Texas is among the leading states that are most quickly embracing renewable energy. As it champions the use of "clean" energy, significant environmental and economic benefits of renewables have been realized within Texas. This talk will present a high-level overview of the challenges encountered to reach such a high penetration level of renewable generation at ERCOT. These challenges are also complicated by the high-dimensional problem spaces unavoidable for a bulk power system and very strict computational time requirement demanded for real-time applications.

In computer science, time and space are the classical measures of the performance of an algorithm. But modern computing systems, both today and in the future, are equally if not more limited by physical constraints imposed on the energy, power, and reliability of their components. So, what happens to algorithm design when we consider these factors?

The feasible region plays a fundamental role in solving optimal power flow (OPF) problems.  OPF solutions do not exist if the corresponding feasible region is an empty set. Any solution algorithm proposed for solving OPF problems will fail if the feasible region does not exist. In addition, the geometry and characteristics of feasible region indeed affect the performance of OPF solution methods. In this talk, a complete characterization of the feasible region of OPF problems will be presented.