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

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At least 163 records · Page 9

Multilayered Network Models for Security: Enhancing System Security Engineering with Orchestration

Security engineering approaches can often focus on a particular domain—physical security, cyber security, or personnel security, for example. Yet, security systems engineering consistently faces challenges requiring socio-technical solutions to address evolving and dynamic complexity. While some drivers of this complexity stem from complex risk environments, innovative adversaries, and disruptive technologies, other drivers are endogenous and emerge from the interactions across security engineering approaches. In response, INCOSE's Systems Security Working Group identified the need to better coordinate “disparate security solutions [that] operate independently” as one of eleven key concepts in their IS21 FuSE Security Roadmap. From this perspective, this need for “security orchestration” aligns with the perspective that security is a property that emerges from interactions within complex systems. Current efforts at Sandia National Laboratories are developing a systems security engineering approach that describes high consequence facility (HCF) security as a multidomain set of interacting layers. The result is a multilayered network (MLN)-based approach that captures the interactions between infrastructure, physical components, digital components, and humans in nuclear security systems. This article will summarize the MLN-based approach to HCF security and describe two preliminary results demonstrating potential benefits from incorporating interactions across disparate security solutions. Here, leveraging the logical structure of networks, this MLN model-based approach provides an example of how security orchestration provides enhanced systems security engineering solutions.

42 ENGINEERING↗

Supramolecular Metal Halide Complexes for High-Temperature Nonlinear Optical Switches

Nonlinear optical (NLO) switching materials, which exhibit reversible intensity modulation in response to thermal stimuli, have found extensive applications across diverse fields, including sensing, photoelectronics, and photonic applications. While significant progress has been made in solid-state NLO switching materials, these materials typically showcase their highest NLO performance near room temperature. However, this performance drastically deteriorates upon heating, primarily due to the phase transition undergone by the materials from non-centrosymmetric to centrosymmetric phase. Here, we introduce a new class of NLO switching materials, solid-state supramolecular compounds 18-Crown-6 ether@Cu 2 Cl 4 ·4H 2 O (1·4H 2 O), exhibiting reversible and stable NLO switching when subjected to near-infrared (NIR) photoexcitation and/or thermal stimuli. The reversible crystal structure in response to external stimuli is attributed to the presence of a weakly coordinated bridging water molecule, facilitated by hydrogen bonding/chelation interactions between the metal halide and crown-ether supramolecules. We observed an exceptionally high second-harmonic generation (SHG) signal under continuous photoexcitation, even at temperatures exceeding 110°C. In addition, the bridging water molecules within the complex can be released and recaptured in a fully reversible manner, all without requiring excessive energy input. This feature allows for precise control of SHG signal activation and deactivation through structural transformations, resulting in a high-contrast off/on ratio, reaching values in the million-fold range.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Interoperable, Inverter - Based Distributed Energy Resources Enable 100% Renewable and Resilient Utility Microgrids

As microgrids transition away from use of conventional generating resources and increasingly rely on renewable resources towards decarbonization goals, it is crucial to evaluate the capability inverter-based resources to provide microgrid stability and resilience. Particularly, microgrids with a high contribution of intermittent solar photo voltaic generation and higher load variability present unique challenges requiring fast voltage and frequency support. At the San Diego Gas & Electric Company(R) (SDG&E(R)) Borrego Springs Microgrid, a battery inverter was upgraded with grid-forming (GFM) capability to serve as island leader, transitioning responsibility away from diesel generators. An interoperable microgrid control scheme was developed, coordinating GFM and grid-following (GFL) inverters. Hardware-in-the-loop (HIL) simulations using relevant power and controller HIL interfaces between real-time simulators and field equipment are being conducted to de-risk field deployment.

battery energy storage↗

Dispatch Manager for NEML2 Constitutive Model Calculations Embedded in MOOSE

This report describes the extended capabilities of the NEML2 constitutive modeling library, including a flexible and efficient work dispatching system designed to leverage both CPU and GPU resources. This enhancement addresses one of the primary computational challenges in large-scale simulations: the ability to distribute and execute batches of material model evaluations across heterogeneous computing devices. The new dispatch system introduces a modular set of dispatcher and scheduler classes that coordinate the flow of data and execution between devices. The dispatcher is responsible for efficiently packaging work, managing device-specific memory operations, and synchronizing results. This modularity allows for extensibility, making it straightforward to integrate additional computing backends in the future. From an implementation standpoint, the dispatcher system interfaces seamlessly with NEML2's existing models. They handle device-aware tensor operations, optimize memory transfers, and support asynchronous execution when applicable. This design ensures that batches of material points can be evaluated concurrently, substantially improving throughput compared to previous single-device or serial implementations. These improvements not only enhance the raw performance of NEML2 but also improve its usability in multiscale and high-fidelity simulations, where the simultaneous evaluation of large material point batches is critical. Benchmarks included in the report demonstrate the system’s scalability, highlighting its effectiveness when leveraging modern GPU architectures.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Parametric reduced-order modeling for component-oriented treatment and localized nonlinear feature inclusion

Abstract We propose coupling a physics-based reduction framework with a suited response decomposition technique to derive a component-oriented reduction (COR) approach, which is suitable for assembly systems featuring localized nonlinearities. Dependencies on influencing parameters are injected into the reduced-order model (ROM), thus ensuring robustness and validity over a domain of parametric inputs, while capturing nonlinear effects. The implemented approach employs individual component modes to capture localized features while additionally relying on reduced modes of a global nature to approximate the system’s dynamics accurately. The global modes are derived from a linear monolithic system, defined as a result of a coordinate separation scheme, which permits the proposed COR-ROM to naturally couple the response between linear and nonlinear subdomains. The derived low-order representation utilizes a proper orthogonal decomposition projection and is additionally reinforced with the inclusion of a hyper-reduction technique to capture the underlying high-fidelity model response while providing accelerated computations. The resulting approach is exemplified in the synthetic case studies of a four-story shear frame with multiple nonlinear regions driven by hysteresis and a large-scale kingpin connection featuring plasticity.

Vlachas, Konstantinos (ORCID:000000029124219X)↗

Protecting and Defending against Autonomous Control Systems and Digital Twin Cyber Attacks: Response Strategy for Hyperparameter attacks of Digital Twin Machine Learning Models in Nuclear Power Plants (Final)

Navigating through the complex tapestry of technological advancements, "Response Strategy for Hyperparameter attacks of Digital Twin Machine Learning Model in Nuclear Power Plants" stands at the intersection of cybersecurity and nuclear power plant operations, embarking on a journey through the intricacies of securing digital twins against malicious cyber activities. As nuclear power plants progressively integrate digital twin technology and machine learning models to optimize operations and ensure system reliability, they inadvertently expose themselves to a new spectrum of vulnerabilities, notably in the realm of hyperparameter attacks. Hyperparameters, integral in machine learning model tuning and optimal performance of digital twins, have emerged as a target for adversaries aiming to destabilize the predictive capabilities and therefore, the operational accuracy of these digital entities within critical infrastructures like nuclear plants. This paper, therefore, meticulously threads the needle through the development of a robust response strategy, poised to shield these digital reflections against calculated hyperparameter manipulations, ensuring that the digital twin can effectively and securely function as a reliable proxy for its physical counterpart. The ensuing sections delve into the orchestrated maelstrom of multi-rate time-changing intelligent coordinated hyperparameter attacks and the implementation of event-triggered predictive control, laying down a structured, predictive, and responsive framework that safeguards the nexus where the digital and physical realms of nuclear power plants coalesce. The operational integrity of digital twins in nuclear power plants depends critically on the security of machine learning hyperparameters. This study makes two different contributions. First, a decision-based idea known as a multi-rate time changing intelligent coordinated hyperparameter attack is put forth. In this attack, many hyperparameters are repeatedly changed using both random and intelligent optimal techniques by the attacker. These assaults introduce varied rates at different attack steps, compromise various amounts of hyperparameters, and improve stealth and flexibility. Second, a technique is developed for event triggered predictive control to rapidly respond to potential hyperparameter attacks. This control integrates a sliding window framework, retaining a history of previous data points and employing linear regression to predict the next data point from the current dataset. The control gain K is determined using the Lyapunov-Krasovskii method, and subsequently, an action is developed. Finally, the outcome of the simulation demonstrates the viability of the proposed method for defending nuclear power plant digital twins from hyperparameter attacks.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

A Positive Charge in the Outer Coordination Sphere of an Artificial Enzyme Increases CO 2 Hydrogenation

The protein scaffold around the active site of enzymes is known to influence catalytic activity, but specific scaffold features responsible for favorable influences are often not known. This study focuses on using an artificial metalloenzyme to probe one specific feature of the scaffold, the position of a positive charge in the outer coordination sphere around the active site. Previous work showed that a small molecular complex, [Rh(P Et 2 N glycine P Et 2 )2 ] – , immobilized covalently within a protein scaffold was activated for CO 2 hydrogenation. In this work, using an iterative design where the effect of arginine, histidine, or lysine residues placed in the outer coordination sphere of the catalytic active site were evaluated, we tested the hypothesis that positively charged groups facilitate CO 2 hydrogenation with seven unique constructs. Single-, double-, and triple-point mutations were introduced to directly compare catalytic activity, as monitored by turnover frequencies (TOFs) measured in real time with 1 H NMR spectroscopy, and evaluate related structural and electronic properties. Two of the seven constructs showed a 2- and 3-fold increase relative to the wild type, with overall rates ranging from 0.2 to 0.7 h –1 , and a crystal structure of the fastest of these shows the positive charge positioned next to the active site. A crystal structure of the arginine-containing complex shows that the arginines are positioned near the metal. Molecular dynamics (MD) studies also suggest that the positive charge is oriented next to the active site in the two constructs with faster rates but not in the others and that the positive charge near the active site holds the CO 2 near the metal, all consistent with a positive charge appropriately positioned in the scaffold benefiting catalysis. The MD studies also suggest that changes in the water distribution around the active site may contribute to catalytic activity, while modest structural changes and movement of the complex within the scaffold do not.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An Empirical Validation of a Constrained Bin Packing Algorithm for a Home Energy Management System

The increasing number of intelligent electrical appliances and home energy management systems provide a big opportunity for demand response services from residential and small commercial buildings to the grid. Simultaneously, direct control of individual devices by utilities can cause communication bottlenecks, as well as coordination and privacy concerns. These challenges can be addressed by combining the constituent devices into a single house battery equivalent for the purposes of demand response, using Minkowski sum and a 2d bin packing problem. However, the well-studied traditional problems have not been tested in a real house, as implementation carries significant challenges of its own. We deploy the packing problem on residential devices in a controllable house. We report the barriers we found, such as charge forecast and scalability of the algorithm, and discuss our solutions. The study serves as an intermediate step between existing theoretical research and possible future steps, such as prototype deployments of systems that provide residential demand response.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Alkylperoxy radicals are responsible for the formation of oxygenated primary organic aerosol

Organic aerosol (OA) is an air pollutant ubiquitous in urban atmospheres. Urban OA is usually apportioned into primary OA (POA), mostly emitted by mobile sources, and secondary OA (SOA), which forms in the atmosphere due to oxidation of gas-phase precursors from anthropogenic and biogenic sources. By performing coordinated measurements in the particle phase and the gas phase, we show that the alkylperoxy radical chemistry that is responsible for low-temperature ignition also leads to the formation of oxygenated POA (OxyPOA). OxyPOA is distinct from POA emitted during high-temperature ignition and is chemically similar to SOA. We present evidence for the prevalence of OxyPOA in emissions of a spark-ignition engine and a next-generation advanced compression-ignition engine, highlighting the importance of understanding OxyPOA for predicting urban air pollution patterns in current and future atmospheres.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

STOCHASTIC OPTIMAL POWER FLOW FOR REAL-TIME MANAGEMENT OF DISTRIBUTED RENEWABLE GENERATION AND DEMAND RESPONSE (Final Report)

To meet the grand challenge of a sustainable energy future, there has been a surge of interest in renewable energy. Today, the uncertainty associated with renewable resources is handled by using operating reserves. The high penetration of renewable resources, however, introduces difficult-to-control dynamics and challenges for power system operation. Decision support tools are necessary at the bulk system operational level to recognize and efficiently utilize renewable resources and distributed demand response products in concert with traditional grid resources. It is envisaged that responsive load can potentially have very significant cost advantages over either spinning or non-spinning ramping reserve. Critical decisions are made during hour(s)-ahead and real-time power system operation regarding the commitment and dispatch of generators to ensure power delivery is both reliable and economic. These decisions are typically made by a security constrained optimal flow, which determines future generator commitments, dispatches, and ensures adequate reserves are available in the event of a contingency (unexpected outage) or if future system conditions deviate from forecasts. However, security has been always based on a pre-specified subset of contingency constraints whose enforcement does not guarantee security under all possible future possibilities while also giving little or no weight to the likelihood of each contingent event or the severity of its consequences. Existing tools, which are based exclusively on deterministic optimization models, do not yield optimal operational decisions to address these new challenges, in terms of both reliability and cost-effectiveness. This project has focused on developing a stochastic optimal power flow (SOPF) framework, which integrates renewable resource uncertainty, load uncertainty, distributed storage (DS), demand response (DR) products, in a holistic manner to address the uncertainty associated with ever-increasing renewable resources, along with the inclusion of distributed demand response products in future power systems. A proof-of-concept problem was created using the Pennsylvania-Jersey-Maryland (PJM) power system network. Synthetic wind generation was added to the system to simulate 50% wind penetration. A 1-hour test of SOPF operation indicated more than 6% operational cost savings. The project continued by adding the Midwestern Independent System Operator (MISO) as a partner, with focus shifting from SOPF to Stochastic Look-Ahead Unit Commitment (SLAC). Unlike PJM, MISO is faced with significant renewable energy resources within its footprint and is challenged with substantial uncertainty in its operations. The SLAC distinguishes itself from existing tools that operators use. At best, today’s tools solve two to three cases independently, where one or two system parameters, such as forecasted load level (e.g., a low, base, and high forecast), are varied and the resulting scenarios are analyzed independently. The stochastic-based optimization of SLAC leverages statistical information from an ensemble of potential operational scenarios and their respective likelihood. The SLAC output can be translated into valuable information to the operator such as suggested commitments, optimal scheduling and dispatch of resources, reserve requirements at both locational and zonal resolutions, ramping availability and requirements, availability of demand response including operational guidance concerning the near-term and real-time coordination between distributed energy resources, and utilization of distributed storage resources. The developed SOPF/SLAC tool, a stand-alone tool compatible with existing EMSs, will provide system operators with unprecedented visibility, flexibility and predictability to these resources and operational guidance concerning the real-time coordination between DERs and DR/DS products. The game changing and practical impact of this disruptive technology will be dramatic and will usher in a new era in the electric power industry, wherein green energy concepts are fully embraced, and electric power costs are lowered throughout the nation.

42 ENGINEERING↗

Monitor support on accelerated processing device

A technique for implementing synchronization monitors on an accelerated processing device (“APD”) is provided. Work on an APD includes workgroups that include one or more wavefronts. All wavefronts of a workgroup execute on a single compute unit. A monitor is a synchronization construct that allows workgroups to stall until a particular condition is met. Responsive to all wavefronts of a workgroup executing a wait instruction, the monitor coordinator records the workgroup in an “entry queue.” The workgroup begins saving its state to a general APD memory and, when such saving is complete, the monitor coordinator moves the workgroup to a “condition queue.” When the condition specified by the wait instruction is met, the monitor coordinator moves the workgroup to a “ready queue,” and, when sufficient resources are available on a compute unit, the APD schedules the ready workgroup for execution on a compute unit.

42 ENGINEERING↗

In Situ Determination of Speciation and Local Structure of NaCl–SrCl 2 and LiF–ZrF 4 Molten Salts

Understanding the local environment of the metal atoms in salt melts is important for modeling the properties of melts and predicting their behavior and thus helping enable the development of technologies such as molten salt reactors and solar-thermal power systems and new approaches to recycling rare-earth metals. Toward that end, we have developed an in situ approach for measuring the coordination of metals in molten salt coupling X-ray absorption spectroscopy (XAS) and Raman spectroscopy. Our approach was demonstrated for two salt mixtures (1.9 and 5 mol % SrCl 2 in NaCl, 0.8 and 5 mol % ZrF 4 in LiF) at up to 1100 °C. Near-edge (X-ray absorption near-edge structure, XANES) and extended X-ray absorption fine structure (EXAFS) spectra were measured. The EXAFS response was modeled using ab initio FEFF calculations. Strontium’s first shell is observed to be coordinated with chlorine (Sr 2+ –Cl – ) and zirconium’s first shell is coordinated by fluorine (Zr 4+ –F – ), both having coordination numbers that decrease with increasing temperature. Multiple zirconium complexes are believed to be present in the melt, which may interfere and distort the EXAFS spectra and result in an anomalously low zirconium first shell coordination number. Finally, the use of boron nitride (BN) powder as a salt diluent for XAFS measurements was found to not interfere with measurements and thus can be used for investigations of such systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

How Improved Forecasting Can Increase the Bulk Power System Value of Price-Responsive Electric Vehicle Managed Charging

Personal light-duty vehicle (LDV) electric vehicle managed charging (EVMC) can reduce power system costs by better aligning electric vehicle (EV) charging with locations and times of low energy cost or infrastructure use. The need to coordinate charging demand across thousands to millions of vehicles while preserving mobility service is a barrier to realizing the value of EVMC. Price-responsive dispatch mechanisms like time-of-use rates (TOU) and hourly real-time prices (RTP) are attractive compared to direct load control (DLC) because they only require one-way communications and local controls. However, increasing participation in price responsive mechanisms can induce costly-to-serve spikes in load and otherwise increase, rather than decrease, production costs. We quantify the ability of improved EVMC forecasting to sustain savings from price responsive mechanisms beyond the limit of 14% of LDVs actively participating observed in previous work. Perfect forecasting of price-responsive EV load makes TOU and RTP value-competitive with a low-error DLC formulation with up to 27% (within-week flexibility) to 45% or more (within-session flexibility) of LDVs participating in EVMC in an envisioned New England power system with 84% clean energy. Additional costs of implementing DLC should be no more than tens of dollars per vehicle-year if DLC is to be value-competitive with accurately forecast price-responsive EVMC for double-digit percentage shares of LDVs participating.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Evidence of Completion of Milestone 3: Experimental Testbed

Construction and deployment of the experimental testbed encountered scheduling delays, and completion was subsequently further delayed by curtailment of LANL operations due to the COVID-19 pandemic. Between March and October, LANL was in a state of “Limited Operations” such that only certain “mission-critical” work was performed with approximately 25% on-site staffing. In spite of this, much of the lab space preparation was executed and the five initial model house” units were constructed and installed during this period. Still, the pace of construction was impacted by difficulty in coordinating personnel and minimizing contact between workers. Currently, LANL is in the mode of “Normal Operations with Maximum Telework,” which continues to limit the availability of on-site personnel. Nevertheless, Milestone 3 is now complete. This document describes the experiment as it is deployed and provides status for each task for this milestone.

99 GENERAL AND MISCELLANEOUS↗

A Scalable and Distributed Algorithm for Managing Residential Demand Response Programs using Alternating Direction Method of Multipliers (ADMM)

For effective engagement of residential demand-side resources and to ensure efficient operation of distribution networks, we must overcome the challenges of controlling and coordinating residential components and devices at scale. To overcome this challenge, we present a distributed and scalable algorithm with a three-level hierarchical information exchange architecture for managing the residential demand response programs. First, a centralized optimization model is formulated to maximize community social welfare. Then, this centralized model is solved in a distributed manner with alternating direction method of multipliers (ADMM) by decomposing the original problem to utility-level and house-level problems. The information exchange between the different layers is limited to the primary residual (i.e., supply-demand mismatch), Lagrangian multipliers, and the total load of each house to protect each customer’s privacy. Simulation studies are performed on the IEEE 33 bus test system with 605 residential customers. The results demonstrate that the proposed approach can save customers’ electricity bills and reduce the peak load at the utility level without much affecting customers’ comfort and privacy. Finally, a quantitative comparison of the distributed and centralized algorithms shows the scalability advantage of the proposed ADMM-based approach, and it gives benchmarking results with achievable value for future research works.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Calista Energy Management Assistance Initiative

The Calista Energy Management Assistance Initiative (CEMAI) provided technical assistance and capacity building for 56 Tribal communities in the Calista Region of Alaska as an effort to reduce costs, improve operational efficiency, enhance human capacity, and job opportunities. CEMAI catalyzed and guided numerous efforts into a consolidated and effective initiative that brought rural energy best practices, economies of scale, operational efficiencies, human capacity, and economic development to the forefront. Calista Corporation (Calista) is one of thirteen Alaska Native Regional Corporations created under the Alaska Native Claims Settlement Act of 1971 (ANCSA) in the settlement of aboriginal land claims. Calista was incorporated in Alaska on June 12, 1972. The Calista Region covers Alaska’s Bethel and Kusilvak (formerly Wade Hampton) Census areas and includes 56 communities. Calista partnered with Nuvista Light and Electric Cooperative (Nuvista) on the Department of Energy, Office of Indian Energy (DOE-OIE), CEMAI project. Nuvista is a non-profit that seeks to reduce energy costs and provide renewable sources of energy to the people of western Alaska. It is founded and led by a non-profit, Tribe, Native Corporations (including Calista), energy organizations, and Alaska Native stakeholders in the Yukon-Kuskokwim Delta (YK-D) Region; covering the same service boundaries and communities served by Calista. This partnership allowed Calista to direct the project work with local energy experts to respond to community needs. In this arrangement, Calista added credibility and regional accountability while Nuvista added energy-specific expertise and skill set in project management. The delivery of the CEMAI Workplan included short-term or on-demand responses to specific technical assistance requests from communities in addition to longer-term strategically directed activities such as workshops, coordinated training, and capacity development efforts across the region. CEMAI’s Workplan aimed to enhance communities’ readiness for establishing renewable energy projects and implementing energy efficiency initiatives. The CEMAI objectives included: (1) Identifying common operational needs and improvement opportunities for entities with an energy interest or responsibility. (2) Providing access to multi-level expertise to address existing challenges. (3) Developing specialized training programs to build local capacity and community readiness. (4) Nurturing the creation of regional support networks. (5) Increasing access to regional, state, and federal energy initiatives, funding, and expertise. (6) Improving technical skills, provide livable wages, and job opportunities.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Pressure-Induced Spectroscopic Changes in a Californium 1D Material Are Twice as Large as Found in the Holmium Analog

Here, in this study, the synthesis, characterization, and pressure response of a 1D californium mellitate (mellitate = 1,2,3,4,5,6-benzenehexacarboxylate) coordination polymer, Cf 2 (mell)(H 2 O) 10 ·4H 2 O (Cf-1), are reported. The Cf–O lengths within the crystal structure are compared to its gadolinium (Gd-1) and holmium (Ho-1) analogs as well. These data show that the average Cf–O bond distance is slightly longer than the average Gd–O bond, consistent with trends in effective ionic radii. UV–vis-NIR absorption spectra as a function of pressure were collected using diamond-anvil techniques for both Cf-1 and Ho-1. These experiments show that the Cf(III) f → f transitions have a stronger dependence on pressure than that of the holmium analog. In the former case, the shift is nearly linear with applied pressure and averages 6.6 cm –1 /GPa, whereas in the latter, it is <3 cm –1 /GPa.

absorption spectroscopy↗

Multiperiod Distribution System Restoration With Routing Repair Crews, Mobile Electric Vehicles, and Soft-Open-Point Networked Microgrids

This paper proposes a distribution system restoration model which is in response to multiple outages caused by natural disasters. The proposed restoration model includes the coordination of routing repair crews (RRCs), mobile batterycarried vehicles (MBCVs), and networked microgrids (NMGs) formed by soft open points (SOPs). The travel and repair time constraints are modeled for each RRC; travel path and charging strategy are modeled for each MBCV; and the network reconfiguration is developed considering the optimal operation of SOP-based NMGs. Furthermore, the proposed model is presented as a mixedinteger linear program which is solved by an auxiliary induce function based algorithm to reduce the computational complexity. The modified IEEE 33-bus and 69-bus distribution systems are tested with multiple outages. The presented results demonstrate the effectiveness of the proposed model

24 POWER TRANSMISSION AND DISTRIBUTION↗