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At least 1,099 records · Page 61

Parallel CFD Algorithms for Aerodynamical Flow Solvers on Unstructured Meshes

The Advisory Group for Aerospace Research and Development (AGARD) has requested my participation in the lecture series entitled Parallel Computing in Computational Fluid Dynamics to be held at the von Karman Institute in Brussels, Belgium on May 15-19, 1995. In addition, a request has been made from the US Coordinator for AGARD at the Pentagon for NASA Ames to hold a repetition of the lecture series on October 16-20, 1995. I have been asked to be a local coordinator for the Ames event. All AGARD lecture series events have attendance limited to NATO allied countries. A brief of the lecture series is provided in the attached enclosure. Specifically, I have been asked to give two lectures of approximately 75 minutes each on the subject of parallel solution techniques for the fluid flow equations on unstructured meshes. The title of my lectures is "Parallel CFD Algorithms for Aerodynamical Flow Solvers on Unstructured Meshes" (Parts I-II). The contents of these lectures will be largely review in nature and will draw upon previously published work in this area. Topics of my lectures will include: (1) Mesh partitioning algorithms. Recursive techniques based on coordinate bisection, Cuthill-McKee level structures, and spectral bisection. (2) Newton's method for large scale CFD problems. Size and complexity estimates for Newton's method, modifications for insuring global convergence. (3) Techniques for constructing the Jacobian matrix. Analytic and numerical techniques for Jacobian matrix-vector products, constructing the transposed matrix, extensions to optimization and homotopy theories. (4) Iterative solution algorithms. Practical experience with GIVIRES and BICG-STAB matrix solvers. (5) Parallel matrix preconditioning. Incomplete Lower-Upper (ILU) factorization, domain-decomposed ILU, approximate Schur complement strategies.

Barth, Timothy J.↗

DC Fast Charging Infrastructure for Electrified Road Trips

To assess DC fast charging station network required for electrified road trips by 2030 in California, a new charging infrastructure simulation tool/model, EVI-Pro (Electric Vehicle Infrastructure Projection) RoadTrip, has been developed. In contrast to the existing EVI-Pro model that is primarily for short-distance travels, EVI-Pro RoadTrip is exclusively focused on road trips (long-distance travels, 100 or miles per day per vehicle). Also, the charging paradigm or strategy is different. EVI-Pro RoadTrip is built upon waypoint charging, in which vehicles are forced to stop to charge or replenish the on-board batteries, along the routes between origins and destinations. On the other hand, EVI-Pro is based on destination charging, in which charging is conducted when vehicles are parked in destinations (e.g., work, home). EVI-Pro RoadTrip takes coordinate-level origin and destination data for road trips (intra-state as well as domestic or international out-of-state) and estimates energy consumption and charging needs along the routes between origins and destinations on a minute-by-minute resolution. Based on charging demands for electrified road trips across the state, the optimal locations of charging stations are determined accounting for preferred land use types (e.g., commercial areas) and station service area (e.g., 5 or less miles). Based on station-by-station charging load profiles, the required number of plugs/connectors is estimated for each station and entire state. By comparing hosting capacity of the electric grid (circuit-level) and the charging load output from EVI-Pro RoadTrip, capacity deficit is also evaluated.

ADVANCED PROPULSION SYSTEMS,ENERGY STORAGE↗

Laboratory Evaluation of Federated, Hierarchical Controls for Distribution Power System Management: Preprint

The connection of more loads and distributed energy resources (DERs) to the distribution power system brings both challenges and opportunities to system operators. There are opportunities to aggregate flexible loads and DERs to provide transmission grid services, but the coordinated actions of DERs being managed by independent, third-party DER aggregators to support transmission system operations can present challenges. We developed a federated DER management architecture and control framework that aims to manage heterogeneous DERs to deliver reliable transmission grid services while respecting distribution system constraints. The controls include stochastic day-ahead optimization, model predictive control, and a simple real-time management scheme. We present simulation results obtained from a realistic laboratory test bed of federated controls managing DERs within a substation service area to make the substation net power follow the optimal net power determined by the day-ahead optimization based on cost and limiting reverse power flow.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Calcium Cosalt Addition to Alter the Cation Solvation Structure and Enhance the Ca Metal Anode Performance

Accessing the energy density and sustainability of calcium metal batteries requires mastering reversible calcium electrodeposition through electrolyte design. Several electrolytes support reversible, ambient temperature deposition but at utilization and rate too low for practical applications. These challenges stem from solvation structures characterized by either high barriers for cation desolvation or thermodynamic instability, leading to parasitic decomposition of the salt and solvent. The optimal solvation structure for the effective delivery of calcium to the electrode interface is not known. In this work, we show that adding a relatively small amount of a weakly associating calcium salt (calcium carba-closo-dodecaborate) to an otherwise strongly associated solution (calcium borohydride in tetrahydrofuran) produces a surprising population of fully solvent-coordinated Ca2+ cations in the form of solvent-separated ion pairs (SSIPs). We further demonstrate that the formation of these SSIPs beneficially impacts the kinetics and thermodynamics of calcium electrodeposition, revealing the unexpected finding that direct coordination of Ca2+ by the BH4– anion limits the electrodeposition process. These findings reveal how the competition between solvent and anion coordination to Ca2+ affects calcium deposition kinetics and cycling stability, setting the stage for a new calcium electrolyte design based on mixed anion electrolytes.

Landers, Alan T.↗

Advanced supramolecular design for direct ink writing of soft materials

The exciting advancements in 3D-printing of soft materials are changing the landscape of materials development and fabrication. Among various 3D-printers that are designed for soft materials fabrication, the direct ink writing (DIW) system is particularly attractive for chemists and materials scientists due to the mild fabrication conditions, compatibility with a wide range of organic and inorganic materials, and the ease of multi-materials 3D-printing. Inks for DIW need to possess suitable viscoelastic properties to allow for smooth extrusion and be self-supportive after printing, but molecularly facilitating 3D printability to functional materials remains nontrivial. While supramolecular binding motifs have been increasingly used for 3D-printing, these inks are largely optimized empirically for DIW. Hence, this review aims to establish a clear connection between the molecular understanding of the supramolecularly bound motifs and their viscoelastic properties at bulk. Herein, extrudable (but not self-supportive) and 3D-printable (self-supportive) polymeric materials that utilize noncovalent interactions, including hydrogen bonding, host–guest inclusion, metal–ligand coordination, micro-crystallization, and van der Waals interaction, have been discussed in detail. In particular, the rheological distinctions between extrudable and 3D-printable inks have been discussed from a supramolecular design perspective. Examples shown in this review also highlight the exciting macroscale functions amplified from the molecular design. Challenges associated with the hierarchical control and characterization of supramolecularly designed DIW inks are also outlined. The perspective of utilizing supramolecular binding motifs in soft materials DIW printing has been discussed. Finally, this review serves to connect researchers across disciplines to develop innovative solutions that connect top-down 3D-printing and bottom-up supramolecular design to accelerate the development of 3D-print soft materials for a sustainable future.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Ensuring thermodynamic consistency with invertible coarse-graining

Coarse-grained models are a core computational tool in theoretical chemistry and biophysics. A judicious choice of a coarse-grained model can yield physical insights by isolating the essential degrees of freedom that dictate the thermodynamic properties of a complex, condensed-phase system. The reduced complexity of the model typically leads to lower computational costs and more efficient sampling compared with atomistic models. Designing “good” coarse-grained models is an art. Generally, the mapping from fine-grained configurations to coarse-grained configurations itself is not optimized in any way; instead, the energy function associated with the mapped configurations is. In this work, we explore the consequences of optimizing the coarse-grained representation alongside its potential energy function. We use a graph machine learning framework to embed atomic configurations into a low-dimensional space to produce efficient representations of the original molecular system. Because the representation we obtain is no longer directly interpretable as a real-space representation of the atomic coordinates, we also introduce an inversion process and an associated thermodynamic consistency relation that allows us to rigorously sample fine-grained configurations conditioned on the coarse-grained sampling. We illustrate that this technique is robust, recovering the first two moments of the distribution of several observables in proteins such as chignolin and alanine dipeptide.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Status Report on Modelling and Simulation Capabilities for Nuclear-Renewable Hybrid Energy Systems

This report summarizes the current status of the modeling and simulation capabilities developed for the economic assessment of Nuclear-Renewable Hybrid Energy Systems (N-R HES). The increasing penetration of variable renewables is altering the profile of the net demand, with which the other generators on the grid have to cope. N-R HES analyses are being conducted to determine the potential feasibility of mitigating the resultant volatility in the net electricity demand by adding industrial processes that utilize either thermal or electrical energy as stabilizing loads. This coordination of energy generators and users is proposed to mitigate the increase in electricity cost and cost volatility through the production of a saleable commodity. Overall, the financial performance of a system that is comprised of peaking units (i.e. gas turbine), baseload supply (i.e. nuclear power plant), and an industrial process (e.g. hydrogen plant) should be optimized under the constraint of satisfying an electricity demand profile with a certain level of variable renewable (wind) penetration. The optimization should entail both the sizing of the components/subsystems that comprise the system and the optimal dispatch strategy (output at any given moment in time from the different subsystems). Some of the capabilities here described have been reported separately in [1, 2, 3]. The purpose of this report is to provide an update on the improvement and extension of those capabilities and to illustrate their integrated application in the economic assessment of N-R HES.

97 MATHEMATICS AND COMPUTING↗

Implementation of a Mesh refinement algorithm into the quasi-static PIC code QuickPIC

Plasma-based acceleration (PBA) has emerged as a promising candidate for the accelerator technology used to build a future linear collider and/or an advanced light source. In PBA, a trailing or witness particle beam is accelerated in the plasma wave wakefield (WF) created by a laser or particle beam driver. The WF is often nonlinear and involves the crossing of plasma particle trajectories in real space and thus particle-in-cell methods are used. The distance over which the drive beam evolves is several orders of magnitude larger than the wake wavelength. This large disparity in length scales is amenable to the quasi-static approach. Three-dimensional (3D), quasi-static (QS), particle-in-cell (PIC) codes, e.g., QuickPIC, have been shown to provide high fidelity simulation capability with 2-4 orders of magnitude speedup over 3D fully explicit PIC codes. In PBA, the witness beam needs to be matched to the focusing forces of the WF to reduce the emittance growth. In some linear collider designs, the matched spot size of the witness beam can be 2 to 3 orders of magnitude smaller than the spot size (and wavelength) of the wakefield. Such an additional disparity in length scales is ideal for mesh refinement where the WF within the witness beam is described on a finer mesh than the rest of the WF. A mesh refinement scheme is described that has been implemented into the 3D QS PIC code, QuickPIC. Very fine (high) resolution is used in a small spatial region that includes the witness beam and progressively coarser resolutions in the rest of the simulation domain. A fast multigrid Poisson solver has been implemented for the field solve on the refined meshes and a Fast Fourier Transform (FFT) based Poisson solver is used for the coarse mesh. The code has been parallelized with both MPI and OpenMP, and the parallel scalability has also been improved by using pipelining. A preliminary adaptive mesh refinement technique is described to optimize the computational time for simulations with an evolving witness beam size. Several test problems are used to verify that the mesh refinement algorithm provides accurate results. Additionally, the results are benchmarked against highly resolved simulations exhibiting near-azimuthal symmetry, performed using QPAD—a novel hybrid QS PIC code that uses a PIC description in the coordinates (r, ct – z) and a gridless description in the azimuthal angle, Φ.

Linear collider↗

Hydropower operation in future power grid with various renewable power integration

Hydropower generation may play an increasingly important role in the power grid under increasing contribution of variable renewable sources such as wind and solar. An improved understanding of the changes to hydropower dispatch under future higher VRE grid conditions reveals research gap that should be informed power grid planning and reservoir water releases policies considering multiple other water uses and varying hydrologic condition. Here this study aims to understand the role of hydropower in a changing power grid by employing a production cost model, PLEXOS, across future power system scenarios, planning horizons, and regions. We explore optimized hydropower dispatch to understand its potential role in minimizing the system cost and renewable curtailment. We also examine the sensitivity of hydropower revenue under various grid scenarios of the Eastern U.S. and hydrology conditions. Results indicate hydropower generation follows net load and compensates for the variability of solar and wind generation. Although energy prices are lower during some periods in the future grid scenarios, there is a potential for higher revenue for hydropower by providing both energy and ancillary services during times of stress. Additionally, hydropower revenue is sensitive to hydrology in the SERC region, which we considered as an example. The feasibility of hydropower dispatching with higher ramps between low and high hourly-capacity factors, as indicated in the optimization model, requires further study to consider other water use and ecology constraints.

13 HYDRO ENERGY↗

Universal parameters of bulk-solvent masks

The bulk solvent is a major component of biomacromolecular crystals that contributes significantly to the observed diffraction intensities. Accurate modelling of the bulk solvent has been recognized as important for many crystallographic calculations. Owing to its simplicity and modelling power, the flat (mask-based) bulk-solvent model is used by most modern crystallographic software packages to account for disordered solvent. In this model, the bulk-solvent contribution is defined by a binary mask and a scale (scattering) function. The mask is calculated on a regular grid using the atomic model coordinates and their chemical types. The grid step and two radii, solvent and shrinkage, are the three parameters that govern the mask calculation. They are highly correlated and their choice is a compromise between the computer time needed to calculate the mask and the accuracy of the mask. It is demonstrated here that this choice can be optimized using a unique value of 0.6 Å for the grid step irrespective of the data resolution, and the radii values adjusted correspondingly. The improved values were tested on a large sample of Protein Data Bank entries derived from X-ray diffraction data and are now used in the computational crystallography toolbox ( CCTBX ) and in Phenix as the default choice.

36 MATERIALS SCIENCE↗

Endogenous Interface Pricing for Consistent Transmission–Distribution Co-Optimization With Discrete Distribution Controls

This paper proposes an endogenous interface pricing model for day-ahead transmission–distribution co-optimization that co-determines the interface locational marginal price (LMP) and the transmission–distribution exchange, ensuring price–dispatch consistency while optimally scheduling discrete distribution controls. The formulation couples a DC optimal power flow (OPF) with a branch-flow AC OPF that schedules distributed energy resources (DERs), tap-changer settings, capacitor banks (CBs), and multi-period energy storage systems (ESSs) under feeder voltage and current limits, and is solved as a mixed-integer second-order cone program (MISOCP). In a T14–D33 system, coordinated device scheduling recovers about 90% of the distribution-to-transmission export achievable in a reference case that ignores distribution network (DN) limits, while satisfying a 1.05 p.u. voltage upper bound. In a T39–D34/D37/D123 system, a sequential decoupled benchmark produces interface LMP distortions up to 12.5% and a 7.28% mismatch in net export energy, whereas the proposed model removes these distortions and the associated settlement mismatches. Second-order cone (SOC) relaxation gaps remain below $10^{-3}$ in all cases.

Noh, Seung-Gil↗

Sequential Service Restoration for Unbalanced Distribution Systems and Microgrids

The resilience and reliability of modern power systems are threatened by increasingly severe weather events and cyber-physical security events. An effective restoration methodology is desired to optimally integrate emerging smart grid technologies and pave the way for developing self-healing smart grids. In this paper, a sequential service restoration (SSR) framework is proposed to generate restoration solutions for distribution systems and microgrids in the event of large-scale power outages. The restoration solution contains a sequence of control actions that properly coordinate switches, distributed generators, and switchable loads to form multiple isolated microgrids. The SSR can be applied for three-phase unbalanced distribution systems and microgrids and can adapt to various operation conditions. Mathematical models are introduced for three-phase unbalanced power flow, voltage regulators, transformers, and loads. Furthermore, the SSR problem is formulated as a mixed-integer linear programming model, and its effectiveness is evaluated via the modified IEEE 123 node test feeder.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Summary of Technical Peer Review on the Risk Assessment Framework proposed in Report INL/RPT-22-68656 for Digital Instrumentation and Control Systems

This report summarizes the peer review activities initiated by Idaho National Laboratory (INL) during fiscal year (FY) 2023 for the evaluation and improvement of the methodology developed under the U.S. Department of Energy (DOE) Light Water Reactor Sustainability (LWRS) Program, Risk Informed Systems Analysis (RISA) Pathway, digital instrumentation and control (DI&C) risk assessment project. In FY 2019, the RISA Pathway initiated a project to develop a risk assessment strategy for delivering a technical basis to support effective and secure DI&C technologies for digital upgrades/designs. A framework was proposed for this strategy, which aims to (1) provide a best-estimate, risk-informed capability to quantitatively and accurately estimate the risk impact of plant modernization, considering the introduction of high safety-significant safety-related (HSSSR) DI&C systems, (2) support and supplement existing risk-informed DI&C design guides by providing quantitative risk information and evidence, (3) offer a capability of design architecture evaluation of various DI&C systems, (4) assure the long-term safety and reliability of HSSSR DI&C systems, and (5) reduce uncertainty in costs and support integration of DI&C systems in the plant. The R&D efforts of this project from FY 2019 through FY 2022 were focused on methodology improvement and demonstration of the proposed framework for the risk assessment and design optimization of safety-critical DI&C systems. Collaborations with the nuclear industry have been initiated to support the reliability and risk assessment of their DI&C systems by using the proposed framework. In FY 2023, the framework has reached to a point for a technical peer review and obtain stakeholder feedback. This peer review activity includes coordination of the reviews performed by a group of industry stakeholders, documentation of the peer review suggestions, providing resolutions and responses to the peer review comments. The objective of this technical peer review is to obtain representative feedback on the proposed framework to improve the technical qualities of its methodology and readiness for deployment to the industry. Feedback may identify potential areas for improvement and further development. The Subject Matter experts were invited to review the latest project report documenting the methodology developed in the project and provide evaluations of the technical qualities of the proposed framework and relevant methods. The reviewed project report is “An Integrated Framework for Risk Assessment of High Safety-significant Safety-related Digital Instrumentation and Control Systems in Nuclear Power Plants: Methodology and Demonstration” INL/RPT-22-68656 (short as “INL/RPT-22-68656” in this report). This peer review report documents the technical questions provided for technical peer review and introduces the technical peer reviewers from the stakeholders including nuclear utilities, regulators, and universities. Comments from technical peer reviewers and the resolutions and responses to these comments are outlined. Insights and lessons learned from the technical peer review are summarized in conclusions and future work. The primary audience of this report are DI&C designers, engineers, and probabilistic risk assessment (PRA) practitioners. This includes stakeholders, such as the nuclear utilities and regulators who consider the deployment and upgrade of DI&C systems, DI&C software developers and reviewers, and cybersecurity specialists.

99 GENERAL AND MISCELLANEOUS↗

A Comparison of Techniques for Scheduling Earth-Observing Satellites

Scheduling observations by coordinated fleets of Earth Observing Satellites (EOS) involves large search spaces, complex constraints and poorly understood bottlenecks, conditions where evolutionary and related algorithms are often effective. However, there are many such algorithms and the best one to use is not clear. Here we compare multiple variants of the genetic algorithm: stochastic hill climbing, simulated annealing, squeaky wheel optimization and iterated sampling on ten realistically-sized EOS scheduling problems. Schedules are represented by a permutation (non-temperal ordering) of the observation requests. A simple deterministic scheduler assigns times and resources to each observation request in the order indicated by the permutation, discarding those that violate the constraints created by previously scheduled observations. Simulated annealing performs best. Random mutation outperform a more 'intelligent' mutator. Furthermore, the best mutator, by a small margin, was a novel approach we call temperature dependent random sampling that makes large changes in the early stages of evolution and smaller changes towards the end of search.

Globus, Al↗

High-Performance Computing Optimization for Aladyn – Adaptive Neural Network Molecular Dynamics Mini-Application

This report provides a description and performance evaluation of the optimization techniques for high performance computing (HPC) implementation of the open source Computational Materials mini-application Aladyn (https://github.com/nasa/aladyn). Aladyn is a basic molecular dynamics code written in FORTRAN 2003, which is designed to demonstrate the use of adaptive neural networks (ANNs) in atomistic simulations. The role of ANNs is to efficiently reproduce the very complex energy landscape resulting from the atomic interactions in materials with the accuracy of the more expensive quantum mechanics-based calculations. The ANN is trained on a large set of atomic structures calculated using the density functional theory (DFT) method. While achieving orders of magnitude faster computational performance than DFT, the ANN-based approach was still very computationally demanding compared to the conventional approach of using empirically fitted energy functions. After its initial development, Aladyn was evaluated and optimized by experts at the NASA Advanced Supercomputing (NAS) division to exploit modern supercomputer architectures. The code has been optimized for execution on multicore central processing units (CPUs), including Intel® Skylake microarchitecture, and on graphic accelerators, such as Nvidia® V100 graphic processing units (GPUs), using Open Multi-Processing (OpenMP) and Open Accelerators (OpenACC) programming interfaces. The optimization achieved a speedup of 4.7 times the baseline version on CPU performance and an additional 2.4 times on CPU+GPU performance. Atomistic computer simulations are a fundamental tool in materials research to model material properties form physics-based first principles. Atomic interaction, governed by Quantum Mechanics (QM) require sophisticated and highly computationally demanding mathematical models to calculate [1]. Classical methods use approximate functional forms, empirically fitted through a set of variable parameters to emulate atomic energies as direct functions of atomic coordinates [2]. While empirical potentials are computationally much simpler, allowing simulations of large-scale systems of up to a trillion (1012) atoms [3], they are substantially less accurate compared to quantum calculations and applicable only to very specific atomic configurations or predefined crystallographic phases. A recently suggested approach is to use heuristic machine learning methods [4], such as those based on Adaptive Neural Networks (ANNs) to predict atomic energies, after being trained on a sufficiently large database of QM-calculated structures [5,6]. This approach reduces significantly the computational complexity, allowing for simulations of orders of magnitude larger systems compared to QM-based methods without compromising accuracy. Still, compared to classical methods using empirical energy functions, ANN methods remain two- to three orders of magnitude more computationally demanding. Hence, the computational cost of simulations, together with the need for extensive training of ANNs, still makes the practical implementation of ANN-based methods quite challenging. The purpose of the Aladyn mini-application software [7], available as open source at https://github.com/nasa/aladyn, is to be a testbed for exploring possible optimization strategies to develop highly scalable parallel algorithms for ANN-based atomistic simulations. Aladyn is aimed at utilizing the architecture of the high-end modern highperformance computing (HPC) hardware based on multicore central processing units (CPUs) equipped with graphic processing unit (GPU) accelerators. Specifically, the goal is to optimize the performance on a single HPC compute node, before implementing scaling to multi-node parallelization using message passing interface (MPI). At the same time, the open source code of Aladyn can serve as a training model for students and professors in academia.

Yamakov, Vesselin I.↗

Dynamically Unveiling Metal–Nitrogen Coordination during Thermal Activation to Design High‐Efficient Atomically Dispersed CoN 4 Active Sites

Abstract We elucidate the structural evolution of CoN 4 sites during thermal activation by developing a zeolitic imidazolate framework (ZIF)‐8‐derived carbon host as an ideal model for Co 2+ ion adsorption. Subsequent in situ X‐ray absorption spectroscopy analysis can dynamically track the conversion from inactive Co−OH and Co−O species into active CoN 4 sites. The critical transition occurs at 700 °C and becomes optimal at 900 °C, generating the highest intrinsic activity and four‐electron selectivity for the oxygen reduction reaction (ORR). DFT calculations elucidate that the ORR is kinetically favored by the thermal‐induced compressive strain of Co−N bonds in CoN 4 active sites formed at 900 °C. Further, we developed a two‐step (i.e., Co ion doping and adsorption) Co‐N‐C catalyst with increased CoN 4 site density and optimized porosity for mass transport, and demonstrated its outstanding fuel cell performance and durability.

He, Yanghua↗

Optimal distribution system restoration using PHEVs

Power outages cost billions of dollars every year and jeopardise the lives of hospital patients. Traditionally, power distribution system takes a long time to recover after a major blackout, due to its top-down operation strategy. New technologies in modern distribution systems bring opportunities and challenges to distribution system restoration. As fast response energy resources, plug-in hybrid electric vehicles (PHEVs) can accelerate the load pickup by compensating the imbalance between available generation and distribution system load. This study provides a bottom-up restoration strategy to use PHEVs for reliable load pickup and faster restoration process. The optimisation problem of finding load pickup sequence to maximise restored energy is formulated as a mixed integer linear programming (MILP) problem. Moreover, the coordination between transmission and distribution restoration is developed to efficiently restore the entire system back to normal operating conditions. Simulation results on one 100-feeder test system demonstrate the efficiency of MILP-based restoration strategy and the benefit from PHEVs to restore more energy in given restoration time. The proposed restoration strategy has great potential to facilitate system operators to achieve efficient system restoration plans. It also provides incentives to deploy a large amount of PHEVs to improve system resiliency.

24 POWER TRANSMISSION AND DISTRIBUTION↗