  This paper outlines an optimization framework for choosing fast and reliable
control actions in a transmission grid emergency situation. We consider
contractual load shedding and generation re-dispatch as exemplary emergency
actions. To achieve computational efficiency and scalability, this novel
formulation of the robust corrective action optimization is stated in terms of
voltages and currents, as opposed to standard formulation in terms of power
flows and voltages. The current-voltage formulation is natural for expressing
voltage and thermal transmission line constraints, and its major advantage is
in the linearity of the power flow equations. The complexity of the
current-voltage formulation, which is mainly related to the transformation of
voltages and currents into active and reactive power injections, can be largely
avoided by stating the cost function directly in terms of currents and using
linearized or robust estimates for load and generation constraints. The paper
considers five different optimization problem formulations, including the full
current-voltage formulation, as well as two convex and two linear approximation
to the problem. In a case study on an illustrative case study for the IEEE
RTS96 system, we demonstrate pros and cons of the different formulations based
on simulations for both normal and contingency operation.
