Contingency ranking with respect to overloads in very large power systems taking into account uncertainty, preventive and corrective actions

This paper deals with day-ahead security management with respect to a postulated
set of contingencies while taking into account uncertainties about the next day
generation/load scenario. In order to help the system operator in decision making
under uncertainty we aim at ranking these contingencies into four clusters according
to the type of control actions needed to cover the worst uncertainty pattern of
each contingency with respect to branch overload. To this end we use a fixed point
algorithm that loops over two main modules: a discrete bi-level program (BLV) that
computes the worst-case scenario, and a special kind of security constrained optimal
power flow (SCOPF) which computes optimal preventive/corrective actions to cover the
worst-case. We rely on a DC grid model, as the large number of binary variables, the
large size of the problem, and the stringent computational requirements preclude the
use of existing mixed integer nonlinear programming (MINLP) solvers. Consequently we
solve the SCOPF using a mixed integer linear programming (MILP) solver while the BLV
is decomposed into a series of MILPs. We provide numerical results with our approach
on a very large European system model with 9241 buses and 5126 contingencies.