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DOE OSTI2020

Performance Limits of an Alternating Current Electroluminescent Device

Abstract The use of an alternating current (AC) voltage is a simple, versatile method of producing electroluminescence from generic emissive materials without the need for contact engineering. Recently, it was shown that AC‐driven, capacitive electroluminescent devices with carbon nanotube network contacts can be used to generate and study electroluminescence from a variety of molecular materials emitting in the infrared‐to‐ultraviolet range. Here, performance trade‐offs in these devices are studied through comprehensive device simulations and illustrative experiments, enhancing understanding of the mechanism and capability of electroluminescent devices based on alternating as opposed to direct current (DC) schemes. AC‐driven electroluminescent devices can overcome several limitations of conventional DC‐driven electroluminescent devices, including the requirement for proper alignment of material energy levels and the need to process emitting materials into uniform thin films. By simultaneously optimizing device geometry, driving parameters, and material characteristics, the performance of these devices can be tuned. Importantly, the turn‐on voltage of AC‐driven electroluminescent devices approaches the bandgap of the emitting material as the gate oxide thickness is scaled, and internally efficient electroluminescence can be achieved using low‐mobility single‐layer emitter films with varying thicknesses and energy barrier heights relative to the contact.

Wang, Vivian↗

DOE OSTI2023

Charge per Micro-Pulse Calculation for Ideal Lujan and WNR beams

A complete redesign of the LANSCE front-end is currently under development for the Los Alamos Modernization Project (LAMP). This includes the replacement of the traditional Cockroft-Walton injection system to the newer radiofrequency quadrupole (RFQ) standard. LANSCE accelerates both H- and H+ beams and therefore requires an unconventional application for RFQ systems. A new facility could consider using an independent RFQ for each beam species. However, with the tight space of the LANSCE injector facility, it would prove difficult to instrument. Our initial studies have shown that a single RFQ could be used. The negatively- and positively-charged direct current (DC) beams are shaped, bunched, and accelerated out of phase to each other, with very little interaction. This would work for all possible H+ beam gates and most H- Beam gates. However, a challenge arises with the Weapons Neutron Research (WNR) beam structure that requires the acceleration of bunched beams at higher charge density per pulse. The Long Bunch Enable Gate (LBEG) used for the Lujan center is the best example of a standard injector beam gate. The beam gate, or Macro-Pulse (MP), is 625-us long, separated by at least 8.3 ms. A chopper is used to dice the MP into 1750 mini-Pulses (mP), which are 290-ns wide. After chopping, the MP contains 100,000 micro-Pulses (uP), which are generated by the linac acceleration structure modulated at 201.25 MHz; that is, the micro-Pulses are separated 5 ns apart from each other. The H+ beam structure will be very similar once a chopper is added to its transport. However, the Multi-Pulse Enable Gate (MPEG) used for WNR is significantly different in structure. In this case, the mP is chopped to be only 35-ns wide. This width is then rotated into a single 201.25 MHz RF bucket using the Low Frequency Buncher (LFB). This is proving difficult for the RFQ design in the LAMP upgrade. We began investigating the amount of current sent to WNR for two reasons. Firstly, we wanted to find a solution to avoid using the Low Frequency Buncher to simplify the LAMP RFQ design. It is simple to inject and accelerate a 35 mA DC beam in the LAMP RFQ (this is done in numerous accelerator facilities). However, injecting a short bunch with a larger current (once compressed to 5 ns to meet the RFQ frequency) may be difficult. Second, we have a technique called PSR2WNR in which we do not employ the Low Frequency Buncher, but rather accumulate 5 LBEG uP (5 ns) in the PSR and deliver the accumulated beam to WNR every 1.8 us. As a result, we could provide to WNR with five accumulated LBEG uPs every shot. The goal here is to create a rapid kicker with a frequency response of 555 kHz. DARHT-II and other accelerator facilities have constructed kickers of this type for other uses, and our engineers consider this technology as feasible.

43 PARTICLE ACCELERATORS↗

DOE OSTI2026

Floating Photovoltaics in Hydropower Reservoirs in the United States

This report presents a comprehensive analysis of the feasibility of floating photovoltaics (FPV) in federally regulated reservoirs within the continental United States (CONUS) and to present a methodology for capturing the true costs of deployment, potential environmental impacts, and regulatory pathways for open-loop hydropower reservoirs. It is intended for stakeholders who may not be solar industry experts but who are interested in exploring the potential for FPV in their reservoirs. While there are promising opportunities, particularly in enhancing dissolved oxygen (DO) levels and potentially improving compliance with existing hydropower licenses, the current capital costs of FPV are not yet competitive with traditional land-based solar installations at the utility-scale when comparing the LCOE results. A competitive financial outlook is achievable when applying a 30% Investment Tax Credit (ITC) and considering a 5% reduction from the baseline capital expenditures (CapEx) at the Tuckertown Reservoir in North Carolina case study. The study is structured around three key pillars of research: technical potential, environmental impacts and regulatory considerations, and technoeconomic analysis. This report provides a nationwide assessment of the opportunities for FPV in terms of capacity, measured in direct current megawatts (MWDC), in reservoirs managed by the U.S. Bureau of Reclamation (USBR), the U.S. Army Corps of Engineers (USACE), and the Federal Energy Regulatory Commission (FERC). Additionally, the report introduces a heuristic model for estimating the CapEx of utility-scale FPV projects (1–100 MW), offering a baseline cost estimate for stakeholders. Finally, the report applies these models to a case study of a hydropower reservoir in North Carolina to present site-specific results.

13 - HYDRO ENERGY↗

NASA NTRS2023

Probabilistic Forecasting of Ground Magnetic Perturbation Spikes at Mid-Latitude Stations

The prediction of large fluctuations in the ground magnetic field (dB/dt) is essential for preventing damage from Geomagnetically Induced Currents. Directly forecasting these fluctuations has proven difficult, but accurately determining the risk of extreme events can allow for the worst of the damage to be prevented. Here we trained Convolutional Neural Network models for eight mid-latitude magnetometers to predict the probability that dB/dt will exceed the 99th percentile threshold 30–60 min in the future. Two model frameworks were compared, a model trained using solar wind data from the Advanced Composition Explorer (ACE) satellite, and another model trained on both ACE and SuperMAG ground magnetometer data. The models were compared to examine if the addition of current ground magnetometer data significantly improved the forecasts of dB/dt in the future prediction window. A bootstrapping method was employed using a random split of the training and validation data to provide a measure of uncertainty in model predictions. The models were evaluated on the ground truth data during eight geomagnetic storms and a suite of evaluation metrics are presented. The models were also compared to a persistence model to ensure that the model using both datasets did not over-rely on dB/dt values in making its predictions. Overall, we find that the models using both the solar wind and ground magnetometer data had better metric scores than the solar wind only and persistence models, and was able to capture more spatially localized variations in the dB/dt threshold crossings.

Michael Coughlan↗

NASA NTRS2004

Construction and Analysis of Electronic circuits

The Aviation Environmental Technical Branch produces many various types of aeronautical research that benefits the NASA mission for space exploration and in turn, produces new technology for our nation. One of the present goals of the Aviation Environmental Technical Branch is to create better engines for airplanes by testing supersonic jet propulsion and safe fuel combustion. During the summer of 2004, I was hired by Vincent Sattenvhite Chief executive of the Aviation Environmental Technical Branch to Assist Yves Lamothe with a fuel igniter circuit. Yves Lamothe is an electrical engineer who is currently working on safe fuel combustion testing. This testing is planned to determine the minimum ignition energy for fuel and air vapors of current and alternative fuels under simulated flight conditions. An air temperature bath will provide simulated flight profile temperatures and the heat fluxes to the test chamber. I was assigned with Yves to help complete the igniter circuit which consists of a 36k voltage supply an oscilloscope, and a high voltage transistor switch. During my tenure in the L.E.C.I.R.P. program I studied the basics of electricity and circuitry along with two other projects that I completed. In the beginning of my internship, I devote all of my time to research the aspects of circuitry so that I would be prepared for the projects that I was assigned to do. I read about lessons on; the basic physical concepts of electronics, Electrical units, Basic dc circuits, direct current circuit analysis, resistance and cell batteries, various types of magnetism , Alternating current basics, inductance, and power supplies. I received work sheets and math equations from my Mentor so that I could be able to apply these concepts into my work. After I complete my studies, I went on to construct a LED chaser circuit which displays a series of light patterns using a 555 timer. I incorporated a switch and motion detector into the circuit to create basic alarm system. This project challenged my ability to interpret a schematic and expand it. While I was still completing the LED chaser circuit I Also was given A Basic Stamp Toddler Robot to build and program. The Toddler robot can walk in 36 various styles using advanced robotics. I used many different programs to create movement and direction of the robot. Also the Toddler can use infrared vision to sense objects. This enables the robot to maneuver indefinitely without running into objects. During my tenure at the NASA Glen Research Center I definite utilized the NASA mission to educate. I learned valuable information to help in my up coming year as a freshman in college.

Thomas, Ashley N.↗

DOE OSTI2020

Current-driven transverse domain wall oscillations in perpendicular spin-valve structures

Spin-transfer-driven oscillations of a transverse domain wall confined to a perpendicular spin-valve structure are investigated using a one-dimensional model. The stack consists of a polarizer, nonmagnetic spacer, soft free layer, and pinned magnetic layer. It is found that the domain-wall oscillation frequency is a nonmonotonic, highly asymmetrical function of applied electric current, showing a strong dependence on the current direction and the relative strengths of the interfacial and bulk spin-transfer torques. Micromagnetic analysis reveals that the surprising and atypical oscillator response is due to an interplay between the interfacial spin-transfer torque, the bulk spin-transfer torque, the exchange torque, and the damping torque. The underlying physical and material responses are examined, including the important role of the domain-wall twist. The competitions between the involved torques under different operating conditions suggest that the oscillator could serve as a model system to investigate magnetic and spintronic phenomena at the nanoscale. Finally, the observed current-dependent twisting of the free-layer magnetization about the axis of precession may further be found interesting for investigations of the interaction between spin-polarized current and chiral spin structures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Hybrid Symbolic-Numerical Modeling and Parametric Stability Analysis of DC–AC Power Systems

Hybrid DC-AC power systems integrating diverse inverter-based resources (IBRs) and multi-terminal high-voltage direct current (MTDC) networks represent a promising architecture for future power grids, while introducing challenges for modeling, stability analysis, and control design. This paper develops a hybrid symbolic-numerical modeling framework and tool to characterize the parametric small-signal stability of DC-AC coupled power systems. The proposed approach constructs parametric state-space models to enable efficient representation of system dynamics under varying control parameters and network configurations, with target parameters retained as symbolic variables and the remainder treated numerically. The stability analysis framework covers eigenvalue, sensitivity, and stability boundary and region characterization. Enhanced linear matrix inequality (LMI) techniques are proposed to directly certify small-signal stability over regions of parameter space while also reducing the conservativeness and computational burden. The resulting tools and frameworks enable rapid parametric model construction across diverse grid conditions, thereby facilitating stability-informed control and operation in complex DC–AC power systems.

DC–AC power systems↗

DOE OSTI2024

Dual Impacts of Space Heating Electrification and Climate Change Increase Uncertainties in Peak Load Behavior and Grid Capacity Requirements in Texas

Around 60% of households in Texas currently rely on electricity for space heating. As decarbonization efforts increase, non‐electrified households could adopt electric heat pumps, significantly increasing peak (highest) electricity demand in winter. Simultaneously, anthropogenic climate change is expected to increase temperatures, the potential for summer heat waves, and associated electricity demand for cooling. Uncertainty regarding the timing and magnitude of these concurrent changes raises questions about how they will jointly affect the seasonality of peak demand, firm capacity requirements, and grid reliability. This study investigates the net effects of residential space heating electrification and climate change on long‐term demand patterns and load shedding potential, using climate change projections, a predictive load model, and a direct current optimal power flow (DCOPF) model of the Texas grid. Results show that full electrification of residential space heating by replacing existing fossil fuel use with higher efficiency heat pumps could significantly improve reliability under hotter futures. Less efficient heat pumps may result in more severe winter peaking events and increased reliability risks. As heating electrification intensifies, system planners will need to balance the potential for greater resource adequacy risk caused by shifts in seasonal peaking behavior alongside the benefits (improved efficiency and reductions in emissions).

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2024

Experimental Validation of a Modular All-Electric Power Take-Off Topology for Wave Energy Converter Enabling Marine Renewable Energy Interconnection

Power electronic converters are an enabling technology for the emerging marine energy applications, such as using ocean waves to produce electricity. This paper outlines the power take-off system and its key components used in a wave energy converter offering modularity and scalability to generate power efficiently. The proposed power take-off system was implemented based on a modular multilevel converter and could be deployed to convert any alternating current electrical energy to a different alternating current for interconnection to grid or non-grid applications. Examples of widespread deployment are supplying electricity to coastal communities or producing clean drinking water. The analysis using both the simulation tests and laboratory experiments verified the design objectives and basic functionality of the developed power take-off system. An acceptable response using a field programmable gate array-based controlled laboratory testbench was achieved, complying with guidelines specified in the prevalent industry standards. Seamless operation during steady-state and transients for the studied wave energy converter was achieved as supported by the obtained results. The key findings of this work were experimentally examined under different load conditions, direct current bus voltage fluctuations, and generator speed–torque regulation. The ability of the power take-off system to generate high-power quality of the waveforms, e.g., against adhering to the IEEE 519-2022 standard for total harmonic distortion limits, is also confirmed.

Engineering↗

DOE OSTI2024

Oxygen vacancy migration and impact on high voltage DC polarization in 0.8BaTiO 3 –0.2BiZn 0.5 Ti 0.5 O 3

Electrical polarization and defect transport are examined in 0.8BaTiO 3 –0.2BiZn 0.5 Ti 0.5 O 3 , an attractive capacitor material for high power electronics. Oxygen vacancies are suggested to be the majority charge carrier at or below 250°C with a grain conduction hopping activation energy of 0.97 eV and 0.92 eV for thermally stimulated depolarization current (TSDC) and impedance spectroscopy measurements, respectively. At higher temperature, thermally generated electronic conduction with an activation energy of 1.6 eV is dominant. Significant oxygen vacancy concentration is indicated (up to ~1%) due to cation vacancy formation (i.e., acceptor defects) from observed Bi (and likely Zn) volatility. Oxygen vacancy diffusivity is estimated to be 10 -12.8 cm 2 /s at 250°C. Low diffusivity and high activation energies are indicative of significant defect interactions. Dipolar oxygen vacancy defects are also indicated, with an activation energy of 0.59 eV from TSDC measurements. In conclusion, the large oxygen vacancy content leads to a short lifetime during high voltage (30 kV/cm), high temperature (250°C) direct current (DC) electrical measurements.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2022

Suppression of toroidal Alfvén eigenmodes by the electron cyclotron current drive in KSTAR plasmas

Advanced operation scenarios such as high poloidal beta ( β P ) or high q min are promising concepts to achieve the steady-state high-performance fusion plasmas. However, those scenarios are prone to substantial Alfvénic activity, causing fast-ion transport and losses. Recent experiments with the advanced operation scenario on KSTAR tokamak have shown that the electron cyclotron current drive (ECCD) is able to mitigate and suppress the beam-ion driven toroidal Alfvén eigenmodes (TAEs) for over several tens of global energy confinement time. Co-current directional intermediate off-axis ECCD lowers the central safety factor slightly and tilts the central q -profile shape so that the continuum damping in the core region increases. Besides, the rise of central plasma pressure and increased thermal-ion Landau damping contribute to TAE stabilization. While the TAEs are suppressed, neutron emission rate and total stored energy increase by approximately 45% and 25%, respectively. Fast-ion transport estimated by TRANSP calculations approaches the classical level during the TAE suppression period. Substantial reduction in fast-ion loss and neutron deficit is also observed. Subsequently, enhancement of fast-ion confinement by suppressing the TAEs leads to an increase of non-inductive current fraction and will benefit the sustainment of the long-pulse high-performance discharges.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2020

A Modeling Approach for Handling Qualities and Controls Safety Analysis of Electric Air Taxi Vehicles

The combination of modern advances in electric propulsion, fly-by-wire controls, autonomy, and increasing demand for short range air taxi operations, is currently producing an outburst of vehicle designs more diverse than ever before. Advanced software tools are needed to support the rapid and safe introduction of any design into the airspace, including the safety of the deployed flight control system and vehicle handling qualities. This paper presents a methodology for building air taxi vehicle models with distributed electric propulsion for use in analyzing flight control system safety at the conceptual design level.The approach builds on existing software tools capable of outputting aeromechanics-based linear perturbation models for Vertical Take-off and Landing vehicles with multiple rotors. Rotor torque inputs are then converted into equivalent voltage control inputs, and the linear state and input dynamics matrices are modified to include electric motor dynamics with common parameters for direct-current electric motors. The linear perturbation dynamics are then stitched across multiple operating points into a quasi-Linear Parameter Varying model that covers the full flight envelope. A Model Predictive Controller is developed for use with the full envelope model, and a tradeoff analysis between handling quality and motor requirements is demonstrated using a six passenger NASA air taxi reference design.

Urban Air Mobility↗

DOE OSTI2026

Electrically Accelerated Mechanochemical Film Formation by a Phosphonium Phosphate Ionic Liquid: An In Situ Chemical Kinetics Investigation

Powertrains in electric vehicles are exposed to stray currents that accelerate wear and cause failure of mechanical components. These durability issues are further aggravated when using low-viscosity lubricants, which are desired for energy efficiency but create harsher contact conditions at sliding interfaces. This study investigates a phosphonium phosphate ionic liquid as a performance-enhancing additive in a low-viscosity base oil for lubricating electrified sliding interfaces. Ionic liquids can adsorb and react on contact interfaces via stress-assisted chemical reactions, generating nanometric tribofilms that provide protection against wear. However, the effect of electric fields on the mechanochemistry of ionic liquids is poorly understood, hindering their adoption in lubricants for electrified powertrains. This article reports an in situ optical interferometry study of ionic liquid derived tribofilm growth kinetics at stressed sliding/rolling interfaces under direct currents. The application of electric currents accelerated tribofilm formation up to a critical current density (∼1.4 A/mm 2 ), beyond which pitting-induced wear dominated. The tribofilms were composed of iron phosphates, iron oxides, and carbon species, with iron oxides becoming predominant under applied currents. These tribofilms prevented the scuffing failure of steel surfaces under electrified conditions. Based on the results, a kinetic model is proposed that integrates electric current effect into the classical stress-assisted thermal activation framework to allow prediction of tribofilm growth at electrified sliding contacts. This framework provides crucial guidance for designing next-generation lubricants for electrified transportation and power generation systems.

additives↗

DOE OSTI2022

A Framework to Analyze the Requirements of a Multiport Megawatt-Level Charging Station for Heavy-Duty Electric Vehicles

Widespread adoption of heavy-duty (HD) electric vehicles (EVs) will soon necessitate the use of megawatt (MW)-scale charging stations to charge high-capacity HD EV battery packs. Such a station design needs to anticipate possible station traffic, average and peak power demand, and charging/wait time targets to improve throughput and maximize revenue-generating operations. High-power direct current charging is an attractive candidate for MW-scale charging stations at the time of this study, but there are no precedents for such a station design for HD vehicles. We present a modeling and data analysis framework to elucidate the dependencies of a MW-scale station operation on vehicle traffic data and station design parameters and how that impacts vehicle electrification. This framework integrates an agent-based charging station model with vehicle schedules obtained through real-world vehicle telemetry data analysis to explore the station design and operation space. A case study applies this framework to a Class 8 vehicle telemetry dataset and uses Monte Carlo simulations to explore various design considerations for MW-scale charging stations and EV battery technologies. The results show a direct correlation between optimal charging station placement and major traffic corridors such as cities with ports, e.g., Los Angeles and Oakland. Corresponding parametric sweeps reveal that while good quality of service can be achieved with a mix of 1.2-megawatt and 100-kilowatt chargers, the resultant fast charging time of 35–40 min will need higher charging power to reach parity with refueling times.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2021

Theoretical Analysis of Experimental Data of Sodium Diffusion in Oxidized Molybdenum Thin Films

In this work, the diffusion process of sodium (Na) in molybdenum (Mo) thin films while it was deposited on soda lime glass (SLG) was studied. A small amount of oxygen was present in the chamber while the direct-current (DC) magnetron sputtering was used for the deposition. The substrate temperatures were varied to observe its effect. Such molybdenum films, with or without oxidations, are often used in thin film solar cells, either as back contact or as hole transport layers. Secondary ion mass spectrometry (SIMS) was used to quantify the concentration of the species. A grain diffusion mechanistic model incorporating the effect of grain and grain boundary geometrical shape and size was developed. The model was used to provide an in-depth theoretical analysis of the sodium diffusion in molybdenum thin films that lead to the measured SIMS data. It was observed that not only diffusion coefficients should be considered when analyzing diffusion processes in thin films but also the ratio of grain boundary size to grain size. Both depend on substrate temperature and directly affect the amount of diffused species in the film. The data were analyzed under the light of the film growth speed versus diffusion front speed, the effect of oxygen content, and the effect of substrate temperature on the overall diffusion process. The temperature inversely affects the ratio of grain boundary size and grain size and directly affects the diffusion coefficient, which leads to a preferable temperature at which the highest amount of alkali can be found in the film.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Power Grid Reliability Estimation via Adaptive Importance Sampling

Electricity production currently generates approximately 25% of greenhouse gas emissions in the USA. Thus, increasing the amount of renewable energy is a key step to carbon neutrality. However, integrating a large amount of fluctuating renewable generation is a significant challenge for power grid operating and planning. Grid reliability, i.e., an ability to meet operational constraints under power fluctuations, is probably the most important of them. In this letter, we propose computationally efficient and accurate methods to estimate the probability of line overflow, i.e., reliability constraints violation, under a known distribution of renewable energy generation. To this end, we investigate an importance sampling approach, a flexible extension of Monte-Carlo methods, which adaptively changes the sampling distribution to generate more samples near the reliability boundary. The approach allows to estimate overload probability in real-time based only on a few dozens of random samples, compared to thousands required by the plain Monte-Carlo. Our study focuses on high voltage direct current power transmission grids with linear reliability constraints on power injections and line currents. Herein, we propose a novel theoretically justified physics-informed adaptive importance sampling algorithm and compare its performance to state-of-the-art methods on multiple IEEE power grid test cases.

power system faults↗

NASA NTRS2016

Modular Stirling Radioisotope Generator

High-efficiency radioisotope power generators will play an important role in future NASA space exploration missions. Stirling Radioisotope Generators (SRGs) have been identified as a candidate generator technology capable of providing mission designers with an efficient, high-specific-power electrical generator. SRGs high conversion efficiency has the potential to extend the limited Pu-238 supply when compared with current Radioisotope Thermoelectric Generators (RTGs). Due to budgetary constraints, the Advanced Stirling Radioisotope Generator (ASRG) was canceled in the fall of 2013. Over the past year a joint study by NASA and the Department of Energy (DOE) called the Nuclear Power Assessment Study (NPAS) recommended that Stirling technologies continue to be explored. During the mission studies of the NPAS, spare SRGs were sometimes required to meet mission power system reliability requirements. This led to an additional mass penalty and increased isotope consumption levied on certain SRG-based missions. In an attempt to remove the spare power system, a new generator architecture is considered, which could increase the reliability of a Stirling generator and provide a more fault-tolerant power system. This new generator called the Modular Stirling Radioisotope Generator (MSRG) employs multiple parallel Stirling convertor/controller strings, all of which share the heat from the General Purpose Heat Source (GPHS) modules. For this design, generators utilizing one to eight GPHS modules were analyzed, which provided about 50 to 450 W of direct current (DC) to the spacecraft, respectively. Four Stirling convertors are arranged around each GPHS module resulting in from 4 to 32 Stirling/controller strings. The convertors are balanced either individually or in pairs, and are radiatively coupled to the GPHS modules. Heat is rejected through the housing/radiator, which is similar in construction to the ASRG. Mass and power analysis for these systems indicate that specific power may be slightly lower than the ASRG and similar to the Multi-Mission Radioisotope Thermoelectric Generator (MMRTG). However, the reliability should be significantly increased compared to ASRG.

Modules↗

DOE OSTI2025

Power Flow Geometry and Approximation

Here, the power flow equations are important in numerous power systems problems of practical interest which consider alternating current power flow (ACPF) physics. Perhaps the most well studied being the alternating current optimal power flow problem (ACOPF), seeking to optimize the operation of an electric power system. Due to their non-linearity, problems which include the power flow equations are typically challenging, particularly in optimization. Interestingly, the set of solutions to the power flow equations forms a smooth manifold. As a result, differential geometry can be used to describe and analyze this set of equations. This approach has proven effective in several engineering applications (e.g., solving ACOPF and analyzing the solution space boundary). Central to the success of this approach is an understanding of the power flow manifold's geometry. In this work, we develop the geometric and topological properties of this manifold using concepts from differential geometry. After demonstrating the convenience of this manifold's representation as a function's graph, computational methods are emphasized: we develop retractions, error bounds for linear approximation, and formulas for evaluating the Riemannian metric (including associated objects such as geodesics and the curvature tensor). Scalar curvature and the second fundamental form play a new role in quantifying the quality of linear approximations, like the popular direct current approximation. All functions are implemented in Julia and available in an online repository. Proofs are included for completeness.

24 POWER TRANSMISSION AND DISTRIBUTION↗