Latent Factor Approximating Models for Stochastic Optimization: Applications to Power System Planning
Open Access
- Author:
- Bukenberger, Jesse
- Graduate Program:
- Industrial Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- March 23, 2021
- Committee Members:
- Mort D Webster, Dissertation Advisor/Co-Advisor
Mort D Webster, Committee Chair/Co-Chair
Vinayak V Shanbhag, Committee Member
Eunhye Song, Committee Member
Steven J Greybush, Outside Member
Steven James Landry, Program Head/Chair - Keywords:
- Transmission Planning
Stochastic Optimization
Principal Components Analysis
Large-Scale Optimization
Discrete Optimization
Approximation Methods
Clustering Methods
Energy Systems
Planning - Abstract:
- This dissertation introduces a school of methods for making decisions under uncertainty, with a focus on planning investments in the electric transmission network. Transmission planning problems are complicated by the large scale of the system, the discreteness of investment options, short-term operational variability, and long-term uncertainty. Planners struggle to identify and articulate the value of major transmission projects in the context of long-term uncertainty. The methods are unified by their use of a covariance estimate that relates uncertain scenarios to one another by their economic response to a sample of candidate expansion plans. This relationship helps to simplify how uncertainty is represented so the relative effects of alternative actions can be accurately predicted with smaller models. Chapter 2 details a method for modeling short-term operational uncertainty in models with a single investment stage. The method selects and weights a small set of short-term points in a way that represents the main sources of cost variation that can be addressed with investment decisions. Chapter 3 introduces a transmission planning model with two investment stages and short-term uncertainty that is specific to the long-term scenario. A method for partitioning, rather than reducing, long-term scenarios is developed so short-term points can be sampled from many scenarios while still reducing the number of discrete investment variables in the model. The partitioned model provides a complete investment policy and upper bounds; probabilistic lower bounds are established with a variance reduced sampling scheme. Chapter 4 extends the partitioning method to multistage transmission planning problems. The partitioned scenario trees aggregate large sets of scenarios into solvable models while preserving the value of adaptive planning. The method gives complete investment policies that will help planners articulate the long-term value of decisions in the context of uncertainty.