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DOE OSTI2024

Simulation-Based Analysis of Feeder Operation with Different PV Smart Inverter Functions on an Actual Distribution System: Preprint

High penetration of photovoltaics (PV) in distribution feeders can cause problems, such as overvoltage, reverse power flow, and large net load changes. Traditional voltage regulation devices, such as capacitors and voltage regulators, can solve some of these problems but might have some delays. Today, smart inverters are gradually being used to provide voltage regulation and frequency support in distribution systems. Different smart inverter settings have been recommended in various rules and standards; however, the potential benefits and their impacts on distribution system operation are not well compared and studied. This paper presents a comparison of different smart inverter settings as applied to a distribution system. An actual feeder model from San Diego Gas & Electric Company is used to conduct the simulation. Additionally, a load disaggregation method is proposed to disaggregate the load and PV profile for each load location using advanced metering infrastructure net load measurements. Then, different smart inverter settings are applied to the PV systems in the feeder, and the simulation results are compared. The results show that the implementation of specific functions of smart inverters can reduce voltage exceedances, and the utility can determine the specific inverter setting based on its operational requirements.

distribution system↗

DOE OSTI2026

High-Burnup LOCA Burst Susceptibility BISON Analysis in PWRs and BWRs

Accurately assessing high-burnup fuel behavior during loss-of-coolant accidents (LOCAs) is essential for understanding fuel fragmentation, relocation, and dispersal (FFRD) risks across the US light-water reactor fleet. This work updates previous Nuclear Energy Advanced Modeling and Simulation (NEAMS) Program multiphysics LOCA analyses for a pressurized water reactor (PWR) and a boiling water reactor (BWR) by incorporating recent model and material property advancements in the BISON fuel performance code, including a high-burnup structure (HBS) model, revised cladding burst criteria, and updated thermal–mechanical correlations. This update was needed to support ongoing industry initiatives and upcoming regulatory changes. Full-core, rod-resolved operating histories generated using Virtual Environment for Reactor Analysis (VERA) and system-level LOCA conditions obtained from TRACE were applied to statistically representative rod samples in BISON to evaluate burst behavior and FFRD susceptibility. These calculations used two cladding burst correlations and three fuel pulverization models so that the predictions of these models could be compared. The updated PWR simulations show markedly improved numerical stability as the number of crashed simulations decreased by 95% compared to the previous study, and hence higher confidence in results. The updated PWR simulations predicted cladding bursts exclusively among once-burned, high-power rods, with two different cladding burst models identifying the same burst-susceptible population. Resulting FFRD susceptibility estimates are significantly reduced compared with earlier studies, driven by cooler predicted fuel and plenum temperatures, lower hoop strains, and reduced fission gas release in the updated models. In contrast, none of the BWR rods were predicted to burst under either burst criterion, reaffirming minimal BWR FFRD susceptibility even with updated HBS and material models. Comparisons between the PWR and BWR end-of-cycle predictions are made. Comparison with prior work highlights significant shifts in PWR fuel performance metrics and confirmation of earlier BWR conclusions. Overall, the updated results underscore the importance of having high-resolution detailed modeling capability and continuously integrating evolving material models and physics into high-resolution multiphysics simulations. The unified assessment presented here strengthens confidence in predicting high-burnup LOCA behavior by improving agreement between different cladding burst correlations. These results also provide an improved foundation for future BISON model development, FFRD susceptibility calculations.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

Umbilical Fatigue Analysis for a Wave Energy Converter

Unique umbilical designs for wave energy converters (WECs), including the ability to handle significantly larger motions and loads over long deployments, are often required when conventional marine umbilical designs for offshore oil and gas and offshore wind may not meet the design and cost needs of wave energy technologies. This study details a fatigue analysis of a dynamic power umbilical attached to a two-body floating point absorber WEC system, using the sea states provided for the PacWave testing facilities. The 6 degrees of freedom motion time history for the WEC was simulated, and the motions of the attachment point for the umbilical on the WEC and respective sea states were used to analyze the dynamic motions and fatigue of the connected power umbilical to predict the fatigue life. The results show that the fatigue damage observed is more significant in shallow water, and extensive fatigue damage may occur because of the larger curvature response of the umbilical. The umbilical configurations departing at 90 deg off incoming waves were found to have the highest fatigue life attributed to less extension or compression of the umbilical. However, additional bend stiffener/limiter features may need to be incorporated into the buoyancy section and touchdown regions to minimize curvature-induced fatigue.

50 EE - Wind and Water Power Program - Water (EE-4↗

DOE OSTI2021

Tribological behavior of ceramic-alloy bearing contacts in molten salt lubrication for concentrating solar power

Molten salts are considered as candidate heat transfer fluids and thermal energy storage media for next generation concentrating solar power (CSP). A molten salt circulates inside the piping and heat exchanger and also functions as a lubricant for the sleeve bearings of the CSP pump. Furthermore, wear- and corrosion-resistant high-temperature bearing materials are critical for the pump efficiency and durability. This study evaluated the tribological performance of candidate bearing materials in lubrication of a molten chloride salt mixture (20% NaCl + 40% MgCl 2 + 40% KCl) at 750 °C in an inert argon gas (a simulative CSP pump environment). Six ceramic-alloy pairs were tested, zirconia and silicon nitride against Haynes 244, Hastelloy C276, and Tribaloy T900 alloy, and ranked by the friction coefficient and wear loss. Characterization of worn surfaces suggested the wear mechanism as a combination of abrasion, adhesion, and tribocorrosion. Results from this study provide fundamental insight for the development and selection of bearing materials for molten salt powered CSP pumps.

14 SOLAR ENERGY↗

NASA NTRS2015

Evaluation of the 7-km GEOS-5 Nature Run

This report documents an evaluation by the Global Modeling and Assimilation Office (GMAO) of a two-year 7-km-resolution non-hydrostatic global mesoscale simulation produced with the Goddard Earth Observing System (GEOS-5) atmospheric general circulation model. The simulation was produced as a Nature Run for conducting observing system simulation experiments (OSSEs). Generation of the GEOS-5 Nature Run (G5NR) was motivated in part by the desire of the OSSE community for an improved high-resolution sequel to an existing Nature Run produced by the European Centre for Medium-Range Weather Forecasts (ECMWF), which has served the community for several years. The intended use of the G5NR in this context is for generating simulated observations to test proposed observing system designs regarding new instruments and their deployments. Because NASA's interest in OSSEs extends beyond traditional weather forecasting applications, the G5NR includes, in addition to standard meteorological components, a suite of aerosol types and several trace gas concentrations, with emissions downscaled to 10 km using ancillary information such as power plant location, population density and night-light information. The evaluation exercise described here involved more than twenty-five GMAO scientists investigating various aspects of the G5NR performance, including time mean temperature and wind fields, energy spectra, precipitation and the hydrological cycle, the representation of waves, tropical cyclones and midlatitude storms, land and ocean surface characteristics, the representation and forcing effects of clouds and radiation, dynamics of the stratosphere and mesosphere, and the representation of aerosols and trace gases. Comparisons are made with observational data sets when possible, as well as with reanalyses and other long model simulations. The evaluation is broad in scope, as it is meant to assess the overall realism of basic aspects of the G5NR deemed relevant to the conduct of OSSEs. However, because of the relatively short record and other practical considerations, these comparisons cannot provide a definitive, statistically sound assessment of all model deficiencies, or guarantee the G5NR's suitability for all OSSE applications. Differences between the observed and simulated behavior also must be judged in the context of basic internal atmospheric variability which can introduce variations that are not necessarily controlled by the prescribed sea surface temperatures used in generating the G5NR. The results show that the G5NR performs well as measured by the majority of metrics applied in this evaluation. Particular benefits derived from the 7-km resolution of G5NR include realistic representations of extreme weather events in both the tropics and extratropics including tropical cyclones, Nor'easters and mesoscale convective complexes; improved representation of the diurnal cycle of precipitation over land; well-resolved surface-atmosphere interactions such as katabatic wind flows over Antarctica and Greenland; and resolution of orographically generated gravity waves that propagate into the upper atmosphere and influence the large scale circulation. Obvious deficiencies in the G5NR include a "splitting" of the inter-tropical convergence zone, which leads to a weaker-than-observed Hadley circulation and related deficiencies in the depiction of stationary wave patterns. Also, while the G5NR captures global cloud features and radiative effects well in general, close comparison with observations reveals higher-than-observed cloud brightness, likely due to an overabundance of cloud condensate; less distinct cloud minima in subtropical subsidence zones, consistent with a weak Hadley circualtion; and too few near-coastal marine stratocumulus clouds.

GEOS-5↗

NASA NTRS2013

Reactor Simulator Testing

As part of the Nuclear Systems Office Fission Surface Power Technology Demonstration Unit (TDU) project, a reactor simulator test loop (RxSim) was design & built to perform integrated testing of the TDU components. In particular, the objectives of RxSim testing was to verify the operation of the core simulator, the instrumentation and control system, and the ground support gas and vacuum test equipment. In addition, it was decided to include a thermal test of a cold trap purification design and a pump performance test at pump voltages up to 150 V since the targeted mass flow rate of 1.75 kg/s was not obtained in the RxSim at the originally constrained voltage of 120 V. This paper summarizes RxSim testing. The gas and vacuum ground support test equipment performed effectively in NaK fill, loop pressurization, and NaK drain operations. The instrumentation and control system effectively controlled loop temperature and flow rates or pump voltage to targeted settings. The cold trap design was able to obtain the targeted cold temperature of 480 K. An outlet temperature of 636 K was obtained which was lower than the predicted 750 K but 156 K higher than the cold temperature indicating the design provided some heat regeneration. The annular linear induction pump (ALIP) tested was able to produce a maximum flow rate of 1.53 kg/s at 800 K when operated at 150 V and 53 Hz. Keywords: fission, space power, nuclear, liquid metal, NaK.

Schoenfeld, Michael P.↗

DOE OSTI2024

Joint Management and Optimization of Residential Natural Gas and Electricity Distribution Networks Coupled via Fuel Cells

The interesting properties of natural gas as well as the growing electric power demand worldwide have led to increasing attention to natural-gas-based distributed generation applications in electric distribution systems. This paper goes over the interdependency between a residential natural gas network and an electric distribution network that are coupled via fuel cells. The modeling of the gas network is introduced first, and then the algorithm for gas flow study is presented. The optimal placement and sizing of fuel cell based distributed generation systems are formulated to minimize the losses in both the gas and electric distribution networks, subject to their model constraints. In addition to this, in order to capture the probabilistic nature of the optimization problem under study, the K-means clustering algorithm is applied to the gas and electricity demands to determine hourly load states and their corresponding probabilities. Furthermore, simulation studies are carried out on an integrated system consisting of the IEEE 69-bus distribution feeder and a radial 27-node natural gas network to verify the developed optimization model and the proposed method.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Building a DFT+U machine learning interatomic potential for uranium dioxide

Despite uranium dioxide (UO 2 ) being a widely used nuclear fuel, fuel performance models rely extensively on empirical correlations of material behavior, leveraging the historical operating experience of UO 2 . Mechanistic models that consider an atomistic understanding of the processes governing fuel performance (such as fission gas release and creep) will enable a better description of fuel behavior under non-prototypical conditions such as in new reactor concepts or for modified UO 2 fuel compositions. To this end, molecular dynamics simulation is a powerful tool for rapidly predicting physical properties of proposed fuel candidates. However, the reliability of these simulations depends largely on the accuracy of the atomic forces. Traditionally, these forces are computed using either a classical force field (FF) or density functional theory (DFT). While DFT is relatively accurate, the computational cost is burdensome, especially for f-electron elements, such as actinides. By contrast, classical FFs are computationally efficient but are less accurate. For these reasons, we report a new accurate machine learning interatomic potential (MLIP) for UO 2 that provides high-fidelity reproduction of DFT forces at a similar low cost to classical FFs. We employ an active learning approach that autonomously augments the DFT training data set to iteratively refine the MLIP. To further improve the quality of our predictions, we utilize transfer learning to retrain our MLIP to higher-accuracy DFT+U data. We validate our MLIPs by comparing predicted physical properties (e.g., thermal expansion and elastic properties) with those from existing classical FFs and DFT/DFT+U calculations, as well as with experimental data when available.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2026

Experimental investigation of a closed vapour box module for a divertor-like configuration in Magnum-PSI

Efficient management of extreme heat fluxes in the divertor region to extend the lifetime of the components remains a critical challenge for the realization of nuclear fusion-based power plants. Among the alternative concepts explored for the divertor region, the use of liquid metals, particularly lithium, is of interest due its ability to dissipate the incoming plasma heat flux through the vapour shielding effect (VS). In this work, we experimentally investigated a ‘closed’ configuration of a dedicated Vapour Box Module (VBM) in the linear plasma device Magnum-PSI. The goal of the experiments is to simulate the vapour box divertor environment conditions and assess its performance in terms of power mitigation and redistribution and lithium confinement. Initial testing without Li demonstrated the efficacy of a closed VBM structure in inducing detachment via neutral gas accumulation. Apertures which enabled non-condensing gas to be effectively pumped while ensuring lithium condensed on the inner surfaces were therefore added. With a lithium capillary porous structure target used, lithium is directly vaporized by the plasma, forming a dense lithium vapour cloud that interacts with the incoming plasma. This resulted in a significant reduction of the target temperature of at least 48%, together with a temperature locking effect, a phenomenon typically observed in the VS regime. Lithium vapour confinement within the VBM was strongly correlated with the wall temperature. Relatively cold walls promoted Li re-condensation and therefore improved Li confinement, although with the expected trade-off of increased hydrogenic retention on lithium-wetted surfaces. As the wall temperature increased, the confinement efficiency decreased, consistent with reduced Li re-condensation and thermally activated Li–H chemistry and remobilization at the walls. Diagnostic measurements through embedded thermocouples and calorimetry revealed that lithium vaporization and re-condensation processes also playedsignificant roles in plasma power dissipation. The results advance the case for a closed divertor chamber with direct lithium evaporation from the strike-points as a viable method to manage divertor heat fluxes in future fusion reactors.

Romano, Fabio [Dutch Institute for Fundamental Ene↗

DOE OSTI2026

Flying focus with arbitrary directionality for spatiotemporal control of laser intensity

Flying focus techniques produce laser pulses whose focal points travel at arbitrary, controllable velocities. While this flexibility can enhance a broad range of laser-based applications, existing techniques constrain the motion of the focal point to the propagation direction of the pulse. Here, we introduce a flying focus configuration that decouples the motion of the focus from the propagation direction. Here, a chirped laser pulse focused and diffracted by a diffractive lens and grating creates a focal point that can move both along and transverse to the propagation direction. The focal length of the lens, grating period, and chirp can be tuned to control the direction and velocity of the focus. Simulations demonstrate this control for a holographic configuration suited to high-power pulses, in which two off-axis pump beams with different focal lengths encode the equivalent phase of a chromatic lens and grating in a gas or plasma. For low-power pulses, conventional solid-state or adaptive optics can be used instead. Multi-dimensional control over the focal trajectory enables new configurations for applications, including laser wakefield acceleration of ions, nonlinear Thomson scattering, and surface-plasmon emission of THz radiation.

Classical optics↗

NASA NTRS2014

Propulsion Electric Grid Simulator (PEGS) for Future Turboelectric Distributed Propulsion Aircraft

NASA Glenn Research Center, in collaboration with the aerospace industry and academia, has begun the development of technology for a future hybrid-wing body electric airplane with a turboelectric distributed propulsion (TeDP) system. It is essential to design a subscale system to emulate the TeDP power grid, which would enable rapid analysis and demonstration of the proof-of-concept of the TeDP electrical system. This paper describes how small electrical machines with their controllers can emulate all the components in a TeDP power train. The whole system model in Matlab/Simulink was first developed and tested in simulation, and the simulation results showed that system dynamic characteristics could be implemented by using the closed-loop control of the electric motor drive systems. Then we designed a subscale experimental system to emulate the entire power system from the turbine engine to the propulsive fans. Firstly, we built a system to emulate a gas turbine engine driving a generator, consisting of two permanent magnet (PM) motors with brushless motor drives, coupled by a shaft. We programmed the first motor and its drive to mimic the speed-torque characteristic of the gas turbine engine, while the second motor and drive act as a generator and produce a torque load on the first motor. Secondly, we built another system of two PM motors and drives to emulate a motor driving a propulsive fan. We programmed the first motor and drive to emulate a wound-rotor synchronous motor. The propulsive fan was emulated by implementing fan maps and flight conditions into the fourth motor and drive, which produce a torque load on the driving motor. The stator of each PM motor is designed to travel axially to change the coupling between rotor and stator. This feature allows the PM motor to more closely emulate a wound-rotor synchronous machine. These techniques can convert the plain motor system into a unique TeDP power grid emulator that enables real-time simulation performance using hardware-in-the-loop (HIL).

electric power grid emulator↗

NASA NTRS1992

Galaxies and gas in a cold dark matter universe

We use a combined gravity/hydrodynamics code to simulate the formation of structure in a random 22 Mpc cube of a cold dark matter universe. Adiabatic compression and shocks heat much of the gas to temperatures of 10 exp 6 - 10 exp 7 K, but a fraction of the gas cools radiatively to about 10 exp 4 K and condenses into discrete, highly overdense lumps. We identify these lumps with galaxies. The high-mass end of their baryonic mass function fits the form of the observed galaxy luminosity function. They retain independent identities after their dark halos merge, so gravitational clustering produces groups of galaxies embedded in relatively smooth envelopes of hot gas and dark matter. The galaxy correlation function is approximately an r exp -2.1 power law from separations of 35 kpc to 7 Mpc. Galaxy fluctuations are biased relative to dark matter fluctuations by a factor b about 1.5. We find no significant 'velocity bias' between galaxies and dark matter particles. However, virial analysis of the simulation's richest group leads to an estimated Omega of about 0.3, even though the simulation adopts Omega = 1.

Katz, Neal↗

NASA NTRS2016

Alternative Bio-Derived JP-8 Class Fuel and JP-8 Fuel: Flame Tube Combustor Test Results Compared using a GE TAPS Injector Configuration

This paper presents results from tests in a NASA Glenn Research Center (GRC) flame tube facility, where a bio-derived alternate fuel was compared with JP-8 for emissions and general combustion performance. A research version of General Electric Aviation (GE) TAPS injector was used for the tests. Results include 2D, planar laser-based imaging as well as basic flow visualization of the flame. Four conditions were selected that simulate various engine power conditions relevant to NASA Fundamental Aeronautics Supersonics and Environmentally Responsible Aviation Projects were tested.

optical diagnostics↗

DOE OSTI2022

Modeling of a 43 GHz microplasma within a photonic crystal

The electron density (n e ) and argon metastable density (1 s 5 ) of a 43GHz microplasma are obtained using the zero-dimensional plasma kinetics solver (ZDPlasKin®) for an incident power of 160 and 1000mW and argon pressures of 10–600Torr (1.3 ×10 3 to 8.0 × 10 4 Pa). These simulations are compared with previously published experimental data. To determine the self-consistent electric field in the modeled plasma, the three-dimensional millimeter wave fields are computed as a function of electron density using ANSYS EM19.2, HFSS®. This electromagnetic field model is coupled to ZDPlasKin such that any increase in the simulated plasma density correctly attenuates the simulated electric field within the microplasma. The electron density is found to be sensitive to argon gas temperature, so a two-zone temperature model was needed to obtain agreement with experimental measurements. The temperature in the central core of the microplasma was determined by a previous experimental study. That temperature was used as an input to the model for the simulation of volume recombination losses. The outer regions of the microplasma are assumed to be in equilibrium with the walls (300K). This second temperature was used in the model to determine diffusion losses. The modeled electron and metastable densities are of the order 10 20 and 10 18 m –3 , respectively. This is in good agreement with those measured experimentally as long as the two-zone temperature model is used. In the absence of a hot gas core, the modeled three-body recombination rates are excessive and the simulation severely under-predicts the electron density and over-estimates the metastable density. We conclude that the millimeter wave microplasma has a hot core (2500K at 600 Torr) that rarifies the argon gas and effectively reduces three-body recombination. Furthermore, this allows one to achieve high electron density on the order of 10 20 m –3 with only 100mW of wave power.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Exploring Building Retrofit Strategies Using AutoBEM Under Future Weather Scenarios

This study evaluates the long-term effectiveness of energy conservation measures (ECMs) on building energy consumption using AutoBEM, a scalable modeling framework driven by the high-resolution Model America dataset. We simulated 18,951 buildings in Flagstaff, Arizona under four climate scenarios using Future Typical Meteorological Year (fTMY) weather files for six time periods spanning from 1980 to 2099. Six ECMs were analyzed across electricity and gas usage, including HVAC fuel-switching, insulation upgrades, and infiltration control. While some measures, such as reducing space infiltration by percentage, showed minimal or even negative impact on total energy savings at the aggregate level, they proved highly effective for specific building types. Conversely, HVAC electrification offers high gas reduction but shifts demand to electricity, highlighting critical trade-offs under different climate trajectories. Building-type-specific analysis under SSP5-RCP8.5 (2080–2099) revealed significant variation in ECM performance, underscoring the need for targeted retrofit strategies. This study demonstrates the power of combining fTMY projections with large-scale simulations to inform data-driven retrofit planning.

Chowdhury, Shovan [ORNL]↗

NASA NTRSDate not supplied

Using Time Series Data Products to Support ASHRAE’s Historic and Future Climate Data Needs through NASA’s POWER Web Services

To address the data needs for resilience and sustainability of building systems within ASHRAE, the NASA Prediction of Worldwide Energy Resource (POWER) project facilitates the use of NASA Earth Science data on a long-term, global scale. Solar data from several NASA projects and meteorological data from NASA assimilation models have been reformatted and disseminated to the public via a user friendly web GIS-enabled based data portal (https://power.larc.nasa.gov) in selectable data formats, immediately amenable to key industry wide decision support tools such as EnergyPlus. Time series of potential climate conditions from downscaled climate simulations are being made available for similar statistics and formats. An emphasis is placed upon obtaining and utilizing time series data to conduct analysis of building system performance for current and planning building systems for energy savings and greenhouse gas emissions. This presentation has the learning following learning objectives for the ASHRAE community: 1) Learn how NASA POWER’s web service suite can provide supplementary solar and surface meteorological data parameters, including a discussion of uncertainty. 2) Learn how downscaled climate scenario information can be provided to evaluate potential future requirements. The presentation is part of a forum entitled, "Weather Data for Large-Scale Building Energy Modeling".

time series↗

NASA NTRS1988

Acceleration ground test program to verify GAS payload No. 559 structure/support avionics and experiment structural integrity

Acceleration ground tests were conducted on the Get Away Special (GAS) payload 559 to verify the structural integrity of the structure/support avionics and two of the planned three flight experiments. The ITA (Integrated Test Area) Standardized Experiment Module (ISEM) structure was modified to accommodate the experiments for payload 559. The ISEM avionics consisted of a heavy duty sliver zinc power supply, three orthogonal-mounted low range microgravity accelerometers, a tri-axis high range accelerometer, a solid state recorder/programmer sequencer, and pressure and temperature sensors. The tests were conducted using the Gravitational Plant Physiology Laboratory Centrifuge of the University City Science Center in Philadelphia, PA. The launch-powered flight steady state acceleration profile of the shuttle was simulated from lift-off through jettison of the External Tank (3.0 g's). Additional tests were conducted at twice the nominal powered flight acceleration levels (6 g's) and an over-test condition of four times the powered flight loads to 12.6 g's. The present test program has demonstrated the value of conducting ground tests to verify GAS payload experiment integrity and operation before flying on the shuttle.

Cassanto, John M.↗

DOE OSTI2024

Joint Management and Optimization of Residential Natural Gas and Electricity Distribution Networks Coupled via Fuel Cells

The attractive features of natural gas as well as the growing electric power demand worldwide have created increasing interest in natural-gas-based distributed generation applications for electric distribution networks. Here, this paper investigates the interdependency between a residential natural gas network and an electric distribution network that are linked together via fuel cells. The modeling of the natural gas network is introduced first, and then the algorithm for gas flow study is presented. The optimal placement and sizing of fuel cell based distributed generation systems are formulated to minimize the losses in both the natural gas network and the electric distribution grid, subject to the constraints imposed by both networks. In addition, a probabilistic model for both gas and electricity demands is developed based on historical electricity and natural gas demand data. A K-means clustering method is used to determine the hourly load states to solve the joint probabilistic optimization problem. Simulation studies are carried out on an integrated system consisting of the IEEE 69-bus distribution network and a radial 27-node natural gas network to verify the developed optimization model and the proposed method.

24 POWER TRANSMISSION AND DISTRIBUTION↗