Tight Conic Formulation of Unit Commitment Problem and Comparison with MINLP/MILP Formulations

© 2018 IEEE. Unit Commitment (UC) in its classical form is a mixed integer non-linear programming (MINLP) problem, which is not scalable to power systems with large number of generators. Mixed integer linear programming (MILP) versions of UC use linear or piece-wise linearized cost functions of the generators, which is computationally efficient for larger systems, and is the state-of-the-art method in some of the existing energy management system (EMS) tools. In this paper, we demonstrate that use of linear cost functions in MILP can lead to suboptimal solutions, thus having larger differences in cost which can be possibly run into millions of dollars. We then develop a tighter conic reformulation of the UC problem that retains the quadratic cost functions of the generators and utilizes convex hull descriptions of harder inter-temporal constraints. This improves on the computational efficiency, and as a result, the formulation shows better scalability than MINLP and significantly lower operational costs compared to MILP. We demonstrate efficacy of the proposed UC formulation using several case studies considering upto 1,000 generators