Multi-level, Multi-stage and Stochastic Optimization Models for Energy Conservation in Buildings for Federal, State and Local Agencies

Energy Conservation Measure (ECM) project selection is made difficult given real-world constraints, limited resources to implement savings retrofits, various suppliers in the market and project financing alternatives. Many of these energy efficient retrofit projects should be viewed as a series of investments with annual returns for these traditionally risk-averse agencies. Given a list of ECMs available, federal, state and local agencies must determine how to implement projects at lowest costs. The most common methods of implementation planning are suboptimal relative to cost. Federal, state and local agencies can obtain greater returns on their energy conservation investment over traditional methods, regardless of the implementing organization. This dissertation outlines several approaches to improve the traditional energy conservations models. Any public buildings in regions with similar energy conservation goals in the United States or internationally can also benefit greatly from this research. Additionally, many private owners of buildings are under mandates to conserve energy e.g., Local Law 85 of the New York City Energy Conservation Code requires any building, public or private, to meet the most current energy code for any alteration or renovation. Thus, both public and private stakeholders can benefit from this research. The research in this dissertation advances and presents models that decision-makers can use to optimize the selection of ECM projects with respect to the total cost of implementation. A practical application of a two-level mathematical program with equilibrium constraints (MPEC) improves the current best practice for agencies concerned with making the most cost-effective selection leveraging energy services companies or utilities. The two-level model maximizes savings to the agency and profit to the energy services companies (Chapter 2). An additional model presented leverages a single congressional appropriation to implement ECM projects (Chapter 3). Returns from implemented ECM projects are used to fund additional ECM projects. In these cases, fluctuations in energy costs and uncertainty in the estimated savings severely influence ECM project selection and the amount of the appropriation requested. A risk aversion method proposed imposes a minimum on the number of “of projects completed in each stage. A comparative method using Conditional Value at Risk is analyzed. Time consistency was addressed in this chapter. This work demonstrates how a risk-based, stochastic, multi-stage model with binary decision variables at each stage provides a much more accurate estimate for planning than the agency’s traditional approach and deterministic models. Finally, in Chapter 4, a rolling-horizon model allows for subadditivity and superadditivity of the energy savings to simulate interactive effects between ECM projects. The approach makes use of inequalities (McCormick, 1976) to re-express constraints that involve the product of binary variables with an exact linearization (related to the convex hull of those constraints). This model additionally shows the benefits of learning between stages while remaining consistent with the single congressional appropriations framework.

MULTI-UNIT ACCIDENT CONTRIBUTIONS TO U.S. NUCLEAR REGULATORY COMMISSION QUANTITATIVE HEALTH OBJECTIVES: A SAFETY GOAL POLICY ANALYSIS USING MODELS FROM STATE-OF-THE-ART REACTOR CONSEQUENCE ANALYSES

The U.S. Nuclear Regulatory Commission implemented a safety goal policy in response to the 1979 Three Mile Island accident. This policy addresses the question “How safe is safe enough?” by specifying quantitative health objectives (QHOs) for comparison with results from nuclear power plant (NPP) probabilistic risk analyses (PRAs) to determine whether proposed regulatory actions are justified based on potential safety benefit. Lessons learned from recent operating experience—including the 2011 Fukushima accident—indicate that accidents involving multiple units at a shared site can occur with non-negligible frequency. Yet risk contributions from such scenarios are excluded by policy from safety goal evaluations—even for the nearly 60% of U.S. NPP sites that include multiple units. This research develops and applies methods for estimating risk metrics for comparison with safety goal QHOs using models from state-of-the-art consequence analyses to evaluate the effect of including multi-unit accident risk contributions in safety goal evaluations.