High-performance Optimization Methods and Distributed Control Techniques for Power Systems: Theory, Algorithms, and Case Studies

The design, planning and operation of an electric power grid depend heavily on several optimization problems such as optimal power flow (OPF), security-constrained OPF, state estimation and unit commitment. Since these problems are large-scale and highly nonlinear, the commonly used algorithms frequently fail to converge, do not scale well, have robustness issues, and may converge to a poor local minimum as opposed to a global solution. Recent studies confirm that the nonlinearity and high dimension of the existing power optimization problems may not allow algorithms used in the power industry to converge to a high-quality solution in a timely manner, which lead to wasting billions of dollars annually. These problems become even more nonlinear, significantly grow in size, and need to be solved faster for future power systems.  To operate an efficient, resilient and sustainable power system, it is essential to design new computational techniques to deal with nonlinearities, develop fast and parallelizable numerical algorithms for large-scale problems, and design optimal distributed controllers to provide guarantees on the real-time performance of the system.

In this talk, we will propose a new mathematical framework to address the above issues regarding the optimization and control of power systems. Our framework rests on recent advances in graph theory, optimization and distributed control, including the notions of OS-vertex sequence and treewidth, matrix completion, semidefinite programming (SDP), and low-rank optimization. In particular, we will study four fundamental mixed-integer power optimization problems, named power flow, security-constrained optimal power flow, state estimation and unit commitment. We will show that real-world power networks have low treewidth, and as a result our computational framework is able to find global or near globally optimal solutions. We will illustrate our results on several real-world power grids with over 13,000 buses described by nonlinear equations subject to noise and corrupted data. We will also offer new results on the distributed control of power systems to maximize the penetration of renewable energy without destabilizing the grid.