On the Pseudo-Bifurcation of Non-Convexity in the Feasible Region of AC Optimal Power Flow

The subject of optimal power flow (OPF) convexity has attracted great interest in the research community. In this brief, it will be shown that a new type of bifurcation can occur in OPF model to alter the convexity property; in particular, a pseudo-bifurcation of OPF feasible region non-convexity can occur when some upper or lower bounds of the inequality constraints are tightened or relaxed. Hence, caution must be taken to state whether a feasible region of an AC OPF model is convex/non-convex without specifying the set of inequality constraints. Numerical studies on several IEEE test systems are conducted to illustrate the impact of this type of pseudo-bifurcation on the feasible region. The applicability of a class of convex relaxation methods is examined via the convex/non-convex feasible region. A guideline derived from our numerical studies is provided to give conditions under which the convex relaxation method is applicable.