  When uncontrollable resources fluctuate, Optimum Power Flow (OPF), routinely
used by the electric power industry to re-dispatch hourly controllable
generation (coal, gas and hydro plants) over control areas of transmission
networks, can result in grid instability, and, potentially, cascading outages.
This risk arises because OPF dispatch is computed without awareness of major
uncertainty, in particular fluctuations in renewable output. As a result, grid
operation under OPF with renewable variability can lead to frequent conditions
where power line flow ratings are significantly exceeded. Such a condition,
which is borne by simulations of real grids, would likely resulting in
automatic line tripping to protect lines from thermal stress, a risky and
undesirable outcome which compromises stability. Smart grid goals include a
commitment to large penetration of highly fluctuating renewables, thus calling
to reconsider current practices, in particular the use of standard OPF. Our
Chance Constrained (CC) OPF corrects the problem and mitigates dangerous
renewable fluctuations with minimal changes in the current operational
procedure. Assuming availability of a reliable wind forecast parameterizing the
distribution function of the uncertain generation, our CC-OPF satisfies all the
constraints with high probability while simultaneously minimizing the cost of
economic re-dispatch. CC-OPF allows efficient implementation, e.g. solving a
typical instance over the 2746-bus Polish network in 20 seconds on a standard
laptop.
