Approximations and Relaxations of Power Flow Equations

The design, control, and operation of the power grid, probably the largest and most expansive system ever engineered, require the solving of optimization problems over the steady-state power flow equations. The resulting mixed nonconvex programs are often computationally challenging and increasingly so with the increased stochasticity in generation and load.

This talk presents a number of advances in approximating and relaxing the power flow equations to address emerging applications in power systems, including large-scale power restoration after blackouts, the design of resilient networks, and the integration of renewable generation. Extensive computational results demonstrate some of the benefits of the proposed techniques.

(Joint work with Carleton Coffrin and Hassan Hijazi)