  Optimal power flow (OPF) is a critical optimization problem for power systems
to operate at points where cost or operational objectives are optimized. Due to
the non-convexity of the set of feasible OPF operating points, it is
non-trivial to transition the power system from its current operating point to
the optimal one without violating constraints. On top of that, practical
considerations dictate that the transition should be achieved using a small
number of small-magnitude control actions. To solve this problem, this paper
proposes an algorithm for computing a transition path by framing it as a
shortest path problem. This problem is formulated in terms of a discretized
piece-wise linear path, where the number of pieces is fixed a priori in order
to limit the number of control actions. This formulation yields a nonlinear
optimization problem (NLP) with a block tridiagonal structure, which we
leverage by utilizing a specialized interior point method. An initial feasible
path for our method is generated by solving a sequence of relaxations which are
then tightened in a homotopy-like procedure. Numerical experiments illustrate
the effectiveness of the algorithm.
