Title: Data-Driven Stochastic Optimization Approaches with Applications in Power Systems

Advisors: Dr. Shabbir Ahmed

               Dr. Nagi Gebraeel

Committee Members:
Dr. Santanu Dey 

Dr. Andy Sun

Dr. Siqian Shen (University of Michigan)

Date and Time: Tuesday, July 9th, 10:00 am
Location: Groseclose 226A

Abstract: 

In this thesis, we focus on data-driven stochastic optimization problems with an emphasis in power systems applications. On the one hand, we address the inefficiencies in maintenance and operations scheduling problems which emerge due to disregarding the uncertainties, and not utilizing statistical analysis methods. On the other hand, we develop a partially adaptive general purpose stochastic programming approach for effectively modeling and solving a class of problems in sequential decision-making.

In the first part of the thesis (Chapter 2 and Chapter 3), we consider maintenance and operations scheduling problem in power systems under uncertainty by leveraging data analytics. In Chapter 2, we develop a stochastic optimization framework for the integrated condition-based maintenance and operations scheduling problem with explicit consideration of sensor-driven unexpected failures. Our approach is based on a model that uses condition-based failure scenarios derived from the remaining lifetime distributions of the generators, as well as a chance constraint to ensure a reliable maintenance plan. The large number of failure scenarios are handled by a combination of sample average approximation and an enhanced scenario decomposition algorithm in a distributed framework. We introduce a number of algorithmic improvements by exploiting the polyhedral structure of the problem, utilizing its time decomposability, and an analysis of the transmission line capacities. Finally, we present a case study demonstrating the significant cost savings and computational benefits of the proposed framework. In Chapter 3, we focus on the tight coupling between the condition of the generators and corresponding operational schedules, significantly affecting reliability of the system. We effectively model and solve an integrated condition-based maintenance and operations scheduling problem for a fleet of generators with an explicit consideration of decision-dependent generator conditions. We propose a sensor-driven degradation framework with remaining lifetime estimation procedures under time varying load levels. We present estimation methods by adapting our model to the underlying signal variability. Then, we develop a stochastic optimization model that considers the effect of the operational decisions on the generators' degradation levels along with the uncertainty of the unexpected failures. As the resulting problem includes nonlinearities, we adopt piecewise linearization along with other linearization techniques and propose formulation enhancements to obtain a stochastic mixed-integer linear programming formulation. We develop a decision-dependent simulation framework for assessing the performance of a given solution. Finally, we present computational experiments demonstrating significant cost savings and reductions in failures in addition to highlighting computational benefits of the proposed approach.

In the second part of the thesis (Chapter 4), we focus on developing a new adaptive stochastic optimization approach for optimizing sequential decision-making processes under uncertainty, which is an inherently complex problem. Two-stage and multi-stage stochastic programming are fundamental techniques for modeling these processes, where stage refers to the decision times in planning. Although both approaches have their individual benefits and limitations, the resulting policies may not be sufficient to address a wide range of business settings due to the level of flexibility required in these processes. To address these settings and find a compromising solution, we propose a novel stochastic programming methodology, labeled as adaptive two-stage stochastic programming, in which the stage times are not predetermined but part of the optimization problem. We provide a generic formulation for the proposed approach under finite stochastic processes and prove that the problem is NP-Hard. We also demonstrate the value of this approach by deriving analytical bounds compared to two-stage and multi-stage stochastic programming methods on a special structure that encompasses various problems including capacity expansion planning. To solve the resulting problem, we develop algorithms with approximation guarantee. Our computational studies on sample generation expansion planning instances highlight the importance of the choice of the revision decisions and demonstrate the benefits of adopting the proposed approach from various perspectives