commitment Problem

The growing uncertainty associated with the increasing penetration of wind and solar power generation has presented new challenges to the operation of large-scale electric power systems. Motivated by these challenges, we present a multistage adaptive robust optimization model for the most critical daily operational problem of power systems, namely, the unit commitment (UC) problem, in the situation where nodal net electricity loads are uncertain. The proposed multistage robust UC model takes into account the time causality of the hourly unfolding of uncertainty in the power system operation process, which we show to be relevant when ramping capacities are limited and net loads present significant variability. To deal with large-scale systems, we explore the idea of simplified affine policies and develop a solution method based on constraint generation. Extensive computational experiments on the IEEE 118-bus test case and a real-world power system with 2,736 buses demonstrate that the proposed algorithm is effective in handling large-scale power systems and that the proposed multistage robust UC model can significantly outperform the deterministic UC and existing two-stage robust UC models in both operational cost and system reliability.