An interval-based two-stage stochastic programming model for the unit commitment problem under net demand uncertainty

The unit commitment problem aims to find a cost-minimizing on/off status and dispatch level for each generator while satisfying the electricity demand and operational requirements. To deal with net demand uncertainty modeled by a given probability distribution, scenario-based stochastic programming models where expected costs are minimized over sampled demand scenarios have been widely studied. However, they often suffer from excessive computational burden as the number of scenarios increases. To address this challenge, we propose an interval-based two-stage stochastic unit commitment model. In the model, the dispatch range for each generator is carefully determined along with its on/off status in each period, allowing dispatch decisions to be made independently across periods. To approximate the expected second-stage cost, we employ a discrete bounding approximation that obviates the need for scenario generation and provides controllable upper and lower bounds. Furthermore, we derive a compact Benders reformulation to reduce the size of the proposed model. Computational experiments on IEEE 118-bus systems show that the proposed model can substantially decrease computation time and achieve lower real-time operating costs compared to the conventional scenario-based two-stage stochastic unit commitment model, while maintaining a small approximation gap.