Long term planning under uncertainty: Models and Algorithms
Open Access
- Author:
- Kumar, Vijay
- Graduate Program:
- Industrial Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- August 31, 2021
- Committee Members:
- Mort Webster, Chair & Dissertation Advisor
Karen Fisher-Vanden, Outside Unit & Field Member
Eunhye Song, Major Field Member
Uday Shanbhag, Major Field Member
Steven Landry, Program Head/Chair - Keywords:
- Electricity Investment Planning
Stochastic Programming
Approximate Dynamic Programming
Climate Change
Extreme Events
Reinforcement Learning
Importance Sampling - Abstract:
- An increase in renewable energy portfolio in the electric grid to reduce emissions from the energy sector has changed grid requirements in terms of flexibility, reliability, and resiliency. Power system planning should consider all these essential characteristics of the grid to ensure a reliable grid in the future. This thesis aims to develop tools and techniques to address power system planning with all the characteristics in a computationally tractable framework. The methods developed are inspired by a framework called approximate dynamic programming or reinforcement learning. Approximate Dynamic Programming(ADP) is a Monte Carlo-based simulation technique that uses low order approximation of the objective function and uses dynamic programming principles to obtain future policies for planning under uncertainty. We exploit the stage-wise and problem decomposition framework present to do adaptive system planning under uncertainty with hourly resolution in simulating operations of the power system. We develop variations of the hourly power system operations, out of which one of them is integrated into long-term planning. Chapter 2 focuses on developing hourly power system operations models, including integrality constraints to represent specific units and other operational constraints such as uptime, downtime, ramping, and reserve constraints, along with transmission constraints. To ensure computational tractability for large systems like Western Electricity Coordinating Council (WECC), we decompose into two separate models with operational constraints and transmission constraints. This approximation was required to integrate the power system model into other physical system models such as water, land, and economy in a computationally tractable framework. We compare this proposed model with different variations of the models used in the power system to estimate the impacts of water stress in the future on the power system and other parts of the economy. Chapter 3 introduces the approximate dynamic programming framework for future power system planning. ADP is a sampling-based optimization technique, and like other techniques within these classes of methods, it suffers from the 'explore vs. exploit' problem. It needs to balance the trade-off between exploring new areas of the search space to improve estimates where the variance could be significant or exploiting the current approximation to obtain better policies. We propose a new algorithm called Q-Importance Sampling (QIS), where importance sampling is defining the sampling policy than weighing costs from some other policy. The disproportionate sampling characteristic in importance sampling addresses the explore vs. exploit problem as the approximation improves. Chapter 4 integrates the hourly power system operations model in Chapter 2 without integrality and operational constraints into long term system planning model based on approximate dynamic programming developed in Chapter 3. We compare the proposed model with other multi-stage stochastic optimization methods such as progressive hedging and stochastic dual dynamic programming for solution quality and computational effort.