Optimization Algorithms for Power Grid Planning and Operational Problems.

Abstract

The modern electrical grid is an engineering marvel. The power grid is an incredibly complex system that largely functions very reliably. However, aging infrastructure and changing power consumption and generation trends will necessitate that new investments be made and new operational regimes be explored to maintain this level of reliability. One of the primary difficulties in power grid planning is the presence of uncertainty. In this thesis, we address short-term (i.e., day-ahead) and long-term power system planning problems where there is uncertainty in the forecasted demand for power, future renewable generation levels, and/or possible component failures. We initially consider a network capacity design problem where there is uncertainty in the nodal supplies and demands. This robust single-commodity network design problem underlies several applications including power transmission networks. Minimum cost capacity expansion decisions are made to ensure that there exists a feasible network flow solution for alpha% of the demand scenarios in the given set, where alpha is a parameter specified by the user. We next consider a day-ahead planning problem that is specifically applicable to the power grid. We present an extension of the traditional unit commitment problem where we additionally consider (1) a more stringent security requirement and (2) a more flexible set of recovery actions. We require that feasible operation is possible for any simultaneous failure of k generators and/or transmission lines (i.e., N-k security), and transmission switching may be used to recover from a failure event. Finally, we consider a transmission expansion planning problem where there is uncertainty in future loads, renewal generation outputs and line failures, and transmission switching is also allowed as a recovery action. We propose a robust optimization model where feasible operation is required for all loads and renewable generation levels within given ranges, and for all single transmission line failures. For all three of these problems, novel algorithms are presented that enable these problems to be solved even when straight-forward formulations are too large to be tractable. Computational results are presented for each algorithm to provide insight into the advantages and limitations of these algorithms in practice