Chance Constrained Optimal Power Flow: Risk-Aware Network Control under   Uncertainty
  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. 
Daniel Bienstock, Michael Chertkov, and Sean Harnett
math.OC cs.SY physics.soc-ph