Contingency-Constrained Unit Commitment with Post-Contingency Corrective Recourse

We consider the problem of minimizing costs in the generation unit commitment problem, a cornerstone in electric power system operations, while enforcing an N-k-e reliability criterion. This reliability criterion is a generalization of the well-known $N$-$k$ criterion, and dictates that at least $(1-e_ j)$ fraction of the total system demand must be met following the failures of $k$ or fewer system components. We refer to this problem as the Contingency-Constrained Unit Commitment problem, or CCUC. We present a mixed-integer programming formulation of the CCUC that accounts for both transmission and generation element failures. We propose novel cutting plane algorithms that avoid the need to explicitly consider an exponential number of contingencies. Computational studies are performed on several IEEE test systems and a simplified model of the Western US interconnection network, which demonstrate the effectiveness of our proposed methods relative to current state-of-the-art

Contingency-Constrained Unit Commitment With Intervening Time for System Adjustments

The N-1-1 contingency criterion considers the con- secutive loss of two components in a power system, with intervening time for system adjustments. In this paper, we consider the problem of optimizing generation unit commitment (UC) while ensuring N-1-1 security. Due to the coupling of time periods associated with consecutive component losses, the resulting problem is a very large-scale mixed-integer linear optimization model. For efficient solution, we introduce a novel branch-and-cut algorithm using a temporally decomposed bilevel separation oracle. The model and algorithm are assessed using multiple IEEE test systems, and a comprehensive analysis is performed to compare system performances across different contingency criteria. Computational results demonstrate the value of considering intervening time for system adjustments in terms of total cost and system robustness.Comment: 8 pages, 5 figure

The role of electron and phonon temperatures in the helicity-independent all-optical switching of GdFeCo

Ultrafast optical heating of the electrons in ferrimagnetic metals can result in all-optical switching (AOS) of the magnetization. Here we report quantitative measurements of the temperature rise of GdFeCo thin films during helicity-independent AOS. Critical switching fluences are obtained as a function of the initial temperature of the sample and for laser pulse durations from 55 fs to 15 ps. We conclude that non-equilibrium phenomena are necessary for helicity-independent AOS, although the peak electron temperature does not play a critical role. Pump-probe time-resolved experiments show that the switching time increases as the pulse duration increases, with 10 ps pulses resulting in switching times of ~sim 13 ps. These results raise new questions about the fundamental mechanism of helicity-independent AOS.Comment: 18 pages, 6 figures and supplementary material

Evaluation of Trace Alignment Quality and its Application in Medical Process Mining

Trace alignment algorithms have been used in process mining for discovering the consensus treatment procedures and process deviations. Different alignment algorithms, however, may produce very different results. No widely-adopted method exists for evaluating the results of trace alignment. Existing reference-free evaluation methods cannot adequately and comprehensively assess the alignment quality. We analyzed and compared the existing evaluation methods, identifying their limitations, and introduced improvements in two reference-free evaluation methods. Our approach assesses the alignment result globally instead of locally, and therefore helps the algorithm to optimize overall alignment quality. We also introduced a novel metric to measure the alignment complexity, which can be used as a constraint on alignment algorithm optimization. We tested our evaluation methods on a trauma resuscitation dataset and provided the medical explanation of the activities and patterns identified as deviations using our proposed evaluation methods.Comment: 10 pages, 6 figures and 5 table

Exponential Convergence of Sinkhorn Under Regularization Scheduling

In 2013, Cuturi [Cut13] introduced the Sinkhorn algorithm for matrix scaling as a method to compute solutions to regularized optimal transport problems. In this paper, aiming at a better convergence rate for a high accuracy solution, we work on understanding the Sinkhorn algorithm under regularization scheduling, and thus modify it with a mechanism that adaptively doubles the regularization parameter $\eta$ periodically. We prove that such modified version of Sinkhorn has an exponential convergence rate as iteration complexity depending on $\log(1/\varepsilon)$ instead of $\varepsilon^{-O(1)}$ from previous analyses [Cut13][ANWR17] in the optimal transport problems with integral supply and demand. Furthermore, with cost and capacity scaling procedures, the general optimal transport problem can be solved with a logarithmic dependence on $1/\varepsilon$ as well.Comment: ACDA23, 13 page

Models and Algorithms for Stochastic Network Design and Flow Problems: Applications in Truckload Procurement Auctions and Renewable Energy.

This dissertation presents novel mathematical models and algorithms for stochastic network design and flow (SNDF) problems: the optimal design and flow of a network under uncertainty to meet specific requirements while minimizing expected total cost. The focus of this dissertation is SNDF problems characterized by uncertainties in node supplies and/or demands and in arc capacities and/or costs. SNDF problems often have characteristics that render them difficult to model and computationally challenging to solve, including nonlinearities, probabilistic constraints, and stochastic parameters, all of which lead to large-scale, nonlinear, and discrete models. The work in this dissertation is motivated by problems in combinatorial truckload procurement auctions (CTPA) and wind farm network design (WFND). We use these two applications both for their own sake, as they present important and computationally challenging practical problems, and as a basis for the development of more general SNDF models and algorithmic approaches. In studying CTPA, we develop a novel bidding framework, the Implicit Bidding Approach (IBA), that permits the solution of fully-enumerated combinatorial auctions in a single round. Using IBA, we can circumvent the computational challenges of CTPAs by reposing the problem as a polynomially-sized integer multicommodity flow problem. We then extend our CTPA models to consider network uncertainties and show that the resulting model is a special case of a two-stage multicommodity flow problem (TS-MFP). We develop an efficient decomposition algorithm for solving problems in this class and provide extensive computational results to demonstrate its efficacy. In WFND, we present the integrated generation- and transmission- expansion planning problem for a network of interconnected wind farms. We develop an efficient decomposition algorithm for solving WFND problems and present computational results to demonstrate its efficacy. We then extend this model to include a probabilistic constraint on loss-of-load-expectation. We demonstrate that this model is extremely challenging and that direct applications of mathematical programming approaches are not viable. We present a hybrid algorithm, which we called Iterative Test-and-Prune (I-T&P), that leverages mathematical programming to solve a series of easy feasibility problems within a larger meta-search algorithm. Computational results for several test systems demonstrate the efficacy of I-T&P.Ph.D.Industrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/76005/1/richchen_1.pd