Electric power is one of the most critical parts of everyday life; from lighting, heating,
and cooling homes to powering televisions and computers. The modern power grids
face several challenges such as efficiency, sustainability, and reliability. Increase in
electrical energy demand, distributed generations, integration of uncertain renewable
energy resources, and demand side management are among the main underlying reasons
of such growing complexity. Additionally, the elements of power systems are
often vulnerable to failures because of many reasons, such as system limits, poor
maintenance, human errors, terrorist/cyber attacks, and natural phenomena. One
common factor complicating the operation of electrical power systems is the underlying
uncertainties from the demands, supplies and failures of system components.
Stochastic optimization approaches provide mathematical frameworks for decision
making under uncertainty. It enables a decision maker to incorporate some knowledge
of the uncertainty into the decision making process to find an optimal trade
off between cost and risk. In this dissertation, we focus on application of three risk-averse
approaches to power systems modeling and optimization. Particularly, we
develop models and algorithms addressing the cost-effectiveness and reliability issues
in power grids with integrations of renewable energy resources.
First, we consider a unit commitment problem for centralized hydrothermal systems
where we study improving reliability of such systems under water inflow uncertainty.
We present a two-stage robust mixed-integer model to find optimal unit
commitment and economic dispatch decisions against extreme weather conditions
such as drought years. Further, we employ time series analysis (specifically vector
autoregressive models) to construct physical based uncertainty sets for water inflow
into the reservoirs. Since extensive formulation is impractical to solve for moderate size networks we develop an efficient Benders' decomposition algorithm to solve this problem. We present the numerical results on real-life case study showing the
effectiveness of the model and the proposed solution method.
Next, we address the cost effectiveness and reliability issues considering the integration
of solar energy in distributed (decentralized) generation (DG) such as microgrids.
In particular, we consider optimal placement and sizing of DG units as
well as long term generation planning to efficiently balance electric power demand
and supply. However, the intermittent nature of renewable energy resources such as
solar irradiance imposes several difficulties in decision making process. We propose
two-stage stochastic programming model with chance constraints to control the risk
of load shedding (i.e., power shortage) in distributed generation. We take advantage
of another time series modeling approach known as autoregressive integrated moving
average (ARIMA) model to characterize the uncertain solar irradiance more accurately.
Additionally, we develop a combined sample average approximation (SAA)
and linearization techniques to solve the problem more efficiently. We examine the
proposed framework with numerical tests on a radial network in Arizona.
Lastly, we address the robustness of strategic networks including power grids and
airports in general. One of the key robustness requirements is the connectivity between
each pair of nodes through a sufficiently short path, which makes a network
cluster more robust with respect to potential disruptions such as man-made or natural
disasters. If one can reinforce the network components against future threats, the goal
is to determine optimal reinforcements that would yield a cluster with minimum risk
of disruptions. We propose a risk-averse model where clusters represents a R-robust
2-club, which by definition is a subgraph with at least R node/edge disjoint paths
connecting each pair of nodes, where each path consists of at most 2 edges. And,
develop a combinatorial branch-and-bound algorithm to compare with an equivalent
mathematical programming approach on random and real-world networks.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/625660 |
| Date | January 2017 |
| Creators | Dashti, Hossein, Dashti, Hossein |
| Contributors | Krokhmal, Pavlo A., Krokhmal, Pavlo A., Cheng, Jianqiang, Jiang, Ruiwei, Zhang, Hao |
| Publisher | The University of Arizona. |
| Source Sets | University of Arizona |
| Language | en_US |
| Detected Language | English |
| Type | text, Electronic Dissertation |
| Rights | Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. |
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