Dissertation
Algorithms to solve power grid expansion optimization problems
University of Iowa
Doctor of Philosophy (PhD), University of Iowa
Summer 2022
DOI: 10.25820/etd.006638
Abstract
With costs of large-scale wind and storage devices decreasing, there is an increasing interest to bring these technologies onto the power grid. The intermittent nature of renewable energy makes it a challenge to determine the optimal location and capacity of these devices.
In this thesis, we first present wind and storage expansion planning as a multi-stage, linear scenario-based optimization problem, where the first stage represents build decisions and subsequent stages represent operations. We explore different operational assumptions involving load, thermal set points, and renewable outputs in a two-stage and three-stage model. Comparing time resolutions and differing numbers of scenarios, we show empirically that increasing the temporal resolution and number of scenarios has a significant impact on the predicted cost and build decisions while increasing computational complexity. To get around these scalability issues, an implementation of the Progressive Hedging Algorithm is used. We also shed light on the tractability issues present on this multi-stage model.
Then we focus on storage expansion exclusively on a smaller network with the same modeling assumptions, comparing existing data-driven methods. We also present a clustering approach based on the net load. The methods we compare are storage optimization and data-driven robust optimization under a different number of scenarios, with an L-Shaped Algorithm with trust region and Constraint and Column Generation Algorithm used to solve the respective problems, as well as a k-means clustering approach to decide representative days based on either the cluster center or worst case inside each cluster. Under a constrained network, we show widely different build decisions occur comparing scenario and robust optimization approaches. We verify that improvements are made as the number of scenarios increases, and we show empirically that clustering on a large number of scenarios, and using the worst case on a cluster can consistently improve on lost load from a scenario optimization perspective, while improving overall cost from a robust optimization perspective.
Details
- Title: Subtitle
- Algorithms to solve power grid expansion optimization problems
- Creators
- Michael Kratochvil
- Contributors
- David Stewart (Advisor)Bruce Ayati (Committee Member)Samuel Burer (Committee Member)Xueyu Zhu (Committee Member)
- Resource Type
- Dissertation
- Degree Awarded
- Doctor of Philosophy (PhD), University of Iowa
- Degree in
- Applied Mathematical and Computational Sciences
- Date degree season
- Summer 2022
- Publisher
- University of Iowa
- DOI
- 10.25820/etd.006638
- Number of pages
- xi, 114 pages
- Copyright
- Copyright 2022 Michael Kratochvil
- Language
- English
- Description illustrations
- illustrations
- Description bibliographic
- Includes bibliographical references (pages 110-114).
- Public Abstract (ETD)
Keeping the power grid operational is as important as it is complicated. On certain networks, rising population leads to increased power usage (called load). If the load becomes high enough, adding new power plants, wind farms, solar panels, and other sources of power generation and storage becomes necessary to maintain constant power flow. Further, if the region in which the power grid operates has certain climate change or pollution targets, using oil, coal, natural gas, and nuclear-based power plants may be not possible. This leaves storage and renewable sources as the possible sources to expand a power network with.
This thesis explores the modeling and optimization of expanding a power network when the available technologies to expand with are large-scale storage and/or wind farms. We determine the best amount and location of these devices on an existing power grid given their high cost to install. We do this by looking at different scenarios of renewable energy output and load on the network.
Setting up the model this way makes the problem very large. The more scenarios we use, the larger the problem is. In this thesis, we explore the computational limitations of this problem, as well as methods to break apart the problem by scenario to make the problem solvable. We also explore new methods to pick the best scenarios so that fewer are needed to solve. We then compare results under different expansion goals.
- Academic Unit
- Interdisciplinary Graduate Program in Applied Mathematical & Computational Sciences
- Record Identifier
- 9984285247202771
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