Stochastic unit commitment problem: A statistical approach

Abstract

The Stochastic Unit Commitment Problem (SUCP) has been widely studied using scenario-based generation to include uncertainty in the mathematical model, transforming the stochastic problem into a large deterministic problem. However, the accuracy of the stochastic problem is highly dependent on the number of scenarios, leading to computational intractability when the number of scenarios is large. This paper proposes a novel paradigm that avoids scenario sampling. Instead, it derives a function that models the expected cost based on a merit order dispatch rule for the thermal units and incorporates the probability distribution of net demand. Thus, the expected cost is explicitly stated in a non-linear function. A piecewise linear approximation method is used to address the new model’s nonlinearity, resulting in a mixed integer linear programming (MILP) model. The proposed model is compared to the traditional scenario-based SUCP in terms of computational effort, solution stability, and costs. Numerical experiments show that the new approach can reach optimality in more instances than the traditional scenario-based model. Moreover, it eliminates memory limitations and provides stable and cost-competitive solutions. Thus resulting in a scalable alternative for large-scale and realistic power systems. To the best of our knowledge, this is the first SUCP formulation that integrates uncertainty without relying on scenario-based methods.