Affinely Adjustable Robust Optimization for Constraint Filtering in AC Security Constrained Optimal Power Flow Under Uncertainties

AC security-constrained optimal power flow under uncertainties (AC SCOPF-UU) is a large scale, non-convex, nonlinear optimization problem. Solving AC SCOPF-UU is extremely computationally demanding. This paper proposes a new methodology that drastically reduces the size of the AC SCOPF-UU, so that it can be manageable by existing methods, and speed-up its solution. The proposed methodology achieves these goals through constraint filtering, i.e. the detection and subsequent filtering of the majority of harmless constraints (constraints that, for a given contingency, in the presence of best corrective actions, are never violated whatever the value of uncertainty in the assumed set) of the AC SCOPF-UU problem. The constraint filtering relies on a new method that solves a linear approximation of the main problem in the form of an affinely adjustable robust SCOPF (AAR-SCOPF). This paper applies for the first-time constraint filtering to the most comprehensive AC SCOPF-UU problem to date. Extensive tests with the proposed methodology in five systems of up to 2,737 nodes, have revealed that it is able to reduce the problem size with up to 82% and achieves solution time saving of up to 95%.