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At least 37 records · Page 2

Virtual tower measurements during the American WAKE ExperimeNt (AWAKEN)

Dual-Doppler lidar measurements were made during the American WAKE ExperimeNt to provide height-resolved measurements of wind speed and direction at multiple locations immediately south of the leading row turbines in the King Plains wind farm in Oklahoma. These so-called virtual tower measurements were performed to characterize the inflow into the wind farm and to assess possible upwind blockage effects due to the collective action of the wind farm. The campaign was conducted from 12 November 2022 to 17 October 2023, during which time 14 unique virtual tower locations were sampled with heights ranging from 240 to 490 m AGL. The wind retrieval algorithm provided estimates of the horizontal winds and their uncertainties with a vertical resolution of about 10 m, while also accounting for the tilt of the lidar platform. The virtual tower results are compared to collocated lidar wind profiling data at the A1 site, which was located roughly 2.4 rotor diameters south of the nearest turbine. The wind speed difference between the wind profiler and the virtual tower was found to be quite sensitive to atmospheric stability and wind direction below 250 m AGL. The largest differences were observed for inflow under stable conditions, where the profiler wind speeds were observed to be about 22% lower than the virtual tower near hub height. These results suggest that there are persistent horizontal gradients in the flow upwind of the wind farm which result in biased estimates using standard ground-based lidar wind profiling methods.

17 WIND ENERGY↗

Future evolution of virtual water trading in the United States electricity sector

Abstract Future transformations in the electricity sector could entail major shifts in power sector technology mixes and electricity trade, with consequences for the trading of virtual water. Previous virtual water trade studies largely focus on historical timeframes. We explore, for the first time, future—through 2050—virtual water trade driven by electricity trade under a range of future electricity sector transformation scenarios using the United States as an example. Under a business-as-usual scenario, virtual water trading in 2050 decreases by 3% relative to 2015 levels. By contrast, virtual water trading increases respectively by 3%, 26%, and 32%, in scenarios characterized by higher socioeconomic growth, higher potential for transmission expansion, and low-carbon transitions. These increases are driven by electricity generation expansion in the western U.S., resulting in higher virtual water trade to the east. In addition, we find that as electricity generation shifts west, an increased amount of nonrenewable groundwater will be consumed to generate electricity that is supplied to the east. Independent of scenario, the US electricity grid largely relies on virtual water exports from only a few states. Our study highlights the need for integrated and national strategies to manage the water and electric systems.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

A computational modeling framework for pre-clinical evaluation of cardiac mapping systems

There are a variety of difficulties in evaluating clinical cardiac mapping systems, most notably the inability to record the transmembrane potential throughout the entire heart during patient procedures which prevents the comparison to a relevant “gold standard”. Cardiac mapping systems are comprised of hardware and software elements including sophisticated mathematical algorithms, both of which continue to undergo rapid innovation. The purpose of this study is to develop a computational modeling framework to evaluate the performance of cardiac mapping systems. The framework enables rigorous evaluation of a mapping system’s ability to localize and characterize (i.e., focal or reentrant) arrhythmogenic sources in the heart. The main component of our tool is a library of computer simulations of various dynamic patterns throughout the entire heart in which the type and location of the arrhythmogenic sources are known. Our framework allows for performance evaluation for various electrode configurations, heart geometries, arrhythmias, and electrogram noise levels and involves blind comparison of mapping systems against a “silver standard” comprised of computer simulations in which the precise transmembrane potential patterns throughout the heart are known. A feasibility study was performed using simulations of patterns in the human left atria and three hypothetical virtual catheter electrode arrays. Activation times (AcT) and patterns (AcP) were computed for three virtual electrode arrays: two basket arrays with good and poor contact and one high-resolution grid with uniform spacing. The average root mean squared difference of AcTs of electrograms and those of the nearest endocardial action potential was less than 1 ms and therefore appears to be a poor performance metric. In an effort to standardize performance evaluation of mapping systems a novel performance metric is introduced based on the number of AcPs identified correctly and those considered spurious as well as misclassifications of arrhythmia type; spatial and temporal localization accuracy of correctly identified patterns was also quantified. This approach provides a rigorous quantitative analysis of cardiac mapping system performance. Proof of concept of this computational evaluation framework suggests that it could help safeguard that mapping systems perform as expected as well as provide estimates of system accuracy.

59 BASIC BIOLOGICAL SCIENCES↗

Single Carrier Modulation Resource Allocation for Massive MIMO with Virtual Antennas

Today’s Massive MIMO cellular operation is dominated by orthogonal frequency division multiplexing (OFDM) modulation. One of the advantages of OFDM is the flexibility to carve up the available spectrum into resource blocks (RBs) that can operate adjacent to one another. Massive MIMO adds spatial multiplexing layers on top of the RBs, enabling the simultaneous operation of dozens of UEs. Cyclic prefixed single carrier modulation (CP-SCM) is an alternative to OFDM that also benefits from massive MIMO and is useful as an OFDM alternative in specific scenarios. However, until recently, no resource allocation method has been proposed for CP-SCM. In this paper, we present a CP-SCM resource allocation scheme using virtual antennas in a massive MIMO time domain duplexed scenario. By creating several virtual antennas for each physical antenna, the benefits of massive MIMO are achieved with a smaller physical antenna count. Resources are quantized into data streams, and each user can be assigned a variable number of simultaneous streams. This paper presents a detailed development and analysis of multi-stream processing (MSP) for both uplink detection and downlink precoding. We also introduce heterogeneous MSP, where CP-SCM and OFDM signals can be processed in the same MSP framework.

5G and beyond communications↗

Arbitrary Order Virtual Element Methods for High‐Order Phase‐Field Modeling of Dynamic Fracture

ABSTRACT Accurate modeling of fracture nucleation and propagation in brittle and ductile materials subjected to dynamic loading is important in predicting material damage and failure under extreme conditions. Phase‐field fracture models have garnered a lot of attention in recent years due to their success in representing damage and fracture processes in a wide class of materials and under a variety of loading conditions. Second‐order phase‐field fracture models are by far the most popular among researchers (and increasingly, among practitioners), but fourth‐order models have started to gain broader acceptance since their more recent introduction. The exact solution corresponding to these high‐order phase‐field fracture models has higher regularity. Thus, numerical solutions of the model equations can achieve improved accuracy and higher spatial convergence rates. In this work, we develop a virtual element framework for the high‐order phase‐field model of dynamic fracture. The virtual element method (VEM) can be regarded as a generalization of the classical finite element method. In addition to many other desirable characteristics, the VEM allows computing on polytopal meshes. Here, we use ‐conforming virtual elements and the generalized‐ time integration method for the momentum balance equation, and adopt ‐conforming virtual elements for the high‐order phase‐field equation. We verify our virtual element framework using classical quasi‐static benchmark problems and demonstrate its capabilities with the aid of numerical simulations of dynamic fracture in brittle materials.

42 ENGINEERING↗

Recent advances in plasma control and physics research in the Large Helical Device

The Large Helical Device (LHD), the largest superconducting helical system in the world, is equipped with advanced heating and diagnostic tools, facilitating plasma control and physics research. Data assimilation was employed for electron temperature control using a real-time Thomson scattering system and real time prediction code. A virtual LHD environment enabled visualization of escaping high-energy tritium ions and demonstrated that these ions impact the rear side of the divertor plate. Pioneering results crucial to plasma control have also been achieved. Real-time wall conditioning using Lithium granule dropping improved bulk ion energy and particle transport while simultaneously enhancing the heavy impurity transport. Progress has also been made in the investigation of turbulence-driven transport. At the confinement bifurcation, ion-scale turbulence decreased, while electron-scale turbulence increased. A change in the anisotropy of turbulent eddies was also observed at the confinement bifurcation. Coexistence of local and non-local turbulence was identified in electron-scale turbulence. Non-local turbulence exhibited the rapid spatial propagation of perturbations throughout the plasma, while local turbulence followed the temperature gradient. A transition between drift-wave turbulence and magnetohydrodynamics (MHD) turbulence was observed with the turbulence minimized at the transition condition. Machine learning analysis was employed to evaluate the temperate and density conditions of this turbulence transition. Then, real-time control of fueling and heating was applied to maintain the turbulence transition condition, improving the energy confinement enhancement factor by 20%. In addition, evidence was obtained for collisionless ion heating by energetic-ion-driven geodesic acoustic modes and MHD bursts. These achievements represent unique contributions to the development of fusion reactors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Immersive Digital Twin Laboratory for Engineering Education (CRADA Final Report)

This project aimed to create an immersive digital twin laboratory that incorporates advanced tracking and visualization capabilities. In collaboration with Fort Lewis College, NREL designed a state-of-the-art physical visualization laboratory, developed a software platform to enable interaction with tracked physical objects in the laboratory, and provided proof-of-concept curricula that included manipulating these tracked objects. The project was initiated to address the growing need for innovative educational tools in engineering education. As renewable energy systems, particularly solar installations, become more complex, there is a pressing need to bridge the gap between theoretical knowledge and practical application. Traditional methods of teaching solar engineering concepts often fall short of providing students with a comprehensive, hands-on understanding. This immersive digital twin laboratory was conceived to fill that gap by creating a safe, non-energized setting where students can interact with augmented solar installation objects, gaining valuable insights into system performance, design, and maintenance. The project utilized extended reality (XR) technologies, including head-mounted displays (HMDs) and a whole-room optical motion tracking system, to connect physical objects with their digital twins in real time. The laboratory was equipped with MagicLeap 2 HMDs, supported by a Vicon Vero 2.2 Optical Tracking System, which provided precise 6-degrees-of-freedom (6-DOF) tracking. We developed a software platform to manage the interaction between the tracked physical objects and their virtual counterparts, enabling real-time data synchronization, object recognition, and virtual overlays. We designed the system to be flexible and extendable, allowing for future integration of additional objects and curriculum. This research advances the field of engineering education by demonstrating the potential of immersive digital twin environments. The laboratory provides a dynamic learning space where students can experiment, collaborate, and learn without the risks associated with live experimentation. The ability to simulate and manipulate solar installation objects under various conditions has broad implications for workforce development, particularly in renewable energy. The project also highlights the economic feasibility of using XR technologies in educational settings, offering a cost-effective solution for institutions looking to enhance their curriculum. By fostering a deeper understanding of solar energy systems, this work contributes to the broader goal of supporting the global energy transition and preparing the next generation of engineers and technicians.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Towards time-resolved MicroED grid preparation using mix-and-inject gas dynamic virtual nozzles

Recent progress in gas dynamic virtual nozzle (GDVN) technologies in combination with high-brilliance synchrotron and X-ray free-electron lasers (XFELs) has allowed the visualization of protein dynamics in crystallo by mixing macromolecular protein crystals with a substrate using tunable mixing times on the order of milliseconds to seconds prior to serial X-ray diffraction data collection. This has become the method of choice for high-resolution structure determination of intermediate states. However, such experiments require large counts of crystals of proper sizes for high-resolution data collection, and premium beam times for screening efforts. Cryogenic microcrystal electron diffraction (MicroED) represents a complementary technique that may be a more accessible avenue for time-resolved nanocrystallography compared with serial X-ray diffraction experiments. MicroED can produce full diffraction datasets from just a few submicrometre-thick crystals, and the approach is more readily accessible, requiring standard cryogenic transmission electron microscopy (TEM) equipment available at many universities and institutes. Cryogenic MicroED, like other forms of cryo-EM, begins with rapidly freezing biological material on electron microscopy grids. In the case of MicroED, micro- to nano-crystals (<500 nm thick) are deposited onto electron microscopy grids and plunge-frozen for subsequent electron diffraction data collection. Here, we have incorporated GDVN technology developed originally for XFEL experiments into the freezing process as a first step towards time-resolved studies. We describe the limited deposition efficiency of the model MicroED protein proteinase K on TEM grids using GDVNs, preceding sample vitrification and successful MicroED data collection. We discuss both the initial results from such experiments and the methodological challenges in developing this approach into a reliable workflow for millisecond-to-second time-resolved structural studies of macromolecules. Our results promise a strategy to deposit crystals on grids using GDVNs and determine high-resolution structures by MicroED, constituting a first step towards development of time-resolved MicroED experiments.

MicroED↗

Back-to-back inclusive dijets in DIS at small x : Sudakov suppression and gluon saturation at NLO

Back-to-back dijet cross-sections in deeply inelastic scattering (DIS) at small xBj are suppressed by many-body multiple scattering and screening effects arising from gluon saturation at high parton densities. They are similarly sensitive in these kinematics to large Sudakov logarithms from soft gluon radiation. Uncovering novel physics in this DIS channel therefore requires understanding the interplay of the two phenomena. In this work, we compute the small $x_\text{Bj}$ inclusive dijet DIS cross-section in back-to-back kinematics at next-to-leading order (NLO) in the Color Glass Condensate effective field theory (CGC EFT). Our result includes, for the first time, all real and virtual NLO contributions to the impact factor. These include all Sudakov double and single logarithm contributions, as well as all other finite $\mathcal{O}(α_s)$ terms that contribute at this order. We demonstrate explicitly that resummations of small x and Sudakov logarithms can be performed simultaneously in the CGC EFT. This requires that the JIMWLK kernel for small x evolution of the Weizsäcker-Williams (WW) gluon distribution satisfies a kinematic constraint imposed by lifetime ordering of successive gluon emissions; the corresponding modifications to the kernel, corresponding to resummations of large double transverse logarithms, are precisely of the type required to stabilize JIMWLK evolution beyond leading logarithmicaccuracy. We compute the azimuthal harmonics of the NLO back-to-back distributions and show their sensitivity to both the unpolarized and linearly polarized WW gluon distributions. Finally, we discuss how TMD factorization is broken by an emergent saturation scale at small $x$.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Immersive Scientific Visualization of Molten-Salt Reactor Waste Characteristics Using Virtual Reality

Immersive visualization is changing how we explore, communicate, and understand complex scientific systems. In nuclear energy, an area in which data are often multidimensional, time-dependent, and difficult to interpret, virtual reality (VR) represents a powerful and intuitive informational medium. This work introduces a VR-based platform that visualizes the post-shutdown behavior and waste management lifecycle of molten-salt reactors (MSRs), a next-generation reactor type with unique operational and safety characteristics. The platform, built in Unity, is streamed on the Meta Quest 3 headset. It transforms high-fidelity simulation data into an interactive, immersive experience. Users can explore time-dependent reactor characteristics such as nuclide decay, which is a key factor for evaluating reactor waste strategies. The datasets were generated using the MOOSE (Multiphysics Object-Oriented Simulation Environment) framework and then processed through ParaView scripting for smooth integration into Unity. From a visualization standpoint, the platform emphasizes spatial storytelling, temporal exploration, and user-centered interaction. Users can navigate 3D reactor geometries, slice through volumetric data, and manipulate time to observe how physical phenomena evolve. Real-scale rendering and embodied interaction make the experience feel tangible. The interface is designed to be accessible, even to those without nuclear or simulation expertise. This lowers the barrier for stakeholders, policymakers, and the general public, while still supporting expert analysis and collaborative decision-making. This work shows how immersive visualization can function as both a scientific tool and a communication interface. By integrating simulation, processing, and visualization into a cohesive workflow, we offer a scalable framework for immersive scientific storytelling. The modular design supports future extensions to other reactor types and lifecycle stages, from shutdown to long-term storage, making the platform adaptable for both research and outreach.

99 - GENERAL AND MISCELLANEOUS↗

Explicit quantification of residence and flushing times in the Salish Sea using a sub-basin scale shoreline resolving model

The Salish Sea, located in the Pacific Northwest region of North America has complex currents and circulation features distributed over numerous interconnected deep basins with islands. Increased risk of exposure to oil spills and untreated wastewater from maritime emergencies and treatment plant failures have led to a need for quantifying residence and flushing characteristics at a sub-basin scale using a shoreline resolving hydrodynamic model. An unstructured grid model of the Salish Sea was developed using FVCOM with a ≈75-100m shoreline resolution. In addition to 7 tides and 23 salinity and temperature monitoring stations, an extensive currents data set from 135 stations collected over a span of three years was used for skill assessment and validation. Explicit forward computations were then conducted to define and quantify residence and flushing times in various sub-basins of interest using (a) Lagrangian particles and (b) Numerical/virtual dye experiments. The results in most basins show expected seasonal variability with longer flushing time associated with summer lower tides and lower freshwater inflows. However, contrary to expectation, flushing time is significantly longer in wintertime in large fjord-like basins such as Hood Canal (≈138 days), likely due to increased stratification and reduced mixing. The flushing time for the Puget Sound region of the Salish Sea is ≈115 days, while Georgia Basin is 240 days when analyzed as stand-alone basins with zero background concentrations. When examined as part of the flushing of the entire Puget Sound filled with virtual dye, the compounded flushing times for embedded sub-basins can be significantly longer in order of magnitudes and largely dictated by the flushing time of Puget Sound. The computed residence and flushing time scales tabulated over 36 sub-basins provide an improved understanding of water renewal in the system, informing pollution management actions.

54 ENVIRONMENTAL SCIENCES↗

Digital Twin for Optimizing Real-time Economy of the Integrated Energy Systems

Economic and safe operation of integrated energy systems (IES) requires real-time optimization (RTO) of the control and actions conducted on each system component. In this regard, digital twins (DTs), which consist of a physical system, a virtual system, and the data communication that occurs between the two, are essential for effective RTO. Through the data warehouse, the virtual system is constantly updated with real-time data from the physical system, and functions as the model in the optimization framework. The reduced-order model of the dynamic process model in the virtual system is used in the optimization framework. The optimization results are then returned, via the data warehouse, as control actions to the physical system. This work demonstrates the software capabilities of DT assets for an IES in the context of preparing a DT for an experimental system comprised of Idaho National Laboratory (INL)’s Thermal Energy Delivery System and battery system. For the virtual demonstration, the DTs encompass (1) a physical system, including the Modelica models of the Thermal Energy Delivery System and the battery system; (2) virtual optimization via the Optimization of Real-Time Capacity Allocation (ORCA) platform; and (3) the open-source data warehouse software DeepLynx. This work assesses the performance of ORCA, which utilizes a reduced-order model built using the Risk Analysis Virtual Environment (RAVEN) and trained on the Modelica models and real-time data pipeline through the graph database hosted in DeepLynx. The proposed optimization workflow will be an RTO model based on DTs and the data they generate.

25 ENERGY STORAGE↗

Strong-field nonsequential double photoionization using virtual-detector theory with path summation

We present an ab initio study of the nonsequential strong-field ionization dynamics of a model two-electron atom with helium character. Single- and double-ionization events are characterized and displayed using detector signals extracted at different points in the two-electron two-dimensional space. The double photoelectron momentum distribution is calculated via coherent path-summation over virtual-particle trajectories. A comparison is made between the momentum distributions obtained with the virtual-detector method, the Schrödinger wave function, and the time-dependent surface flux method developed by Tao and Scrinzi [New J. Phys. 14, 013021 (2012)]. Insights into different ionization and electron recollision pathways are gained from detailed virtual-particle tracking and energy-time readouts. Furthermore, this study demonstrates the extension of virtual-detector theory to strong-field multielectron quantum dynamics and highlights the importance of the evolving quantum phase in quasiclassical electron propagation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Stability Considerations for Virtual Capacitor Control in Constant Power DC Loads

In a DC grid, constant power loads (CPLs) necessitate a large bus capacitor to prevent negative impedance instability. Some of the capacitance can be realized virtually through CPL control to reduce the bus capacitor size. Here, this paper analytically studies system stability with virtual capacitor control. We demonstrate that the effectiveness of virtual capacitor control is highly sensitive to the implementation of the derivative action required to emulate the capacitor. For the first time, we theoretically demonstrate that a virtual capacitor can stabilize the system without any physical bus capacitor, provided that a set of analytically derived conditions are met. However, this stabilization is not achievable in practice due to the influence of non-idealities. In an example system requiring a $14$ mF capacitor to stably support the CPL, we show that stability can be achieved through virtual capacitor control, using only a 2 mF physical capacitor to account for the switching ripple non-idealities. Hardware-in-the-loop tests verify the analysis.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Visual feedback and guided balance training in an immersive virtual reality environment for lower extremity rehabilitation

Balance training is essential for physical rehabilitation procedures, as it can improve functional mobility and enhance cognitive coordination. However, conventional balance training methods may have limitations in terms of motivation, real-time objective feedback, and personalization, which a virtual reality (VR) setup may provide a better alternative. In this work, we present an immersive VR training environment for lower extremity balance rehabilitation with real-time guidance and feedback. The VR training environment immerses the user in a 3D ice rink model where a virtual coach (agent) leads them through a series of balance poses, and the user controls a trainee avatar with their own movements. Here we developed two coaching styles: positive-reinforcement and autonomous-supportive, and two viewpoints of the trainee avatar: first-person and third-person. The proposed environment was evaluated in a user study with healthy, non-clinical participants (n = 16, 24.4 ± 5.7 years old, 9 females). Our results show that participants showed stronger performance in the positive-reinforcement style compared to the autonomous-supportive style. Additionally, in the third-person viewpoint, the participants exhibited more stability in the positive-reinforcement style compared to the autonomous-supportive style. For viewpoint, participants exhibited stronger performance in the first-person viewpoint compared to third-person in the autonomous-supportive style, while they were comparable in the positive-reinforcement style. We observed no significant effects on the foot height and number of mistakes. Furthermore, we report the analysis of user performance with balance training poses and subjective measures based on questionnaires to assess the user experience, usability, and task load. The proposed VR balance training could offer an interactive, adaptive, and engaging environment and open new potential research directions for lower extremity rehabilitation.

97 MATHEMATICS AND COMPUTING↗

Solving the Orszag–Tang vortex magnetohydrodynamics problem with physics-constrained convolutional neural networks

We study the 2D Orszag–Tang vortex magnetohydrodynamics (MHD) problem through the use of physics-constrained convolutional neural networks (PCNNs) for forecasting the density, ρ, and the magnetic field, B, as well as the prediction of B given the velocity field v of the fluid. In addition to translation equivariance from the convolutional architecture, other physics constraints were embedded: absence of magnetic monopoles, non-negativity of ρ, use of only relevant variables, and the periodic boundary conditions of the problem. The use of only relevant variables and the hard constraint of non-negative ρ were found to facilitate learning greatly. The divergenceless condition ∇·B=0 was implemented as a hard constraint up to machine precision through the use of a magnetic potential to define B=∇×A. Residual networks and data augmentation were also used to improve performance. This allowed for some of the residual models to function as surrogate models and provide reasonably accurate simulations. For the prediction task, the PCNNs were evaluated against a physics-informed neural network, which had the ideal MHD induction equation as a soft constraint. Several models were able to generate highly accurate fields, which are visually almost indistinguishable and have low mean squared error. Only methods with built-in hard constraints produced physical fields with ∇·B=0. The use of PCNNs for MHD has the potential to produce physically consistent real-time simulations to serve as virtual diagnostics in cases where inferences must be made with limited observables.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Validation of Microgrid Algorithms using At-Scale Simulation and Emulation Real-Time (ASSERT) Framework

This paper presents a novel framework for validating microgrid algorithms using a At-Scale Simulation and Emulation Real-Time (ASSERT) setup. The proposed universal microgrid validation framework was developed at Advanced Research on Integrated Energy Systems (ARIES) platform at National Renewable Energy Laboratory in Golden, Colorado, USA. As the number of intercommunicating devices grow in power systems, along with more integration of inverter-based resources, developing and validating microgrid operation and control algorithms is becoming complex and time-consuming task. The ASSERT framework is designed to provide a comprehensive, accurate, and efficient solution for validating microgrid algorithms. It combines at-scale simulations and real-time emulation to create a virtual environment that closely mimics the behavior of a physical microgrids which are characteristic of future smart distribution systems, such as: (1) increasing variability in the physical size of new energy technologies; (2) requiring control large numbers of interconnected devices, and (3) integrating diverse technologies that have not previously worked together. The paper describes the technical details of the ASSERT framework, its validation process, and its benefits over traditional validation methods. The framework's ability to validate the performance of various algorithms is demonstrated through a case study, which shows that it can effectively identify the weaknesses of an algorithm and optimize its performance. Overall, the ASSERT framework is a promising tool that can significantly enhance the development and validation of microgrid algorithms, leading to more reliable and efficient microgrid operation.

at-scale↗

Optimal Energy Scheduling and Sensitivity Analysis for Integrated Power-Water-Heat Systems

The conventionally independent power, water, and heating networks are becoming more tightly connected, which motivates their joint optimal energy scheduling to improve the overall efficiency of an integrated energy system. However, such a joint optimization is known as a challenging problem with complex network constraints and couplings of electric, hydraulic, and thermal models that are nonlinear and nonconvex. We formulate an optimal power-water-heat flow (OPWHF) problem and develop a computationally efficient heuristic to solve it. The proposed heuristic decomposes OPWHF into subproblems, which are iteratively solved via convex relaxation and convex-concave procedure. Simulation results validate that the proposed framework can improve operational flexibility and social welfare of the integrated system, wherein the water and heating networks respond as virtual energy storage to time-varying energy prices and solar photovoltaic generation. Moreover, we perform sensitivity analysis to compare two modes of heating network control: by flow rate and by temperature. Our results reveal that the latter is more effective for heating networks with a wider space of pipeline parameters.

24 POWER TRANSMISSION AND DISTRIBUTION↗