A robust multi-objective statistical improvement approach to electric power portfolio selection

Motivated by an electric power portfolio selection problem, a sampling method is developed for simulation-based robust design that builds on existing multi-objective statistical improvement methods. It uses a Bayesian surrogate model regressed on both design and noise variables, and makes use of methods for estimating epistemic model uncertainty in environmental uncertainty metrics. Regions of the design space are sequentially sampled in a manner that balances exploration of unknown designs and exploitation of designs thought to be Pareto optimal, while regions of the noise space are sampled to improve knowledge of the environmental uncertainty. A scalable test problem is used to compare the method with design of experiments (DoE) and crossed array methods, and the method is found to be more efficient for restrictive sample budgets. Experiments with the same test problem are used to study the sensitivity of the methods to numbers of design and noise variables. Lastly, the method is demonstrated on an electric power portfolio simulation code.PhDCommittee Chair: Mavris, Dimitri; Committee Member: Duncan, Scott; Committee Member: Ender, Tommer; Committee Member: German, Brian; Committee Member: Paredis, Chri

Offtake Strategy Design for Wind Energy Projects under Uncertainty

Energy use from wind, solar, and other renewable sources is a public policy at the federal and state levels to address environment, energy, and sustainability concerns. As the cost of renewable energy is still relatively high compared to fossil fuels, it remains a critical challenge to make renewable energy cost competitive, without relying on public subsidies. During recent years, much advance has been made in our understanding of technology innovations and cost structure optimization of renewable energy. A knowledge gap exists on the other side of the equation - revenue generation. Considering the complexity and stochastic nature of renewable energy projects, there is great potential to optimize the revenue generation mechanisms in a systematic fashion for improved profitability and growth. This dissertation examines two primary revenue generation mechanisms, or offtake strategies, used in wind energy development projects in the U.S. While a short-term offtake strategy allows project developers to benefit from price volatility in the wholesale spot market for profit maximization, a long-term offtake strategy minimizes the market risk exposure through a long-term Power Purchase Agreement (PPA). With Conditional Value-at-Risk (CVaR) introduced as a risk measure, this dissertation first develops two stochastic programming models for optimizing offtake designs under short and long-term strategies respectively. Furthermore, this study also proposes a hybrid offtake strategy that combines both short and long-term strategies. The two-level stochastic model demonstrates the merit of the hybrid strategy, i.e. obtaining the maximized profit while maintaining the flexibility of balancing and hedging against market and resource risks efficiently. The Cape Wind project in Massachusetts has been used as an example to demonstrate the model validity and potential applications in optimizing its revenue streams. The analysis shows valuable implications on the optimal design of renewable energy project development in regard to offtake arrangements

Robust optimization methods for chance constrained, simulation-based, and bilevel problems

The objective of robust optimization is to find solutions that are immune to the uncertainty of the parameters in a mathematical optimization problem. It requires that the constraints of a given problem should be satisfied for all realizations of the uncertain parameters in a so-called uncertainty set. The robust version of a mathematical optimization problem is generally referred to as the robust counterpart problem. Robust optimization is popular because of the computational tractability of the robust counterpart for many classes of uncertainty sets, and its applicability in wide range of topics in practice. In this thesis, we propose robust optimization methodologies for different classes of optimization problems. In Chapter 2, we give a practical guide on robust optimization. In Chapter 3, we propose a new way to construct uncertainty sets for robust optimization using the available historical data information. Chapter 4 proposes a robust optimization approach for simulation-based optimization problems. Finally, Chapter 5 proposes approximations of a specific class of robust and stochastic bilevel optimization problems by using modern robust optimization techniques

Metamodel-based inverse uncertainty quantification of nuclear reactor simulators under the Bayesian framework

Mathematical modeling and computer simulations have long been the central technical topics in practically all branches of science and technology. Tremendous progress has been achieved in revealing quantitative connections between numerical predictions and real-world observations. However, because computer models are reduced representations of the real phenomena, there are always discrepancies between ideal in silico designed systems and real-world manufactured ones. As a consequence, uncertainties must be quantified along with the simulation outputs to facilitate optimal design and decision making, ensure robustness, performance or safety margins. Forward uncertainty propagation requires knowledge in the statistical information for computer model random inputs, for example, the mean, variance, Probability Density Functions (PDFs), upper and lower bounds, etc. Historically, ``expert judgment'' or ``user self-evaluation'' have been used to specify the uncertainty information associated with random input parameters. Such ad hoc characterization is unscientific and lacks mathematical rigor. In this thesis, we attempt to solve such ``lack of uncertainty information'' issue with inverse Uncertainty Quantification (UQ). Inverse UQ is the process to seek statistical descriptions of the random input parameters that are consistent with available high-quality experimental data. We formulate the inverse UQ process under the Bayesian framework using the ``model updating equation''. Markov Chain Monte Carlo (MCMC) sampling is applied to explore the posterior distributions and generate samples from which we can extract statistical information for the uncertain input parameters. To greatly alleviate the computational burden during MCMC sampling, we used systematically and rigorously developed metamodels based on stochastic spectral techniques and Gaussian Processes (also known as Kriging) emulators. We demonstrated the developed methodology based on three problems with different levels of sophistication: (1) Point Reactor Kinetics Equation (PRKE) coupled with lumped parameter thermal-hydraulics feedback model based on synthetic experimental data; (2) best-estimate system thermal-hydraulics code TRACE physical model parameters based on OECD/NRC BWR Full-size Fine-Mesh Bundle Tests (BFBT) benchmark steady-state void fraction data; (3) fuel performance code BISON Fission Gas Release (FGR) model based on Risø-AN3 on-line time-dependent FGR measurement data. Metamodels constructed with generalized Polynomial Chaos Expansion (PCE), Sparse Gird Stochastic Collocation (SGSC) and GP were applied respectively for these three problems to replace the full models during MCMC sampling. We proposed an improved modular Bayesian approach that can avoid extrapolating the model discrepancy that is learnt from the inverse UQ domain to the validation/prediction domain. The improved approach is organized in a structure such that the posteriors achieved with data in inverse UQ domain is informed by data in the validation domain. Therefore, over-fitting can be avoided while extrapolation is not required. A sequential approach was also developed for test source allocation (TSA) for inverse UQ and validation. This sequential TSA methodology first select tests for validation that has a full coverage of the test domain to avoid extrapolation of model discrepancy term when evaluated at input setting of tests for inverse UQ. Then it select tests that tend to reside in the unfilled zones of the test domain for inverse UQ, so that inverse UQ can extract the most information for posteriors of calibration parameters using only a relatively small number of tests. The inverse UQ process successfully quantified the uncertainties associated with input parameters that are consistent with the experimental observations. The quantified uncertainties are necessary for future uncertainty and sensitivity study of nuclear reactor simulators in system design and safety analysis. We applied and extended several advanced metamodeling approaches to nuclear engineering practice to greatly reduce the computational cost. The current research bridges the gap between models and data by solving ``lack of uncertainty information'' issue, as well as providing guidance for improving nuclear reactor simulators through the validation process