Title: Optimization methods for power grid reliability
Description: This dissertation focuses on two specific problems related to the reliability of the modern power grid. The first part investigates the economic dispatch problem with uncertain power sources. The classic economic dispatch problem seeks generator power output levels that meet demand most efficiently; we add risk-awareness to this by explicitly modeling the uncertainty of intermittent power sources using chance-constrained optimization and incorporating the chance constraints into the standard optimal power flow framework. The result is a dispatch of power which is substantially more robust to random fluctuations with only a small increase in economic cost. Furthermore, it uses an algorithm which is only moderately slower than the conventional practice. The second part investigates “the power grid attack problem”: aiming to maximize disruption to the grid, how should an attacker distribute a budget of “damage” across the power lines? We formulate it as a continuous problem, which bypasses the combinatorial explosion of a discrete formulation and allows for interesting attacks containing lines that are only partially damaged rather than completely removed.

The result of our solution to the attack problem can provide helpful information to grid planners seeking to improve the resilience of the power grid to outages and disturbances. Both parts of this dissertation include extensive experimental results on a number of cases, including many realistic large-scale instances.