A Polyhedral Study of the Integrated Minimum-Up/-Down Time and Ramping Polytope

2016

52 citations recorded by the source corpus.

In this paper, we study the polyhedral structure of an integrated minimum-up/-down time and ramping polytope, which has broad applications in variant industries. The polytope we studied includes minimum-up/-down time, generation ramp-up/-down rate, logical, and generation upper/lower bound constraints. By exploring its specialized structures, we derive strong valid inequalities and explore a new proof technique to prove these inequalities are sufficient to provide convex hull descriptions for variant two-period and three-period polytopes, under different parameter settings. For multi-period cases, we derive generalized strong valid inequalities (including one, two, and three continuous variables, respectively) and further prove that these inequalities are facet-defining under mild conditions. Moreover, we discover efficient polynomial time separation algorithms for these inequalities to improve the computational efficiency. Finally, extensive computational experiments are conducted to verify the effectiveness of our proposed strong valid inequalities by testing the applications of these inequalities to solve both self-scheduling and network-constrained unit commitment problems, for which our derived approach outperforms the default CPLEX significantly.

Subfields: Electrical and Electronic Engineering, Industrial and Manufacturing Engineering

View Paper: https://www.semanticscholar.org/paper/21012ad57b50129688090d367ca5a1cebc6e952c

Citations in the corpus

A Convex Primal Formulation for Convex Hull Pricing (2016, unknown): “Ramping constraints are a set of private constraints that limit the increase or decrease of power output from one time period to the next [20]: We redeﬁne the feasible set for each unit to be 15) , (16) , (34) , (35) } .”
A State Transition MIP Formulation for the Unit Commitment Problem (2018, unknown): “In fact, these (along with many others) were the motivation behind studying tighter ramping constraints and valid inequalities in [13], [14], [27], [28].”