A new paper among MINOA Partners: University of Pisa and CNR-IASI

Abstract. The Unit Commitment (UC) problem in electrical power production requires to optimally operate a set of power generation units over a short time horizon (one day to a week). Operational constraints of each unit depend on its type (e.g., thermal, hydro, nuclear, \ldots), and can be rather complex. For thermal units, typical ones concern minimum and maximum power output, minimum up- and down-time, start-up and shut-down limits, ramp-up and ramp-down limits. Also, the objective function is often nonlinear. Thus, even the Single-Unit Commitment (1UC) problem, in which only one unit is present, has a rich combinatorial structure. In this  work we present the first MINLP formulation that describes the convex hull of the feasible solutions of (1UC) comprising all the above constraints, and convex power generation costs. The new formulation has a polynomial number of both variables and constraints, and it is based on the efficient Frangioni-Gentile Dynamic Programming algorithm  together with the Perspective Reformulation technique. We then analyze the effect of using it to develop tight formulations for the more general (UC). Since the formulation, despite being polynomial-size, is rather large, we also propose two new formulations, based on partial aggregations of variables, with different trade-offs between quality of the obtained bound and cost of the solving the corresponding continuous relaxation. Our results show that navigating these trade-offs may lead to improved performances for the partial enumeration approach used to solve the problem.

Keywords: Unit Commitment problem, Ramp Constraints, MIP Formulations, Dynamic Programming, Convex Costs

Cite as: T. Bacci, A. Frangioni, C. Gentile, K. Tavlaridis-Gyparakis, New MINLP Formulation for the Unit Commitment Problems with Ramping Constraints.  Optimization online.

An additional note. A previous version of the paper for MI-SOCP  formulations was published as IASI Research Report 19-04. Moreover, IASI Research Report 19-03 presents a counterexample to a previous work for an exact MINLP formulation for the single-unit Unit Commitment problem with ramping constraints and convex objective function.

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