Mitigating failure risk in an aging electric power transmission system

As the electric transmission system in the U.S. ages, mitigating the risk of high-voltage transformer failures becomes an increasingly important issue for transmission owners and operators. This thesis addresses the problem of allocating high-voltage transformers throughout the electric grid in order to mitigate this risk.;We introduce two models that investigate different characteristics of the problem. The first model focusses on the spatial allocation of transformers in a static, two-stage context. Algorithmically, this model investigates the use of approximate dynamic programming (ADP) for solving large scale stochastic facility location problems. The ADP algorithms that we develop consistently obtain near optimal solutions for problems where the optimum is computable and outperform a standard heuristic on more complex problems. Our computational results show that the ADP methodology can be applied to stochastic facility location problems that cannot be solved with exact algorithms.;The second model optimizes the acquisition and the deployment of high-voltage transformers dynamically over time. We formulate the problem as a Markov Decision Process which cannot be solved for realistic problem instances. Instead we solve the problem using approximate dynamic programming using a number of different value function approximations, which are compared against an optimal solution for a simplified version of the problem. The best-performing approximation produces solutions within a few percent of the optimum with very fast convergence. The results show that ADP can used to solve large scale resource allocation problems when resources have long lead times.;This thesis emphasizes numerical work. We apply our best performing algorithms to realistic problem instances based on a real-world transformer population, which gives insights into a broad range of transformer management issues of practical interest. We also analyze existing transformer management policies and show how our models and algorithms can be used to reduce risk and costs.