On the Loadability Sets of Power Systems—Part II: Minimal Representations

The first part of this two-part paper developed the framework for characterizing the feasibility regions of power systems in the demand space. This characterization, however, leads to the generation of a large number of extraneous constraints as an unwelcome byproduct. This shortcoming motivates the second part of this paper series, whose objective is the achievement of a minimal representation for loadability sets through an offline process. Thus, in this paper, we set forth to eliminate efficiently redundant constraints with the proposal of an enhanced umbrella constraint discovery (E-UCD) problem formulation. The use of E-UCD in this paper is fourfold: 1) It serves to identify redundant line flow constraints not potentially shaping the feasibility regions of power systems in the generation-demand space. 2) It serves to determine the maximum number of line flow limits that could ever become active simultaneously in a given power system. 3) It pinpoints the generators who have the ability to become pivotal in relieving network congestion. 4) It is used to identify redundant constraints generated, while generation dispatch variables are projected from the generation-demand space onto the demand space. Experiments are carried out on the standard IEEE test systems to show that the minimal representations of loadability sets contain a reasonable number of constraints. Thus, the application of loadability sets to operation and planning problems will result in computational savings.