Tightening QC Relaxations of AC Optimal Power Flow through Improved Linear Convex Envelopes
arxiv(2023)
摘要
AC optimal power flow (AC OPF) is a fundamental problem in power system
operations. Accurately modeling the network physics via the AC power flow
equations makes AC OPF a challenging nonconvex problem. To search for global
optima, recent research has developed a variety of convex relaxations that
bound the optimal objective values of AC OPF problems. The well-known QC
relaxation convexifies the AC OPF problem by enclosing the non-convex terms
(trigonometric functions and products) within convex envelopes. The accuracy of
this method strongly depends on the tightness of these envelopes. This paper
proposes two improvements for tightening QC relaxations of OPF problems. We
first consider a particular nonlinear function whose projections are the
nonlinear expressions appearing in the polar representation of the power flow
equations. We construct a convex envelope around this nonlinear function that
takes the form of a polytope and then use projections of this envelope to
obtain convex expressions for the nonlinear terms. Second, we use certain
characteristics of the sine and cosine expressions along with the changes in
their curvature to tighten this convex envelope. We also propose a coordinate
transformation that rotates the power flow equations by an angle specific to
each bus in order to obtain a tighter envelope. We demonstrate these
improvements relative to a state-of-the-art QC relaxation implementation using
the PGLib-OPF test cases. The results show improved optimality gaps in 68
these cases.
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