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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 919 records · Page 51
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

40 Ca transverse response function from coupled-cluster theory

Here, we present calculations of the 40 Ca transverse response function obtained from coupled-cluster theory used in conjunction with the Lorentz integral transform method. We employ nuclear forces derived at next-to-next-to leading order in chiral effective field theory with and without Δ degrees of freedom. We first benchmark this approach on the 4 He nucleus and compare both the transverse sum rule and the response function to earlier calculations based on different methods. As expected from the power counting of the chiral expansion of electromagnetic currents and from previous studies, our results retaining only one-body term underestimate the experimental data for 4 He by about 20%. However, when the method is applied to 40 Ca at the same order of the expansion, response functions do not lack strength and agree well with the world electron scattering data. We discuss various sources of theoretical uncertainties and comment on the comparison of our results with the available experiments.

39 ≤ A ≤ 58↗
DOE OSTI2026

Autoregressive long-horizon prediction of plasma edge dynamics *

Accurate modeling of scrape-off layer (SOL) and divertor-edge dynamics is vital for designing plasma-facing components in fusion devices. High-fidelity edge fluid/neutral codes such as SOLPS-ITER capture SOL physics with high accuracy, but their computational cost limits broad parameter scans and long transient studies. We present transformer-based, autoregressive surrogates for efficient prediction of 2D, time-dependent plasma edge state fields. Trained on SOLPS-ITER spatiotemporal data for the KSTAR tokamak, the surrogates forecast electron temperature, electron density, and radiated power over extended horizons. We evaluate model variants trained with increasing autoregressive horizons (1–100 steps) on short- and long-horizon prediction tasks. Longer-horizon training systematically improves rollout stability and mitigates error accumulation, enabling stable predictions over hundreds to thousands of steps and reproducing key dynamical features such as the motion of high-radiation regions. Measured end-to-end wall-clock times show the surrogate is orders of magnitude faster than SOLPS-ITER, enabling rapid parameter exploration. Prediction accuracy degrades when the surrogate enters physical regimes not represented in the training dataset, motivating future work on data enrichment and physics-informed constraints. Overall, this approach provides a fast, accurate surrogate for computationally intensive plasma edge simulations, supporting rapid scenario exploration, control-oriented studies, and progress toward real-time applications in fusion devices.

autoregressive deep learning↗
DOE OSTI2020

Developing inductively driven diagnostic X-ray sources to enable transformative radiography and diffraction capabilities on Z

Penetrating X-rays are one of the most effective tools for diagnosing high energy density experiments, whether through radiographic imaging or X-ray diffraction. To expand the X-ray diagnostic capabilities at the 26-MA Z Pulsed Power Facility, we have developed a new diagnostic X-ray source called the inductively driven X-pinch (IDXP). This X-ray source is powered by a miniature transmission line that is inductively coupled to fringe magnetic fields in the final power feed. The transmission line redirects a small amount of Zs magnetic energy into a secondary cavity where 150+ kA of current is delivered to a hybrid X-pinch. In this report, we describe the multi-stage development of the IDXP concept through experiments both on Z and in a surrogate setup on the 1 MA Mykonos facility. Initial short-circuit experiments to verify power ow on Z are followed by short-circuit and X-ray source development experiments on Mykonos. The creation of a radiography-quality X-pinch hot spot is verified through a combination of X-ray diode traces, laser shadowgraphy, and source radiography. The success of the IDXP experiments on Mykonos has resulted in the design and fabrication of an IDXP for an upcoming Z experiment that will be the first-ever X-pinch fielded on Z. We have also pursued the development of two additional technologies. First, the extended convolute post (XCP) has been developed as an alternate method for powering diagnostic X-pinches on Z. This concept, which directly couples the current owing in one of the twelve Z convolute posts to an X-pinch, greatly increases the amount of available current relative to an IDXP (900 kA versus 150 kA). Initial short-circuit XCP experiments have demonstrated the efficacy of power ow in this geometry. The second technology pursued here is the inductively driven transmission line (IDTL) current monitor. These low-current IDTLs seek to measure the current in the final power feed with high fidelity. After three generations of development, IDTL current monitors frequently return cleaner current measurements than the standard B-dot sensors that are fielded on Z. This is especially true on high-inductance experiments where the harshest conditions are created in the nal power feed.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

A semi–automatic analytical methodology for characterizing the energy consumption of MRI systems using load duration curves

Background and purpose: Magnetic resonance imaging (MRI) scanners are a major contributor to greenhouse gas emissions from the healthcare sector, and efforts to improve energy efficiency and reduce energy consumption rely on quantification of the characteristics of energy consumption. The purpose of this work was to develop a semi-automatic analytical methodology for the characterization of the energy consumption of MRI systems using only the load duration curve (LDC). LDCs are a fundamental tool used across various fields to analyze and understand the behavior of loads over time. Methods: An electric current transformer sensor and data logger were installed on two 3T MRI scanners from two vendors, termed M1 (outpatient scanner) and M2 (inpatient/emergency scanner). Data was collected for 1 month (7/11/2023 to 8/11/2023). Active power was calculated, assuming a balanced three-phase system, using the average current measured across all three phases, a 480 V reference voltage for both machines, and vendor-provided power factors. An LDC was constructed for each system by sorting the active power values in descending order and computing the cumulative time (in units of percentage) for each data point. The first derivative of the LDC was then computed (LDC’), smoothed by convolution with a window function (sLDC’), and used to detect transitions between different system modes including (in descending power levels): scan, prepared-to-scan, idle, low-power, and off. The final, segmented LDC was used to measure time (% total time), total energy (kWh), and mean power (kW) for each system mode on both scanners. The method was validated by comparing mean power values, computed using the segmented 1-month LDC, for each nonproductive system mode (i.e., prepared-to-scan, idle, lower-power, and off) against power levels measured after a deliberate system shutdown was performed for each scanner (1 day worth of data). Results: The validation revealed differences in mean power values <1.4% for all nonproductive modes and both scanners. In the scan system mode, the mean power values ranged from 29.8 to 37.2 kW and the total energy consumed for 1 month ranged from 11 106 to 14 466 kWh depending on the scanner. Over the course of 1 month, the portion of time the scanners were in nonproductive modes ranged from 76% to 80% across scanners and the nonproductive energy consumption ranged from 8010 to 6722 kWh depending on the scanner. The M1 (outpatient) scanner consumed 99.9 and 183.9 kWh/day in idle mode for weekdays and weekends, respectively, because the scanner spent 23% more time proportionally in idle mode on the weekends. Conclusions: A semi-automatic method for quantifying energy consumption characteristics of MRI scanners was introduced and validated. This method is relatively simple to implement as it requires only power data from the scanners and avoids the technical challenges associated with extracting and processing scanner log files. Finally, the methodology enables quantitative evaluation of the power, time, and energy characteristics of MRI scanners in scan and nonproductive system modes, providing baseline data and the capability of identifying potential opportunities for enhancing the energy efficiency of MRI scanners.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2021

Rotor blade imbalance fault detection for variable-speed marine current turbines via generator power signal analysis

Marine hydrokinetic (MHK) turbines extract renewable energy from oceanic environments. However, due to the harsh conditions that these turbines operate in, system performance naturally degrades over time. Thus, ensuring efficient condition-based maintenance is imperative towards guaranteeing reliable operation and reduced costs for marine hydrokinetic power. This work proposes a novel framework aimed at identifying and classifying the severity of rotor blade pitch imbalance faults experienced by marine current turbines (MCTs). In the framework, a Continuous Morlet Wavelet Transform (CMWT) is first utilized to acquire the wavelet coefficients encompassed within the 1P frequency range of the turbine's rotor shaft. From these coefficients, several statistical indices are tabulated into a six-dimensional feature space. Next, Principle Component Analysis (PCA) is employed on the resulting feature space for dimensionality reduction, and then the application of a K-Nearest Neighbor (KNN) machine learning algorithm is utilized for fault detection and severity classification. The effectiveness of the proposed framework is validated using a high-fidelity MCT numerical simulation platform, where results demonstrate that the presence of a pitch imbalance fault can be accurately detected 100% of the time and correctly classified based upon severity more than 97% of the time.

42 ENGINEERING↗
DOE OSTI2021

Quantization effects in semiconductor nanostructures and singlet fission in molecular chromophores for photovoltaics and solar fuels

Hot carriers in semiconductors are electrons and/or holes that have energies greater than carriers that reside at the top and bottom of the conduction and valence bands, respectively; the latter carriers are in equilibrium with the lattice and have a temperature equal to the lattice (ambient) temperature. Hot carriers are created in semiconductors upon the absorption of photons with energies greater than the bandgap. The excess energy above the bandgap energy is in the form of kinetic energy. The hot carriers can cool to the lattice temperature via electron–phonon scattering and establish separate Boltzmann distributions for electrons and holes at the band edges. Thus, upon cooling, the excess kinetic energy of the hot carriers is transformed into heat and is unavailable to be converted into electrical or chemical free energy in a solar photon-converting cell. This hot-carrier cooling process significantly limits the maximum possible power conversion efficiency (PCE) of the free energy of solar photons into electrical free energy or chemical free energy in chemical bonds of fuels. However, if hot-carrier cooling can be slowed such that the hot carriers can be extracted before cooling to create higher photovoltages, or utilized to create additional electron-hole pairs through carrier multiplication, then beneficial use can be made of the excess energy of hot carriers and the maximum thermodynamic PCE can be dramatically increased. Quantization effects in semiconductor nanostructures, unique properties of some bulk semiconductors, and exciton multiplication in both semiconductors and molecular chromophores that undergo singlet fission have shown a path forward for potential dramatic increases in the PCEs of solar photons into electricity and solar fuels. The status, history, and future promise of the science and technology of these future approaches for different types of photovoltaic cells and cells for solar fuels will be discussed.

14 SOLAR ENERGY↗
DOE OSTI2025

Quantum Gravity and Laser Interferometry: Towards Observable Predictions

Understanding quantum gravity remains one of the deepest challenges in modern physics, as direct experimental access to Planck-scale effects is beyond current technological reach. However, recent theoretical advances indicate that quantum fluctuations of spacetime may produce measurable effects in precision experiments, particularly near causal horizons. This opens new avenues for testing quantum gravity phenomena through high-precision measurement techniques. This dissertation develops multiple theoretical models to characterize these effects and examines their potential observational signatures in future gravitational wave interferometers. We begin by investigating the role of quantum fluctuations in near-horizon geometries through the lens of the AdS/CFT correspondence, which provides a powerful framework for understanding the interplay between quantum field theory and general relativity via holographic principles. By modeling stochastic energy-momentum sources in Rindler-AdS spacetime, we demonstrate that vacuum fluctuations transform the Einstein equations into a Langevin-type stochastic differential equation, leading to potentially observable fluctuations in photon traversal times. Extending this approach to Minkowski spacetime, we establish a correspondence between gravitational shockwaves and fluid dynamics, showing that near-horizon perturbations satisfy an equation analogous to that governing incompressible fluids, thereby reinforcing the membrane paradigm and hydrodynamic analogies in the context of the fluid/gravity duality. Furthermore, we construct the covariant phase space of a spherically symmetric causal diamond in Minkowski spacetime, identifying two fundamental charges that govern its evolution. These results provide a foundation for quantizing causal horizons and understanding their microscopic degrees of freedom. Building upon these theoretical developments, we further examine a related stochastic phenomenon: the gravitational wave memory background arising from the cumulative memory steps produced by supermassive black hole mergers. After reviewing the standard stochastic gravitational wave background, gravitational memory effects, and BMS symmetries, we model the stochastic memory background using a Brownian motion framework. We show that while the cumulative memory background initially appears above the sensitivity curve of space-based interferometers like LISA, the realistic subtraction of individually resolvable merger events substantially suppresses the residual signal, making its detection more challenging. This highlights the critical importance of source subtraction when evaluating the detectability of gravitational memory effects. By bridging fundamental theory with experimental prospects, this dissertation contributes to the ongoing effort to uncover the quantum nature of spacetime through precision measurement techniques. Whether through detecting quantum spacetime fluctuations, gravitational memory backgrounds, or probing the symmetries of causal horizons, the pursuit of observable quantum gravity phenomena continues to expand the frontiers of both theory and experiment.

Zhang, Yiwen [Caltech] (ORCID:0000000323559416)↗
DOE OSTI2020

A Tool for Performing Link Analysis, Operational Sequence Analysis, and Workload Analysis to Support Nuclear Power Plant Control Room Modernization

Nuclear power continues to have an imperative role for the U.S.’s electricity generation. However, for these nuclear power plants (NPPs) to remain economically viable, new strategies for reducing operations and maintenance costs must be explored. The U.S. Department of Energy Light Water Reactor Sustainability Program is researching how to digitally transform existing analog and hybrid main control rooms into a fully integrated control room that addresses this challenge. The transformation will fundamentally change the conduct of operations for these U.S. NPPs. Human factors engineering has a vital role in this effort, where traditional task analysis methods are important in informing the design of advanced human-system interface displays. This work describes a preliminary tool to support task analysis for the development of these advanced displays. Details on the use of this tool, including the specific task analysis methods offered, are presented in this paper.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2021

From Machine Learning to Nuclear Digital Twins

This presentation provides multiple case studies of Machine Learning, Uncertainty Quantification, Reduced Order Modeling, to achieve digital transformation and provide the components for nuclear digital twinning. The presentation is for an international virtual event titled: Consultancy Meeting on Applications of AI and Pattern Recognition Techniques for Uncertainty Quantification in Nuclear Power Modelling and Simulation held Oct 21-22, 2021.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2026

Vanishing dynamic strength measured in a transient high-pressure phase of tin

This work reports two independent experimental estimations of the dynamic strength of the body-centered tetragonal (bct) 𝛾 phase of tin, which occurs at pressures above about 9 GPa and transforms promptly back to the ambient 𝛽 phase upon pressure release. Measuring strength in such a transient high-pressure phase is challenging. One measurement used free-surface Richtmyer-Meshkov instabilities generated with gas gun impact. Another set of measurements used ramp-release loading in a pulsed-power facility. Strength estimations came from comparison to simulations using a comprehensive multiphase modeling framework that includes equation of state, shear moduli, and strength separately for each phase, and treats mixed-phase regions. Both experimental methods found the 𝛾-phase strength to be very low, within experimental uncertainty of zero. The existing literature on other materials, by contrast, almost universally reports higher strength in transient high-pressure phases compared with ambient phases. Recent Molecular-Dynamics simulations on tin in the literature showed almost zero deviatoric strength during a deformation-induced bct → bct transformation in which one of the 𝛾-phase 𝑎 axes “flips” to the 𝑐 axis. This reorientation currently provides the most plausible explanation for the low observed strength in 𝛾-phase tin.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Integration of a DER Management System in Riverside. Final report

The tasks in this project covered various aspects, including algorithm development, algorithm integration into a commercial Active Network Management (ANM) platform, hardware-in-the-loop (HIL) testing in an industry-standard testing platform, pilot demonstration in Riverside, California, and also cost and benefit analysis. The DERMS platform in this project can host different algorithms developed on different platforms (e.g., MATLAB and Python) and it can interact with different hardware devices (e.g., different PV inverters, battery inverters, and different sensors). The DER control solution are based on an advanced model-free, layered, and clustered DER control paradigm. At the core of the DER control algorithms was the concept of Extremum Seeking (ES), which is a model-free probing-based control technique. The ES-based control algorithms were tested on major real-world inverters; both individually and in a cluster. It was shown that even legacy equipment (or when paired with a few additional advanced equipment) can support such advanced control. The monitoring algorithms utilize a heterogeneous set of legacy and advanced sensor measurements, such as behind-the-meter DER sensors, distribution-level Phase Measurement Units, distribution-substation Supervisory Control and Data Acquisition (SCADA), and line current sensors, with their limited availability; in order to infer practical network conditions. Sensor data are utilized to achieve resource forecasting, phase identification, and distribution system state estimation. The technology that was developed and demonstrated in this project could be transformational to utilities, including the smaller municipal utilities such as in Riverside, which may not have the resources to deploy advanced distribution system and DERMS solutions in order to support high penetration of solar power integration. This project created a real-world prototype to provide utilities with an assessment of smart grid monitoring and control technologies.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Final Technical Report Wireless Microsensors System for Monitoring Deep Subsurface Operations

This final technical report describes the main findings of the project Wireless Microsensors System for Monitoring Deep Subsurface Operations (FE0031850). The project was part of the U.S. Department of Energy National Energy Technology Laboratory FOA 1998 program to develop new sensor systems for direct observation of parameters associated with CO2 injection and to provide data collection without being disruptive to operations. The overall DOE program was aimed at developing and validating innovative transformational sensor systems, amenable for integration with autonomous intelligent monitoring systems, that are capable of being deployed within the casing annulus and do not have casing perforation or wires/cables in the annulus for installation, power supply, or data transmission needs. Project accomplishments included 1) design and fabrication of a wireless downhole sensor system to monitor parameters for CO2 storage, 2) field testing of the sensor system in two legacy oil & gas wells, and 3) development of an analysis approach that validates the measurements and demonstrates the application of the technology to depict CO2 movement in the subsurface. The project leveraged new sensor technologies along with specialized wellbore telemetry, deployment, and analysis methods designed to address the challenges and risks related to CO2 storage in the subsurface. Results from field testing were a mixture of successes and challenges. The temperature sensor rings, installation procedures in legacy oil & gas wells, wireless powering demonstration, automated data collection, and material compatibility were successful. The wireless data transfer through cement to the wellhead via the sensor relays was not functional beyond the first relay. Consequently, work in the last year of the project included some additional testing of data transmission through different materials along with modeling and analysis of field data for CO2 monitoring applications. This work suggested there are options like polymer cements and open hole annuli that may allow point-to-point transmission along the borehole. The techno-economic analysis suggests that the sensor system is ~40% less expensive than fiber optic distributed temperature system. Modeling of CO2 storage applications suggests temperature can provide an indicator of CO2 saturation but would be best combined with pressure sensors.

47 OTHER INSTRUMENTATION↗
DOE OSTI2026

Transformational Molecular Layer Deposition Tailor-Made Size-Sieving Sorbents for Post-Combustion CO 2 Capture

This report summarizes the carbon capture research and development conducted by The State University of New York at Buffalo (UB), University of South Carolina (USC), GTI Energy (GTI), and Rensselaer Polytechnic Institute (RPI) for U.S. Department of Energy (DOE) project DE-FE0031730 titled “Transformational Molecular Layer Deposition Tailor-made Size-Sieving Sorbents for Post-Combustion CO 2 capture.” The objective of this project was to develop a transformational molecular layer deposition (MLD) tailor-made size-sieving sorbent integrated with a pressure swing adsorption (PSA) cycle schedule that can be installed in new or retrofitted into existing pulverized coal (PC) power plants for CO 2 capture with a cost of electricity at least 30% lower than a supercritical PC power with CO 2 capture, or approximately $\$$30 per tonne of CO 2 captured, and with it being ready for demonstration by 2030.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2024

Major Drivers of Long-Term Distribution Transformer Demand

Distribution transformers, used to step-down medium voltage to service-voltage level for end-use electrical consumption, are currently experiencing major shortages. Utilities are experiencing extended lead times for transformers of up to 2 years (a 4x increase on lead times pre-2022) and prices have gone up by as much as 5-6 times in the past 2 years. Current shortages have been attributed to pent-up post-pandemic demand, workforce shortages and low retention rates, component supply chain challenges, and materials shortages (grain-oriented electrical steel, aluminum, and copper). The supply of this equipment is critical for the reliability and growth of the power system, and in meeting administration climate goals in terms of electrification of demand and the growth of renewable energy. This report details some of the initial analysis conducted by the National Renewable Energy Laboratory (NREL), supported by the Department of Energy's Office of Electricity and Office of Policy, in assessing the long-term demand trends for distribution transformers. Expected increased demand is due to a confluence of not only electrification and renewable energy growth, but also in the context of aging electric infrastructure, increased frequency and severity of extreme weather events, and utility-driven investments in reliability and resiliency of the electricity distribution system.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2025

Summary of Factory Fueling and Testing Risks to Support the Transformation of Regulatory Requirements for Microreactors

Microreactors have the potential to open new markets and applications for nuclear energy. New manufacturing and operational regimes, such as factory fueling and testing prior to site installation, are being proposed to meet these new markets. The radiological hazards associated with traditional commercial power reactors are not the same as the hazards of a reactor being constructed in a factory. Currently, a reactor operating license specified under 10 CFR Part 50, Part 52, or (in the near future) Part 53 is required prior to loading fuel in the reactor. This is logical for plants that are immediately to begin full-power operations soon after fuel loading. However, for microreactors, this may not be the case. Some deployment concepts may stage reactors as “ready to go” in a factory prior to site installation and startup. This approach is being considered in the case of diesel generator replacements, mobile or roaming mining operations, and emergency response situations, such as after a major disaster event. Therefore, it is necessary to evaluate hazards assuming low power operation for a short irradiation time. This report investigates the primary hazards unique to microreactors associated with low power reactor and physics tests necessary to confirm core safety assumptions, neutronic and core design performance parameters, and other assumptions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Probabilistic Look-ahead Contingency Analysis Integration with Commercial Tool and Practical Data

This paper presents an initial effort of integrating a smart sampling-based probabilistic look-ahead contingency analysis algorithm with General Electric (GE) Grid Solutions’ commercial energy management system (EMS) tool as a proof-of-concept for a seamless research tool integration using real world large-scale grid data. With the increasing impact of random forces such as variable generation and load, their stochastic behaviors cannot be ignored. However, the current practices are still dominated by deterministic tools. They are becoming increasingly inadequate for the future grid. The developed look-ahead contingency analysis algorithm incorporates forecast errors of variable energy and load to address the challenges brought by the increasing uncertainty of power system. The algorithm can reveal the potential violations caused by the variance of variable energy and load that are not normally detected by traditional deterministic approaches. To test its performance under practical environments ( real data with real commercial tool), significant efforts have been made to prepare test cases, modify GE EMS tool, and adapt an extreme value distribution algorithm to analyze the GE EMS’s violation-only outputs. The test results clearly demonstrate the effectiveness of the developed algorithm as new transformer violations that were not previously detected have been identified. This performance provides better situational awareness to engineers for their decision-making process under uncertainty. Moreover, with the discussion of computational performance and future work, this paper has shown a clear path for integrating the probabilistic algorithm with commercial tools to make us better equipped for the changing power system.

Modeling and simulation of power systems, constrai↗
DOE OSTI2022

Propagating Parameter Uncertainty in Power System Nonlinear Dynamic Simulations Using a Koopman Operator-Based Surrogate Model

In this work, we propose a Koopman operator-based surrogate model for propagating parameter uncertainties in power system nonlinear dynamic simulations. First, we augment a priori known state-space model by reformulating parameters deemed uncertain as pseudo-state variables. Then, we apply the Koopman operator theory to the resulting state-space model and obtain a linear dynamical system model. This transformation allows us to analyze the evolution of the system dynamics through its Koopman eigenfunctions, eigenvalues, and modes. Of particular importance for this letter, the obtained linear dynamical system is a surrogate that enables the evaluation of parameter uncertainties by simply perturbing the initial conditions of the Koopman eigenfunctions associated with the pseudo-state variables. Simulations carried out on the New England test system reveal the excellent performance of the proposed method in terms of accuracy and computational efficiency.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

A Bilevel Voltage Regulation Operation for Distribution Systems With Self-Operated Microgrids

The emerging of microgrids in distribution systems has significantly enhanced the resilience of power grids. However, the operators of a distribution system and microgrids therein can be different and have accessibility to different devices. To model the operation of such a grid, this work proposes a bilevel formulation and probes into the voltage regulation operation, considering the interaction between different systems. The proposed bilevel formulation considers the cooperation of active energy resources (AER), transformer tap-changers, and capacitor banks that are controlled by different operators. To facilitate the solution time of the target bilevel optimization, the lower-level problems with different objectives are modeled using deep neural networks (DNNs) which are then converted into a set of constraints. Hence, the bilevel problem can be reformed to a single-level problem. Lastly, the proposed solution procedures are validated using a customized joint system constructed by the IEEE 123-bus system and a real distribution system in Iowa. According to the numerical validation results, the solution time of the proposed nonlinear activation function based DNN model is 69 times faster than other methods in solving voltage regulation with a bilevel structure.

24 POWER TRANSMISSION AND DISTRIBUTION↗