  We propose a novel feasible-path algorithm to solve the optimal power flow
(OPF) problem for real-time use cases. The method augments the seminal work of
Dommel and Tinney with second-order derivatives to work directly in the reduced
space induced by the power flow equations. In the reduced space, the
optimization problem includes only inequality constraints corresponding to the
operational constraints. While the reduced formulation directly enforces the
physical constraints, the operational constraints are softly enforced through
Augmented Lagrangian penalty terms. In contrast to interior-point algorithms
(state-of-the art for solving OPF), our algorithm maintains feasibility at each
iteration, which makes it suitable for real-time application. By exploiting
accelerator hardware (Graphic Processing Units) to compute the reduced Hessian,
we show that the second-order method is numerically tractable and is effective
to solve both static and real-time OPF problems.
