Uncertainty analysis of power systems using collocation

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2008.Includes bibliographical references (p. 93-97).The next-generation all-electric ship represents a class of design and control problems in which the system is too large to approach analytically, and even with many conventional computational techniques. Additionally, numerous environmental interactions and inaccurate system model information make uncertainty a necessary consideration. Characterizing systems under uncertainty is essentially a problem of representing the system as a function over a random space. This can be accomplished by sampling the function, where in the case of the electric ship a "sample" is a simulation with uncertain parameters set according to the location of the sample. For systems on the scale of the electric ship, simulation is expensive, so we seek an accurate representation of the system from a minimal number of simulations. To this end, collocation is employed to compute statistical moments, from which sensitivity can be inferred, and to construct surrogate models with which interpolation can be used to propagate PDF's. These techniques are applied to three large-scale electric ship models. The conventional formulation for the sparse grid, a collocation algorithm, is modified to yield improved performance. Theoretical bounds and computational examples are given to support the modification. A dimension-adaptive collocation algorithm is implemented in an unscented Kalman filter, and improvement over extended Kalman and unscented filters is seen in two examples.by Joshua Adam Taylor.S.M

Conic optimization of electric power systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 103-115).The electric power grid is recognized as an essential modern infrastructure that poses numerous canonical design and operational problems. Perhaps most critically, the inherently large scale of the power grid and similar systems necessitates fast algorithms. A particular complication distinguishing problems in power systems from those arising in other large infrastructures is the mathematical description of alternating current power flow: it is nonconvex, and thus excludes power systems from many frameworks benefiting from theoretically and practically efficient algorithms. However, advances over the past twenty years in optimization have led to broader classes possessing such algorithms, as well as procedures for transferring nonconvex problem to these classes. In this thesis, we approximate difficult problems in power systems with tractable, conic programs. First, we formulate a new type of NP-hard graph cut arising from undirected multicommodity flow networks. An eigenvalue bound in the form of the Cheeger inequality is proven, which serves as a starting point for deriving semidefinite relaxations. We next apply a lift-and-project type relaxation to transmission system planning. The approach unifies and improves upon existing models based on the DC power flow approximation, and yields new mixed-integer linear, second-order cone, and semidefinite models for the AC case. The AC models are particularly applicable to scenarios in which the DC approximation is not justified, such as the all-electric ship. Lastly, we consider distribution system reconfiguration. By making physically motivated simplifications to the DistFlow equations, we obtain mixed-integer quadratic, quadratically constrained, and second-order cone formulations, which are accurate and efficient enough for near-optimal, real-time application. We test each model on standard benchmark problems, as well as a new benchmark abstracted from a notional shipboard power system. The models accurately approximate the original formulations, while demonstrating the scalability required for application to realistic systems. Collectively, the models provide tangible new tradeoffs between computational efficiency and accuracy for fundamental problems in power systems.by Joshua Adam Taylor.Ph.D

Transmission Expansion Planning Using Cycle Flows

The common linear optimal power flow (LOPF) formulation that underlies most transmission expansion planning (TEP) formulations uses bus voltage angles as auxiliary optimization variables to describe Kirchhoff's voltage law. As well as introducing a large number of auxiliary variables, the angle-based formulation has the disadvantage that it is not well-suited to considering the connection of multiple disconnected networks, It is, however, possible to circumvent these auxiliary variables and reduce the required number of constraints by expressing Kirchhoff's voltage law directly in terms of the power flows, based on a cycle decomposition of the network graph. In computationally challenging benchmarks such as generation capacity expansion with multi-period LOPF, this equivalent reformulation was shown in previous work to reduce solving times for LOPF problems by an order of magnitude. Allowing line capacity to be co-optimized in a discrete TEP problem makes it a non-convex mixed-integer problem. This paper develops a novel cycle-based reformulation for the TEP problem with LOPF and compares it to the standard angle-based formulation. The combinatorics of the connection of multiple disconnected networks is formalized for both formulations, a topic which has not received attention in the literature. The cycle-based formulation is shown to conveniently accommodate synchronization options. Since both formulations use the big-$M$ disjunctive relaxation, useful derivations for suitable big-$M$ values are provided. The competing formulations are benchmarked on a realistic generation and transmission expansion model of the European transmission system at varying spatial and temporal resolutions. The cycle-based formulation solves up to 31 times faster for particular cases, while averaging at a speed-up of factor 4.Comment: Accepted for ACM e-Energy 2020, 11 pages, 12 Figures, 2 Table

Carbon Free Boston: Buildings Technical Report

Part of a series of reports that includes: Carbon Free Boston: Summary Report; Carbon Free Boston: Social Equity Report; Carbon Free Boston: Technical Summary; Carbon Free Boston: Transportation Technical Report; Carbon Free Boston: Waste Technical Report; Carbon Free Boston: Energy Technical Report; Carbon Free Boston: Offsets Technical Report; Available at http://sites.bu.edu/cfb/OVERVIEW: Boston is known for its historic iconic buildings, from the Paul Revere House in the North End, to City Hall in Government Center, to the Old South Meeting House in Downtown Crossing, to the African Meeting House on Beacon Hill, to 200 Clarendon (the Hancock Tower) in Back Bay, to Abbotsford in Roxbury. In total, there are over 86,000 buildings that comprise more than 647 million square feet of area. Most of these buildings will still be in use in 2050. Floorspace (square footage) is almost evenly split between residential and non-residential uses, but residential buildings account for nearly 80,000 (93 percent) of the 86,000 buildings. Boston’s buildings are used for a diverse range of activities that include homes, offices, hospitals, factories, laboratories, schools, public service, retail, hotels, restaurants, and convention space. Building type strongly influences energy use; for example, restaurants, hospitals, and laboratories have high energy demands compared to other commercial uses. Boston’s building stock is characterized by thousands of turn-of-the-20th century homes and a postWorld War II building boom that expanded both residential buildings and commercial space. Boston is in the midst of another boom in building construction that is transforming neighborhoods across the city. [TRUNCATED]Published versio

The FENIKS Survey: Spectroscopic Confirmation of Massive Quiescent Galaxies at z ~ 3-5

The measured ages of massive, quiescent galaxies at $z\sim 3-4$ imply that massive galaxies quench as early as $z\sim 6$. While the number of spectroscopic confirmations of quiescent galaxies at $z < 3$ has increased over the years, there are only a handful at $z > 3.5$. We report spectroscopic redshifts of one secure ($z=3.757$) and two tentative ($z = 3.336$, $z=4.673$) massive ($\log(M_\ast/M_\odot) > 10.3$) quiescent galaxies with 11 hours of Keck/MOSFIRE $K$-band observations. Our candidates were selected from the FENIKS survey, which uses deep Gemini/Flamingos-2 $K_b$ $K_r$ imaging optimized for increased sensitivity to the characteristic red colors of galaxies at $z > 3$ with strong Balmer/4000 \AA\ breaks. The rest-frame $UVJ$ and $(ugi)_s$ colors of 3/4 quiescent candidates are consistent with $1-2$ Gyr old stellar populations. This places these galaxies as the oldest objects at these redshifts, and challenges the notion that quiescent galaxies at $z > 3$ are all recently-quenched, "post-starburst'' galaxies. Our spectroscopy shows that the other quiescent-galaxy candidate is a broad-line AGN ($z = 3.594$) with strong, redshifted $H\beta$+[O III] emission with a velocity offset $>1000$ km/s, indicative of a powerful outflow. The star-formation history of our highest redshift candidate suggests that its progenitor was already in place by $z \sim 7-11$, reaching $\sim$ 10$^{11} M_{\odot}$ by $z \simeq 10$. These observations reveal the limit of what is possible with deep near-infrared photometry and targeted spectroscopy from the ground and demonstrate that secure spectroscopic confirmation of quiescent galaxies at $z > 4$ is only feasible with JWST.Comment: 20 pages, 11 figures, submitted to Ap

Reevaluating the evidence for a Hadean-Eoarchean dynamo.

The time of origin of the geodynamo has important implications for the thermal evolution of the planetary interior and the habitability of early Earth. It has been proposed that detrital zircon grains from Jack Hills, Western Australia, provide evidence for an active geodynamo as early as 4.2 billion years (Ga) ago. However, our combined paleomagnetic, geochemical, and mineralogical studies on Jack Hills zircons indicate that most have poor magnetic recording properties and secondary magnetization carriers that postdate the formation of the zircons. Therefore, the existence of the geodynamo before 3.5 Ga ago remains unknown

Reevaluating the evidence for a Hadean-Eoarchean dynamo

The time of origin of the geodynamo has important implications for the thermal evolution of the planetary interior and the habitability of early Earth. It has been proposed that detrital zircon grains from Jack Hills, Western Australia, provide evidence for an active geodynamo as early as 4.2 billion years (Ga) ago. However, our combined paleomagnetic, geochemical, and mineralogical studies on Jack Hills zircons indicate that most have poor magnetic recording properties and secondary magnetization carriers that postdate the formation of the zircons. Therefore, the existence of the geodynamo before 3.5 Ga ago remains unknown