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.

DESIGN, FABRICATION, AND PERFORMANCE CHARACTERIZATION OF MULTIFUNCTIONAL STRUCTURES TO HARVEST SOLAR ENERGY FOR FLAPPING WING AERIAL VEHICLES

Flapping Wing Aerial Vehicles (FWAVs) have the capability to combine the benefits of both fixed wing vehicles and rotary vehicles. However, flight time is limited due to limited on-board energy storage capacity. For most Unmanned Aerial Vehicle (UAV) operators, frequent recharging of the batteries is not ideal due to lack of nearby electrical outlets. This imposes serious limitations on FWAV flights. The approach taken to extend the flight time of UAVs was to integrate photovoltaic solar cells onto different structures of the vehicle to harvest and use energy from the sun. Integration of the solar cells can greatly improve the energy capacity of an UAV; however, this integration does effect the performance of the UAV and especially FWAVs. The integration of solar cells affects the ability of the vehicle to produce the aerodynamic forces necessary to maintain flight. This PhD dissertation characterizes the effects of solar cell integration on the performance of a FWAV. Robo Raven, a recently developed FWAV, is used as the platform for this work. An additive manufacturing technique was developed to integrate photovoltaic solar cells into the wing and tail structures of the vehicle. An approach to characterizing the effects of solar cell integration to the wings, tail, and body of the UAV is also described. This approach includes measurement of aerodynamic forces generated by the vehicle and measurements of the wing shape during the flapping cycle using Digital Image Correlation. Various changes to wing, body, and tail design are investigated and changes in performance for each design are measured. The electrical performance from the solar cells is also characterized. A new multifunctional performance model was formulated that describes how integration of solar cells influences the flight performance. Aerodynamic models were developed to describe effects of solar cell integration force production and performance of the FWAV. Thus, performance changes can be predicted depending on changes in design. Sensing capabilities of the solar cells were also discovered and correlated to the deformation of the wing. This demonstrated that the solar cells were capable of: (1) Lightweight and flexible structure to generate aerodynamic forces, (2) Energy harvesting to extend operational time and autonomy, (3) Sensing of an aerodynamic force associated with wing deformation. Finally, different flexible photovoltaic materials with higher efficiencies are investigated, which enable the multifunctional wings to provide enough solar power to keep the FWAV aloft without batteries as long as there is enough sunlight to power the vehicle.

MULTI-BAND BOSE HUBBARD MODELS AND EFFECTIVE THREE-BODY INTERACTIONS

Experiments with ultracold atoms in optical lattice have become a versatile testing ground to study diverse quantum many-body Hamiltonians. A single-band Bose-Hubbard (BH) Hamiltonian was first proposed to describe these systems in 1998 and its associated quantum phase-transition was subsequently observed in 2002. Over the years, there has been a rapid progress in experimental realizations of more complex lattice geometries, leading to more exotic BH Hamiltonians with contributions from excited bands, and modified tunneling and interaction energies. There has also been interesting theoretical insights and experimental studies on “un- conventional” Bose-Einstein condensates in optical lattices and predictions of rich orbital physics in higher bands. In this thesis, I present our results on several multi- band BH models and emergent quantum phenomena. In particular, I study optical lattices with two local minima per unit cell and show that the low energy states of a multi-band BH Hamiltonian with only pairwise interactions is equivalent to an effec- tive single-band Hamiltonian with strong three-body interactions. I also propose a second method to create three-body interactions in ultracold gases of bosonic atoms in a optical lattice. In this case, this is achieved by a careful cancellation of two contributions in the pair-wise interaction between the atoms, one proportional to the zero-energy scattering length and a second proportional to the effective range. I subsequently study the physics of Bose-Einstein condensation in the second band of a double-well 2D lattice and show that the collision aided decay rate of the con- densate to the ground band is smaller than the tunneling rate between neighboring unit cells. Finally, I propose a numerical method using the discrete variable repre- sentation for constructing real-valued Wannier functions localized in a unit cell for optical lattices. The developed numerical method is general and can be applied to a wide array of optical lattice geometries in one, two or three dimensions.