  Optimal power flow (OPF) is a key problem in power system operations. OPF
problems that use the nonlinear AC power flow equations to accurately model the
network physics have inherent challenges associated with non-convexity. To
address these challenges, recent research has applied various convex relaxation
approaches to OPF problems. The QC relaxation is a promising approach that
convexifies the trigonometric and product terms in the OPF problem by enclosing
these terms in convex envelopes. The accuracy of the QC relaxation strongly
depends on the tightness of these envelopes. This paper presents two
improvements to these envelopes. The first improvement leverages a polar
representation of the branch admittances in addition to the rectangular
representation used previously. The second improvement is based on a coordinate
transformation via a complex per unit base power normalization that rotates the
power flow equations. The trigonometric envelopes resulting from this rotation
can be tighter than the corresponding envelopes in previous QC relaxation
formulations. Using an empirical analysis with a variety of test cases, this
paper suggests an appropriate value for the angle of the complex base power.
Comparing the results with a state-of-the-art QC formulation reveals the
advantages of the proposed improvements.
