  This paper investigates the impact of the changes in the demand of power
systems on the quality of the solution procured by the convex relaxation
methods for the AC optimal power flow (ACOPF) problem. This investigation needs
various measures to evaluate the tightness of the solution procured by the
convex relaxation approaches. Therefore, three tightness measures are leveraged
to illustrate the performance of convex relaxation methods under different
demand scenarios. The main issue of convex relaxation methods is recovering an
optimal solution which is not necessarily feasible for the original non-convex
problem in networks with cycles. Thus, a cycle measure is introduced to
evaluate the performance of relaxation schemes. The presented case study
investigates the merit of using various tightness measures to evaluate the
performance of various relaxation methods under different circumstances.
