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At least 73 records · Page 4

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DOE OSTI2023

A hybrid data-driven and model-based approach for computationally efficient stochastic unit commitment and economic dispatch under wind and solar uncertainty

Stochastic unit commitment (UC) and economic dispatch (ED) are imperative in dealing with uncertainty in renewable forecast for power system operation and planning such that the overall expected production cost is minimized over the planning horizon. However, accurate calculation of the expected production cost requires assessment of a very large number of different scenarios of uncertain renewable resources, such as solar and wind, which is practically infeasible to simulate in real time. This article proposes a hybrid datadriven and physics-based model-predictive paradigm to efficiently solve for stochastic unit commitment and economic dispatch considering uncertainty in wind and solar power forecasts. Here, the novelty of the approach lies in decoupling the production cost estimation from the unit commitment and economic dispatch optimization problems under uncertainty without compromising on the fidelity of the solutions. A data-driven machine learning model is first developed to predict the mean optimal production cost. A physics-based inverse problem is then solved to get the stochastic UC and ED profiles from the expected cost. The presented approach considers, for the first time, solar uncertainty in UC/ED determination and enables efficient and accurate propagation of wind and solar uncertainty to estimate the statistics of the production cost. The effectiveness of the developed approach is demonstrated systematically on a stylized RTS-GMLC single-node system. The overall framework predicts the expected cost 62.5% more accurately than the existing state-of-the-art, on unforeseen days during the entire year, and yields, for the first time, the associated physically consistent UC and ED profiles. The solutions are also shown to be flexible in providing adequate daily reserves to address any statistical deviations from probabilistic power forecasts. The computational time associated with the presented method is only about 10 s compared to over 24 h needed for a conventional stochastic UC/ED determination under uncertainty on an Intel Core i9 processor with 32 GB of RAM.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2022

Atomistic and cluster dynamics modeling of fission gas (Xe) diffusivity in TRISO fuel kernels

TRISO fuel particles are candidates for use in next generation reactors including gas reactors, fluoride salt-cooled high temperature reactors, and micro-reactors. The UCO fuel kernel consists of a uranium dioxide (UO) and uranium carbide mixture. The addition of UC helps suppress the formation of carbon monoxide gas, which led to failures during initial TRISO development. The addition of uranium carbide alters the chemistry of the UO kernel, which is known to influence performance parameters such as fission gas diffusivity, although the impact has not been quantified and no models exist that take the change in chemistry into account. Therefore, better understanding and more accurate models of the impact of chemistry on fuel performance are of high priority. In this paper, a first-principles density functional theory (DFT) and empirical potential based multi-scale study has been carried out to model the diffusivity of fission gas xenon (Xe) in UCO TRISO fuel kernels. The focus is on the UO component in the UCO fuel kernels, as that represents the largest volume fraction of the fuel kernels. The study relies on DFT and empirical potential calculations to determine Xe and point defect properties, which are then used in thermodynamic and kinetic models to predict diffusion for intrinsic conditions. In addition, the information is utilized in cluster dynamics simulations using the Centipede code to estimate the impact of irradiation on defect transport. Additionally, the presence of UC or UC in the UCO fuel kernels is shown to have a substantial impact on the UO non-stoichiometry by inducing oxygen vacancies and driving UO sub-stoichiometric, which causes much slower Xe diffusion in UCO compared to light water reactor UO fuel. The application of this model in fuel performance simulations using the Bison code is also demonstrated.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Disentangling error structures of precipitation datasets using decision trees

Characterizing error structures in precipitation products not only facilitates their proper applications for scientific and practical purposes but also helps improve their retrieval algorithms and processing methods. Despite the fact that multiple precipitation products have been assessed in the literature, factors that affect their error structures remain inadequately addressed. By interpreting 60 binary decision trees, this study disentangles the error characteristics of precipitation products in terms of their spatiotemporal patterns and geographical factors. Three independent precipitation products - two satellite-based and one reanalysis datasets: the Integrated Multi-satellitE Retrievals for GPM (Global Precipitation Measurement) late run (IMERG-L), Soil Moisture to Rain-Advanced SCATterometer (SM2RAIN-ASCAT), and the Modern-Era Retrospective analysis for Research and Applications, Version 2 uncorrected precipitation output (MERRA2-UC), are evaluated across the contiguous United States from 2010 to 2019. Here, the ground-based Stage IV precipitation dataset is used as the ground truth. Results indicate that the MERRA2-UC outperforms the IMERG-L and SM2RAIN-ASCAT with higher accuracy and more stable interannual patterns for the analysis period. Decision trees cross-assess three spatiotemporal factors and find that the underestimation of MERRA2-UC occurs in the east of the Rocky Mountains, and SM2RAIN-ASCAT underestimates precipitation over high latitudes, especially in winter. Additionally, the decision tree method ascribes system errors to nine different geographical characteristics, of which the distance to the coast, soil type, and DEM are the three dominant features. On the other hand, the land cover type, topography position index, and aspect are three relatively weak factors.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Indole-3-carbinol ameliorates necroptosis and inflammation of intestinal epithelial cells in mice with ulcerative colitis by activating aryl hydrocarbon receptor

Highlights: • AHR activated by I3C plays an important role in protecting IECs from necroptosis and inflammation, in vivo and in vitro. • AHR could ubiquitinate RIPK1, promote IAPs expression and inhibit NF-κB activation in NCM460 cells. • I3C is a good candidate as a natural product to prevent and treat UC. Ulcerative colitis (UC) is a disease characterized by inflammation and disruption of the intestinal epithelial barrier. Necroptosis plays a critical role in disease progression. Indole-3-carbinol (I3C), a natural dietary agonist of aryl hydrocarbon receptor (AHR), has shown alleviating effects on UC. However, its mechanisms of action have not been comprehensively elucidated. Therefore, we aimed at investigating the protective role of I3C in DSS-induced colitis mice models. I3C significantly ameliorated body weight loss, colon length shortening and colonic pathological damage in colitis mice, reduced disease activity index (DAI) and histological (HI) scores, as well as alleviated colonic necroptosis and inflammation. In vitro, I3C attenuated necroptosis and inflammation of colonoids and NCM460 cells. AHR, activated by I3C, inhibits activation of receptor-interacting protein kinase 1 (RIPK1) and the subsequent assembly of necrosome in a time-dependent manner, as well as suppressing NF-κB activation and decreasing TNF-α, IL-1β, IL-6 and IL-8 expression. Silencing of AHR aggravated necroptosis and inflammation of NCM460 cells, and did not be ameliorated by I3C. Furthermore, AHR activation induces the expression of inhibitor of apoptosis proteins (IAPs) and the ubiquitination of RIPK1. In conclusion, I3C exerts a protective effect in DSS-induced colitis mice models by alleviating the necroptosis and inflammation of IECs through activating AHR.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2020

Photochemical Upconversion in Water Using Cu(I) MLCT Excited States: Role of Energy Shuttling at the Micellar/Water Interface

Photochemical upconversion (UC) through triplet–triplet annihilation (TTA), which employs a visible absorbing triplet photosensitizer and an annihilator, is a process that generates a high energy photon from two lower energy photons. TTA-UC has been largely developed in pure organic solvents and solid-state polymeric constructs while featuring near exclusive use of rare and expensive metals within the photosensitizer. In this current investigation, we demonstrate that TTA-UC from the long lifetime earth-abundant photosensitizer [Cu(dsbtmp) 2 ](PF) 6 (dsbtmp = 2,9-di(sec-butyl)-3,4,7,8-tetramethyl-1,10-phenanthroline), abbreviated as Cu-PS, functions in water through encapsulation within a cationic-based assembly. Cetyltrimethylammonium bromide was the surfactant of choice as it electrostatically binds the negatively charged water-soluble 10-phenylanthracene-9-carboxylate (PAC) acceptor/annihilator and ultimately facilitates energy transfer across the interface. Efficient triplet–triplet energy transfer (TTET) from Cu-PS to the PAC acceptor was achieved in this aqueous assembly. Unfortunately, the hindered mobility of the PAC moieties ultimately hampered the annihilation process, and this was reflected in attenuated TTA rates and efficiencies. The combined experimental data illustrated that the water-soluble PAC acceptor was able to vectorially deliver the excited-state energy stored in Cu-PS across the interface into the bulk aqueous solution by engaging in excited-state electron transfer with methyl viologen acceptors. Lastly, these results are important for remotely operating photoredox reactions in water while rendering a photosensitizer spatially isolated in the hydrophobic core of a micelle.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Understanding the interface interaction between U3Si2 fuel and SiC cladding

Abstract Triuranium disilicide (U 3 Si 2 ) fuel with silicon carbide (SiC) composite cladding is being considered as an advanced concept/accident tolerant fuel for light water reactors thus, understanding their chemical compatibility under operational and accident conditions is paramount. Here we provide a comprehensive view of the interaction between U 3 Si 2 and SiC by utilizing density functional theory calculations supported by diffusion couple experiments. From the calculated reaction energies, we demonstrate that triuranium pentasilicide (U 3 Si 5 ), uranium carbide (UC), U 20 Si 16 C 3 , and uranium silicide (USi) phases can form at the interface. A detailed study of U 3 Si 2 and SiC defect formation energies of the equilibrated materials yielding the interfacial phases U 20 Si 16 C 3 , U 3 Si 5 and UC reveal a thermodynamic driving force for generating defects in both fuel and cladding. The absence of either the U 3 Si 2 or SiC phase, however, causes the defect formation energies in the other phase to be positive, removing the driving force for additional interfacial reactions. The diffusion couple experiments confirm the conclusion with demonstrated restricted formation of U 3 Si 5 , UC, and U 20 Si 16 C 3 /USi phases at the interface. The resulting lack of continuous interaction between the U 3 Si 2 and SiC, reflects the diminishing driving force for defect formation, demonstrating the substantial stability of this fuel-cladding system.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Dynamic soil columns simulate Arctic redox biogeochemistry and carbon release during changes in water saturation

Thawing Arctic permafrost can induce hydrologic change and alter redox conditions, shifting the balance of soil organic matter (SOM) decomposition. There remains uncertainty about how soil saturation and redox transitions impact dissolved and gas phase carbon fluxes, and efforts to link hydrobiogeochemical processes to ecosystem-scale models are limited. This study evaluates SOM decomposition of Arctic tundra soils using column experiments, water chemistry measurements, microbial community analysis, and a PFLOTRAN reactive transport model. Soil columns from a thermokarst channel (TC) and an upland tundra (UC) were exposed to cycles of saturation and drainage, which controlled carbon emissions. During saturation, an outflow of dissolved organic carbon from the UC soil correlated with elevated reduced iron and decreased pH; during drainage, UC carbon dioxide fluxes were 70% higher than TC fluxes. Intermittent methane release was observed for TC, consistent with higher methanogen abundance. Slower drainage in the TC soil correlated with more subtle biogeochemical changes. PFLOTRAN simulations captured experimental trends in soil carbon fluxes, oxygen concentrations, and water contents. The model was then used to evaluate additional soil water drainage rates. This study emphasizes the importance of considering hydrologic change when evaluating and simulating SOM decomposition in dynamic Arctic tundra environments.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

User-Centric Communication With Aerial Network for 6G: A Reinforcement Learning Approach

Meeting the diverse needs of user verticals requires innovative cellular architectures that can offer additional degrees of freedom to provide on-demand services. The terrestrial user-centric radio access network (UC-RAN) stands out as an excellent choice for this purpose. However, a drawback of UC-RAN is its tendency to prioritize high-priority verticals, often resulting in a subpar quality of experience for low-priority verticals. This issue is particularly exacerbated in hotspot areas. Here, to address this problem, we introduce an aerial network integrated with terrestrial UC-RAN to provide coverage to users which are not served by the terrestrial network. Furthermore, we analyze the impact of key configuration and optimization parameters (COPs), such as location, transmit power, altitude, and beamwidth of aerial base stations (ABSs) on system key performance indicators (KPIs), such as coverage, latency satisfaction, average spectral efficiency, and energy efficiency. We formulate a robust multiobjective function to maximize these KPIs without biasing toward any specific KPI(s). Finally, we propose a deep reinforcement learning optimization framework based on the state-of-the-art soft actor-critic algorithm to control ABS COPs and optimize system KPIs. Experimental evaluations demonstrate that the proposed optimization framework can converge to near-optimal solutions derived from the pseudo brute force in a few thousand epochs.

6G↗

DOE OSTI2025

Risk-Aware Reinforcement Learning Framework for User-Centric O-RAN

The evolution of Open Radio Access Networks (O-RAN) presents an opportunity to enhance network performance by enabling dynamic orchestration of configuration and optimization parameters (COPs) through online learning methods. However, leveraging this potential requires overcoming the limitations of traditional cell-centric RAN architectures, which lack the necessary flexibility. On the other hand, despite their recent popularity, the practical deployment of online learning frameworks, such as Deep Reinforcement Learning (DRL)-based COP optimization solutions, remains limited due to their risk of deteriorating network performance during the exploration phase. In this article, we propose and analyze a novel risk-aware DRL framework for user-centric RAN (UC-RAN), which offers both the architectural flexibility and COP optimization to exploit this flexibility. We investigate and identify UC-RAN COPs that can be optimized via a soft actor-critic algorithm implementable as an O-RAN application (rApp) to jointly maximize latency satisfaction, reliability satisfaction, area spectral efficiency, and energy efficiency. We use the offline learning on UC-RAN to reliably accelerate DRL training, thus minimizing the risk of DRL deteriorating cellular network performance. Results show that our proposed solution approaches near-optimal performance in just a few hundred iterations with a decrease in risk score by a factor of ten.

6G and beyond↗

DOE OSTI2023

A Predictive Prescription Framework for Stochastic Unit Commitment Using Boosting Ensemble Learning Algorithms

To take unit commitment (UC) decisions under uncertain load, most existing stochastic optimization (SO) frameworks adopt a generic representation of uncertainty. While load levels that materialize on a particular day are influenced by various covariates (such as the day of the week or temperature), SO frameworks typically disregard such side observations, wasting actionable information that could significantly enhance decision quality. Here, this article proposes a contextual SO (CSO) framework for UC under uncertain load, which can effectively exploit covariate observations in conjunction with a class of machine learning (ML) algorithms to improve the out-of-sample performance of UC decisions. It shows how three ML algorithms, adaptive boosting, gradient boosted trees, and extreme gradient boosting, can be used to this end, constituting the first application of these algorithms in any CSO framework. Using real-world data harvested from the New York ISO grid, we measure the out-of-sample performance of the framework in terms of total operation cost, shed load values, locational marginal prices, and total payments by the loads, against several benchmark methods proposed in the literature. The article has an online companion (Yurdakul et al.), wherein we present additional results and lay out further mathematical formulations used in this work.

42 ENGINEERING↗

DOE OSTI2022

JET EROSION OF PARTICLE BEDS: PROJECTING CRITICAL SUSPENSION VELOCITIES FROM EFFECTIVE CLEARING / CLEANING RADII

Here we explore the relationship between effective cleaning/clearing radii, ECR, and critical suspension velocities, Ucs. Although one set of physics controls both the radial extent of erosion (i.e., the ECR) and the velocity needed to erode from the center of jet impingement to any given location (i.e., Ucs, typically defined from nozzle center to the vessel center), the relationship between these two remains unexplored quantitatively. Here we advance the model of Kuhn, et al., (PNNL-22816, 2013) as described by Pease, et al. (FEDSM2017-69444, 2017) to evaluate the relationship between the effective clearing/cleaning radius and the nozzle velocity on flat surfaces including flat bottomed vessels. Two governing dimensionless groups are identified. We present both a closed form analytical but transcendental solution and a non-iterative approximation modeled after the Serghides approximation of Colebrook’s nonlinear equation for both ECR versus nozzle velocity and Ucs. Comparison of the model to data from flume testing on a flat surface finds reasonable agreement.

jet, erosion, critical suspension velocity, effect↗

DOE OSTI2024

Average Incremental Cost Pricing for the AC Unit Commitment Problem [Rev. 1]

Unit Commitment (UC) problems that consider the Alternating Current (AC) model of the transmission network have long been considered intractable to solve at scale by the power system community. Recently, the Grid-Optimization (GO) Competition held by the Advanced Research Project Agency-Energy (ARPA-E) has facilitated the development of the first algorithms to solve large-scale ACUC problems. This new capability opens a path towards the explicit consideration of the AC transmission network model in UC problems used to clear day-ahead electricity markets. This calls for the analysis of electricity market structures that accommodate both the continuous non-linearity of the AC transmission network and the discrete non-linearity of the UC problem simultaneously. This paper serves as an initial effort to do so by proposing an Average Incremental Cost (AIC) pricing structure that is designed around the ACUC problem. In particular, an AIC one-pass pricing problem is proposed that represents a continuously constrained variant of the ACUC problem and allows for the computation of Locational Incremental Prices (LIPs) for both real and reactive power as the local optimal Lagrange multipliers of the power balance constraints. To avoid degeneracy, the pricing problem includes a small parameter ϵ > 0. Under certain assumptions market participants are shown to realize profit that converges to a non-negative value as ϵ approaches zero, practically ensuring profitability for small values of ϵ. We additionally provide many simple and important examples that provide intuition and insights into the proposed prices. Examples illustrate the basic concept of AIC pricing, the derived profitability results, the existence of multiple LIPs, the importance of including reactive power in the dispatch and pricing problems, the need for reactive power prices, and the improved incentives exhibited by LIPs as compared to traditional Locational Marginal Prices (LMPs). We additionally indicate many directions for future work including analysis of larger test cases.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

NASA NTRS1975

Creep behavior of uranium carbide-based alloys

The present work gives the results of experiments on the influence of zirconium carbide and tungsten on the creep properties of uranium carbide. The creep behavior of high-density UC samples follows the classical time-dependence pattern of (1) an instantaneous deformation, (2) a primary creep region, and (3) a period of steady-state creep. Creep rates for unalloyed UC-1.01 and UC-1.05 are several orders of magnitude greater than those measured for carbide alloys containing a Zr-C and/or W dispersoid. The difference in creep strength between alloyed and unalloyed materials varies with temperature and applied stress.

Seltzer, M. S.↗

NASA NTRS1989

The morphologies and physical properties of ultracompact H II regions

Seventy-five ultracompact (UC) H II regions are observed 0.4 arcsec resolution at 2 and 6 cm using the Very Large Array, and their radio continuum brightness distributions are presented in the form of contour plots. H-76 alpha recombination line profiles are obtained for six sources using a 4.4 arcsec beam. It is shown that these UC H II regions have electron densities of at least approximately 10,000 per cubic cm, emission measures of at least approximately 10 to the 7th pc cm to the -6th, and diameters no more than approximately 0.1 pc, consistent with their being small photoionized nebulae produced by O and B stars embedded in clouds of molecular gas and dust. At high angular resolution five different morphologies of the ionized gas are seen: spherical or unresolved (43 percent), cometary (20 percent), core-halo (16 percent), shell (4 percent), and irregular or multiply peaked (17 percent). Evidence is presented that the UC H II region phase of a massive star must last for a significant fraction of its main-sequence lifetime.

Wood, Douglas O. S.↗

NASA NTRS2001

STS-100 Photo-op/Shut-up/Depart O&C/Launch Endeavour On Orbit/Landing/Crew Egress

This video shows an overview of crew activities from STS-100. The crew of Space Shuttle Shuttle Endeavour includes: Commander Kent Rominger; Pilot Jeffrey Ashby; and Mission Specialists Chris Hadfield, John Phillips, Scott Parazynski, Umberto Guidoni, and Yuri Lonchakov. Sections of the video include: Photo-op; Suit-up; Depart O&C; Ingress; Launch with Playbacks; On-orbit; Landing with Playbacks; Crew Egress & Departure. Voiceover narration introduces the astronauts at their pre-flight meal, and continues during the video, except for the launch and landing sequences. Launch playback views include: NEXT; Beach Tracker; VAB; PAD-A; Tower-1; UCS-15; Grandstand; OTV-60; OTV-70; OTV-71; DOAMS; UCS-10 Tracker; UCS-23 Tracker; On-board Ascent Camera. The On-orbit section of the video shows preparations for an extravehicular activity (EVA) to install Canadarm 2 on the International Space Station (ISS). Preparation for docking with the ISS, and the docking of the orbiter and ISS are shown. The attachment of Canadarm 2 and the Raffaello Logistics Module, a resupply vehicle, are shown. The crew also undertakes some maintenance of the ISS. Landing playback views include: TV-1; TV-2; LRO-1; LRO-2; PPOV.

Source record↗

NASA NTRS2001

STS-102 Photo-op/Suit-up/Depart O&C/Launch Discovery On Orbit/Landing/Crew Egress

The spacecrews of STS-102 and the Expedition 1 and 2 crews of the International Space Station (ISS) are seen in this video, which presents an overview of their activities. The crew consists of Commander Jim Wetherbee, Pilot James Kelly, and Mission Specialists Andrew Thomas, and Paul Richards. The sections of the video include: Photo-op, Suit-up, Depart O&C, Ingress, Launch with Playbacks, On-orbit, Landing with Playbacks, and Crew Egress & Departs. The prelaunch activities are explained by two narrators, and the crew members are assisted in the White Room just before boarding the Space Shuttle Discovery. Isolated views of the shuttle's launch include: VAB, PAD-B, DLTR-3, UCS-23 Tracker, PATRICK IGOR, UCS-10 Tracker, Grandstand, Tower-1, OTV-160, OTV-170, OTV-171, and On-board Camera. The video shows two extravehicular activities (EVAs) to perform work on the ISS, one by astronauts Helms and Voss from Expedition 2, and another by Richards and Thomas. The attachment of the Leonardo Multipurpose Logistics Module, a temporary resupply module, is shown in a series of still images. The on-orbit footage also includes a view of the Nile River, and a crew exhange ceremony between Expedition 1 (Commander Yuri Gidzenko, Flight Engineer Sergei Krikalev) and Expedition 2 (Commander Yury Usachev, Flight Engineers James Voss, Susan Helms). Isolated views of the landing at Kennedy Space Center include: North Runway Camera, VAB, Tower-1, Mid-field, Midfield IR, Tower-2, and UCS-12 IR. The Crew Transfer Vehicle (CTV) for unloading the astronauts is shown, administrators greet the crew upon landing, and Commander Wetherbee gives a briefing.

Source record↗

NASA NTRS2001

STS-105/Discovery/ISS 7A.1: Pre-Launch Activities, Launch, Orbit Activities and Landing

The crew of Space Shuttle Discovery on STS-105 is introduced at their pre-launch meal and at suit-up. The crew members include Commander Scott Horowitz, Pilot Rick Sturckow, and Mission Specialists Patrick Forrester and Daniel Barry, together with the Expedition 3 crew of the International Space Station (ISS). The Expedition 3 crew includes Commander Frank Culbertson, Soyuz Commander Vladimir Dezhurov, and Flight Engineer Mikhail Tyurin. When the astronauts depart for the launch pad in the Astrovan, their convoy is shown from above. Upon reaching the launch pad, they conduct a walk around of the shuttle, display signs for family members while being inspected in the White Room, and are strapped into their seats onboard Disciovery. The video includes footage of Discovery in the Orbiter Processing Facility, and some of the pre-launch procedures at the Launch Control Center are shown. The angles of launch replays include: TV-1, Beach Tracker, VAB, Pad A, Tower 1, UCS-15, Grandstand, OTV-70, Onboard, IGOR, and UCS-23. The moment of docking between Discovery and the ISS is shown from inside Discovery's cabin. While in orbit, the crew conducted extravehicular activities (EVAs) to attach an experiments container, and install handrails on the Destiny module of the ISS. The video shows the docking and unloading of the Leonardo Multipurpose Logistics Module (MPLM) onto the ISS. The deployment of a satellite from Discovery with the coast of the Gulf of Mexico in the background is shown. Cape Canaveral is also shown from space. Landing replays include VAB, Tower 1, mid-field, South End SLF, North End SLF, Tower 2, Playalinda DOAMS, UCS-23, and Pilot Point of View (PPOV). NASA Administrator Dan Goldin meets the crew upon landing and participates in their walk around of Discovery. The video concludes with a short speech by commander Horowitz.

Source record↗

DOE OSTI2023

Solving the Unit Commitment Problem: Polyhedral Theory, Symmetry, and Power Flow

In this talk, I will give an overview of mixed integer linear programming (MILP) formulations and extensions thereof which enable the effective solution of the unit commitment problem (UC) when paired with a commercial MILP solver. First, we will place UC in context, stressing the importance of achieving a (near) optimal solution. Then we will discuss the importance of perfect and "good-enough" formulations for individual generators / market participants. Some of these formulations enable symmetry-aware reformulations for identical market participants, which can be critical when symmetry is present. Finally, we will discuss approximations of AC power flow currently used in practice, and the challenges with including these approximations within the UC formulation.

MATHEMATICS AND COMPUTING↗