Perspective Cuts for the ACOPF with Generators

Abstract

The alternating current optimal power flow problem is a fundamental problem in the management of smart grids. In this paper we consider a variant which includes activation/deactivation of generators at some of the grid sites. We formulate the problem as a mathematical program, prove its NP-hardness w.r.t. activation/deactivation, and derive two perspective reformulations.

Mathematical programming formulations for the alternating current optimal power flow problem

“…Improved formulations with binary variables for switching generators on and off were proposed in Salgado et al (2018b, a). The ACOPF is NP-hard (Bienstock and Verma 2019), and remains hard even when the goal is to minimize the number of active generators (Salgado et al 2018a).…”

Mathematical Programming formulations for the Alternating Current Optimal Power Flow problem

“…To the best of our knowledge, the first paper exhibiting computational results for the ACOPF with binary variables used for design purposes is [69], where binary variables are used to switch generators and shunts on and off. Improved formulations with binary variables for switching generators on and off were proposed in [72,71]. The ACOPF is NP-hard [12], and remains hard even when the goal is to minimize the number of active generators [71].…”

“…Improved formulations with binary variables for switching generators on and off were proposed in [72,71]. The ACOPF is NP-hard [12], and remains hard even when the goal is to minimize the number of active generators [71].…”

Power Network Design with Line Activity

“…To the best of our knowledge, the first paper exhibiting computational results for the ACOPF with binary variables used for design (rather than approximation) purposes is [11], where binary variables are used to switch generators and shunts on and off: a local NLP solver is deployed on a well-known continuous NLP reformulation of the corresponding nonconvex MINLP. A perspective cut based relaxation of an ACOPF formulation with binary variables for switching generators on and off was proposed in [12]. Another possible approach for working with ACOPF involving binary variables is to apply network design modeling techniques involving binary variables to an LP or SOCP relaxation of the ACOPF.…”

“…DDP [14] is a MP technique to approximate the Semidefinite (PSD) cone using LP. The ACOPF is NP-hard [15], and remains hard even when the goal is to minimize the number of active generators [12].…”