Interior Point Methods for Optimal Power Flow Formulations

Security Constrained Optimal Power Flow is an increasingly important problem for power systems operation both in its own right and as a subproblem for more complex problems such as transmission switching or
unit commitment.

The structure of the problem resembles stochastic programming problems in that one aims to find a cost optimal operation schedule that is feasible for all possible equipment outage scenarios
(contingencies). Due to the presence of power flow constraints (in their "DC" or "AC" version), the resulting problem is a large scale linear or nonlinear programming problem.

However it is known that only a small subset of the contingencies is active at the solution. We show how Interior Point methods can exploit this structure both by simplifying the linear algebra operations as
well as generating necessary contingencies on the fly and integrating them into the algorithm using IPM warmstarting techniques. The final problem solved by this scheme is significantly smaller than the full
contingency constrained problem, resulting in substantial speed gains.

Numerical and theoretical results of our algorithm will be presented.