Abstract. When uncontrollable resources fluctuate, optimal power flow (OPF), routinely used by the electric power industry to redispatch 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 our simulations of real grids, is considered undesirable in power engineering practice. Possibly, it can lead to a risky outcome that compromises grid stability-line tripping. 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 redispatch. CC-OPF allows efficient implementation, e.g., solving a typical instance over the 2746-bus Polish network in 20 seconds on a standard laptop.Key words. optimization, power flows, uncertainty, wind farms, networks AMS subject classifications. 15A15, 15A09, 15A23
DOI. 10.1137/130910312The power grid, one of the greatest engineering achievements of the 20th century, delivers social development and resulting political stability of billions of people around the globe through control sophistication and careful long-term planning, with only very rare disruptions. *