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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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DOE OSTI2022

Adaptive Fault Detection Based on Neural Networks and Multiple Sampling Points for Distribution Networks and Microgrids

Smart networks such as microgrid (MG) and active distribution networks (ADN) have been recently playing an important role in power system operation. The design and implementation of appropriate protection systems for such networks must be addressed, which imposes new technical challenges. This paper presents the implementation and validation aspects of an adaptive fault detection strategy based on neural networks (NNs) and multiple sampling points for ADN and MG. The solution is implemented on an edge device. Artificial NNs are used to derive a data-driven model that uses only local measurements to detect fault states of the network without the need for communication infrastructure. Multiple sampling points are used to derive a data-driven model, which allows the generalization considering the implementation in physical systems. The adaptive fault detector model is implemented on a Jetson Nano system, which is a single-board computer (SBC) with a small Graphic Processing Unit (GPU) intended to run machine learning loads at the edge. The proposed method is tested in a physical, real-life, low-voltage network located at Universidad del Norte, Colombia. This testing network is based on the IEEE-13 Node Test Feeder scaled down to 220 V. The validation in a simulation environment shows the accuracy and dependability above 99.6%, while the real-time tests show the accuracy and dependability of 95.5% and 100%, respectively. Without hard-to-derive parameters, the easy-to-implement embedded model highlights the potential for real-life applications.

42 ENGINEERING↗
DOE OSTI2021

Transactive Implementation of Decentralized Electricity Market for Grid-Edge Systems

The electricity landscape is evolving towards more decentralized approaches due to the proliferation of distributed energy resources and the participation of increasingly smart consumers and producers (prosumers). Recent advances in information and communication technologies and smart metering, provides strategic opportunities for “prosumers” to reform their conventional energy practices towards more consumer-centric economies. From an operational perspective, managing power distribution networks is becoming more difficult with such active grid-edge systems providing limited to no visibility or control. Transactive Energy (TE) has been emerging as a key enabler towards effectively and efficiently integrating prosumers into competitive electricity markets. This work presents a transactive implementation of community-centric markets. A co-simulation framework is developed for evaluating the proposed market structure with high-fidelity models. Case studies on the IEEE-123 node test system demonstrate that community-centric transactive markets can enable communities of prosumers to operate collaboratively as grid-edge systems. The potential benefits of implementing community-centric TE systems are also illustrated.

transactive, microgrids, centralized market operat↗
DOE OSTI2026

SuperLab 2.0 Showcase: Connecting Five Labs to Tackle Grid Complexity and Unlock Unique Grid Asset Potential

SuperLab 2.0 (5-Lab Demo) is a collaborative, national-scale experiment showcasing the coordination of geographically distributed energy assets in real time. The demonstration integrates 25 physical and digital assets, spanning wind, PV, batteries, electrolyzers, DC fast chargers, microgrid controllers, building automation systems, small modular reactor (SMR), control centers, and gas turbines, across five DOE national laboratories-NLR, INL, NETL, LBNL, and SNL. These assets are unified using Energy Sciences Network (ESnet), a low-latency, high-performance U.S. Department of Energy's (DOE) network, and controlled via a centralized energy controller hosted at NLR's ARIES facility. The demonstration validates the ability to stress-test hybrid energy systems under dynamic scenarios to de-risk advanced control strategies for greater resilience and flexibility. SuperLab 2.0 (5-Lab Demo) showcased a major advancement in federated national laboratory collaboration, enabling real-time, cross-laboratory experimentation to coordinate geographically dispersed distributed energy resources (DERs) using various communication protocols and networks. SuperLab 2.0 (5-Lab Demo) built on previous demonstrations conducted between NLR-PNNL and NLR-INL connecting diverse assets including distant protection devices, a SMR simulator, and a high temperature electrolyzer (HTE). Previous demos were based on a single connection between two labs with minimal coordination challenges. The 5-Lab demo with a centralized controller, distributed testbeds across different geographical locations, and use of protocols-based communication represents a scenario closer to real-world grid operations that coordinate resources across a region to meet system needs. This experiment studied how local DER controllers interact with a centralized energy controller during normal and abnormal events to maintain reliability. The SuperLab team across the five labs implemented a notional power system model equivalent of transmission and distribution lines, represented by the data networks interconnecting the labs. Each lab continuously exchanged local parameters (such as P and Q) from its Hardware-In-Loop (CHIL) and Power Hardware-In-Loop (PHIL) assets through centralized energy controller at NLR, enabling real-time interaction and coordination across sites. By leveraging ESnet as the communication backbone, the team successfully operated the distributed assets as a unified power system, with each bus represented by a different laboratory. This setup mirrors how assets interact in real-world power systems across dispersed locations with various protocols and latencies. At each lab site, assets were operated using their own local controllers which were coordinated through an overarching operation and control layer of centralized energy controller, equivalent to how an energy management system (EMS) orchestrates assets across a regional or national grid. SuperLab's federated connectivity utilized a Digital Real-Time Simulators (DRTS)-type gateway to connect Controller Hardware-In-Loop (CHIL) and PHIL assets between labs. To enable this federated connection through ESnet, a deterministic network was established where latency variations were consistent. This consistency allowed the development of digital filters for the power system assets across CHIL and PHIL interfaces to avoid unstable and unreliable grid conditions. This report provides an overview of the cross-laboratory configuration and offers insights into interconnecting geographically distributed research assets to test them as if they were co-located. This experiment represents a step toward linking nine DOE national laboratories, enabling nation-wide simulations that can address utility-driven challenges with grid resilience, flexibility, and modernization.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Electrical Fault and Power Quality Detection Algorithms and Customer-Owned DERs Monitoring with a Cyber Grid Guard System and DLT

In this study, the electrical fault and power quality detection algorithms and customer-owned DERs monitoring use cases were implemented, with a Cyber Grid Guard system and DLT. Electrical utilities continue to deploy more intelligent electronic devices (IEDs) inside and outside electrical substations, and are associated with customer-owned distributed energy resources (DERs). Data from these IEDs, such as power meters and protection relays, must be kept confidential and of high integrity. Blockchain technology has the potential to increase microgrid resilience by enhancing data sharing security. The growing use of IEDs and customer-owned renewable energy sources (DERs) may make it necessary to connect Distributed Ledger Technology (DLT) with power system applications. We implemented the electrical faulted phase detection and power quality monitoring algorithms with a Cyber Grid Guard (CGG) system using DLT. In addition, the DERs (wind turbine farms) use case and protective relay cyber-event tests were assessed, by using the CGG system with DLT. In the experimental model, the testbed was created by using a real-time simulator and CGG system with power meters/ protective relays in the loop. The data collected from the CGG system and IEDs were compared with the same time stamp source. These results showed the successful assessment of protection, control and monitoring applications using a CGG system with DLT. In the future, power system applications for the ESGT with DERs and the CGG system will be based on executing smart contracts between electrical utilities and customer-owned DERs.

Piesciorovsky, Emilio↗
DOE OSTI2026

Science Uses Deployment Operations-Advanced Wireless: Exploring Open Radio Access Network Technologies for Energy Science

Open Radio Access Network is emerging as a solution to the increasing demand for more flexible, cost-effective, and advanced mobile network infrastructures. This evolution is driven by advancements in wireless technologies and the growing complexity of deploying and managing these networks. O-RAN represents a significant shift in wireless technology, building upon the 3rd Generation Partnership Project framework to foster openness, flexibility, and interoperability. By decoupling hardware and software components, Open Radio Access Network enables a multi-vendor ecosystem that encourages innovation and diverse solutions. Open Radio Access Network's potential extends beyond traditional wireless applications, with growing interest in its role in advancing energy systems, particularly in the context of smart grids, microgrids, and the integration of renewable energy sources. While the role of open-wireless technologies in driving energy transformation is increasingly recognized, further exploration is needed. Vendors and utilities are investigating how Open Radio Access Network technologies can optimize energy use cases and improve the performance of 5G and beyond applications. This report outlines efforts under the Science Uses Deployment Operations Advance Wireless project, a collaboration between the National Laboratory of the Rockies' Cybersecurity Research Center, Argonne National Laboratory, Lawrence Berkeley National Laboratory, and the Department of Energy's Energy Science Network research and operations staff. The focus of this project is on due diligence, through testing and evaluation, preparing for the deployment of advanced wireless infrastructure for scientific use cases, with an emphasis on Open Radio Access Network technology, its components, integrations, and its ability to support vertical stack application across the energy sector. Additionally, the report highlights the value cases for utilities, underscoring how adopting open wireless standards can accelerate the evolution of energy systems, foster innovation, and improve the integration of critical energy technologies.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Advanced Distributed Wind Turbine Controls Series: Part 3-Wind Energy in Grid-Connected Deployments – Microgrids, Infrastructure Resilience, and Advanced Controls Launchpad (MIRACL)

In recent years the technical ability and requirement for distributed wind turbines to provide grid support services beyond maximum energy production has increased. Ancillary services leveraged through advance controls of a wind turbine support grid reliability and resilience. One ancillary service that is significant to a grid-connected wind turbine deployment is fault ride through (FRT) in response to the voltage and frequency events in the power system. As part of the Microgrids, Infrastructure Resilience, and Advanced Controls Launchpad (MIRACL) this paper demonstrates, through desktop simulations, the wind turbine's FRT capabilities to support stable grid operation. We establish that the wind turbine models exceed FRT performance requirements stipulated in IEEE 1547-2018, regarding interconnection and interoperability of distributed energy resources. Utilizing a standalone CART2 (600 kW) wind turbine connected to the NREL's Flatirons Campus grid, we study voltage and frequency FRT utilizing various test cases. One of the test cases under study is a Category III voltage fault defined in IEEE 1547-2018 and derived from CA Rule 21. Some distributed wind turbines were unable to connect to the grid following the Rule 21 enforcement in California. Even if this is not a general requirement elsewhere, the grid codes might evolve in this direction. This study illustrates how a distributed wind turbine can provide some of these FRT services and enable a pathway toward a higher contribution of renewable energy in a distribution grid.

17 WIND ENERGY↗
DOE OSTI2022

2022 Peer Review Project Summary: Advanced Protection for Microgrids and DER in Secondary Networks and Meshed Distribution Systems

Although there are increasing numbers of distributed energy resources (DERs) and microgrids being deployed, current IEEE and utility standards generally strictly limit their interconnection inside secondary networks. Secondary networks are low-voltage meshed (non-radial) distribution systems that create redundancy in the path from the main grid source to each load. This redundancy provides a high level of immunity to disruptions in the distribution system, and thus extremely high reliability of electric power service. There are two main types of secondary networks, called grid and spot secondary networks, both of which are used worldwide. In the future, primary networks in distribution systems that might include looped or meshed distribution systems at the primary-voltage (mediumvoltage) level may also become common as a means for improving distribution reliability and resilience. The objective of this multiyear project is to increase the adoption of microgrids in secondary networks and meshed distribution systems by developing novel protection schemes that allow for safe reliable operation of DERs in secondary networks. We will address these challenges by working with the appropriate stakeholders of secondary network operators, protection vendors, and standards committee. The outcomes of this project include: a) development and/or demonstration of candidate methods for enabling protection of secondary networks containing high levels of DER; b) development of modeling and testing tools for protection systems designed for use with secondary networks including DERs; and c) development of new industrial partnerships to facilitate widespread results dissemination and eventual commercialization of results as appropriate.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

SOLAr Critical Infrastructure Energization (SOLACE): Leveraging Distributed Energy Resources to Provide Local Power

This document is a technical report based on a large-scale DOE-funded project conducted between 2019 and 2022. The project, called SOLAr Critical infrastructure Energization (SOLACE), is aimed at leveraging distributed energy resources (DERs) to provide local power to communities, feeders, or other regions. The project included a particular focus on high-value critical loads such as municipal water supply, telecommunication hubs, and disaster shelters. The key developments of the project were: (1) A comprehensive pre-event power system analysis methodology that identifies and characterizes the viable local power options. (2) A DMS-based example control system for activating and operating the local power solution during a time of crisis. (3) Grid-forming inverter technology to enable isolated local power operation and black-starting. (4) Cyber-security considerations for isolated systems when wider-area communication may be offline. This report describes the overall process that identifies and assesses the viable DER-based local power solutions for a given facility, region, or community. The report documents the process, including the key analysis steps, tools required, data requirements, and recommended pass/fail criteria for each step. It also provides a sample implementation of this process through a test case. Finally, it provides details of how a viable pre-event plan can be selected and activated at go-time when an event has occurred.

14 SOLAR ENERGY↗
DOE OSTI2023

Electrical substation grid testbed for DLT applications of electrical fault detection, power quality monitoring, DERs use cases and cyber-events

Electrical utilities continue to deploy more intelligent electronic devices (IEDs) inside and outside electrical substation, and are associated with customer-owned distributed energy resources (DERs). The integrity and confidentiality of data from these IEDs, like power meters and protective relays, is crucial. Blockchain technology could improve the resilience of microgrids by improving the security of data sharing. The penetration of customer-owned DERs (renewable energy sources) and the increasing deployment of IEDs can lead to integrate power system applications with Distributed Ledger Technology (DLT). In this study, we implemented the electrical faulted phase detection and power quality monitoring algorithms with a Cyber Grid Guard (CGG) system using DLT. In addition, the DERs (wind turbine farms) use case and protective relay cyber-event tests were assessed, by using the CGG system with DLT. In the experimental model, the testbed was created by using a real-time simulator and CGG system with power meters/ protective relays in-the-loop. The data collected from the CGG system and IEDs were compared with the same time stamp source. These results had shown the successful assessment of protection, control and monitoring applications using a CGG system with DLT. In the future, the ESGT with DERs and the CGG system will be used in other power system applications, based on implementing smart contracts between electrical utilities with customer-owned DERs.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Security Enhancements for Distributed Energy Resource Systems Interconnected with Distribution Networks: Final Technical Report

The revised IEEE 1547 Standard defines new complex communication-adjustable voltage and frequency regulation and ride-through characteristics, while maintaining the general antiislanding requirement for unintentional islanding situations. Unintentional islanding is prohibited while intentional islanding is specifically allowed, thus effectively enabling microgrid operation mode. Further, IEEE 1547-2018 Standard introduces new requirements in terms of interoperability so that the DER plant/circuit segments may be seamlessly integrated with the utility networks but at the same time become vulnerable to a cyber-attack. Traditional cybersecurity measures including encryption, authentication and role-based access control may not be fully implementable to all communication protocols specified in the IEEE 1547 Standard. Therefore, in this project we have identified, researched, implemented and tested several cyberphysical approaches that rely mostly on the behavior of the DER circuit and may help with validating the incoming command and control action potentially coming through an insecure communications channel. Additionally, we have built semantic models and communications profiles for DER facilities and have implemented lightweight IEC 61850 based publisher-subscriber GOOSE messaging mechanism, with security extensions in terms of authentication and encryption. The project proposed information models for integration into UCA OpenFMB 2.0 profiles focusing on grid code compliance.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

A Robust Hierarchical Dispatch Scheme for Active Distribution Networks Considering Home Thermal Flexibility

Distribution networks are changing from passive absorbers of electric energy to active distribution networks (ADNs) capable of operating and participating in electricity markets. In the context of residential microgrids, which is a type of ADNs, aggregated home heating, ventilation and air-conditioning (HVAC) loads present a key opportunity to drive operational and economic objectives, facilitate high renewable energy penetration, and enhance both system resiliency and flexibility. A robust, hierarchical dispatch scheme is developed and presented in this paper, which connects an upper level multi-phase distribution optimal power flow (DOPF) to a lower level model predictive control (MPC)-based HVAC fleet controller. The approach is tested and verified on a modified IEEE 13 bus system in an intraday market application. The results demonstrate that the proposed hierarchical dispatch scheme is able to drive both economic and operational objectives for the ADN operator.

Rooks, Cody D.↗
DOE OSTI2022

Low Voltage Network Protection Utility Workshop (Summary and Next Steps)

Increased penetration of Distributed Energy Resources and microgrids have fundamentally changed the operation al characteristics of Low Voltage (LV) network systems. Current LV network protection philosophy and practice are due for a significant re vamp to keep up with changing operating conditions. This workshop invites four of the major LV network users in the US to discuss the challenges they face today and the new technologies they have been experimenting with in light of this workshop discussion, use cases for further hardware-in-the-loop testing efforts are proposed to evaluate new LV network protection solutions.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

RAFT: Reconfigurable Array of High-Efficiency Ducted Turbines for Hydrokinetic Energy Harvesting

Diversifying the energy harvesting portfolio is crucial to achieving the ambitious goal of transitioning to clean energy by 2030. Marine hydrokinetic energy has garnered renewed interest due to its high harvesting potential in the U.S., and the resource's reliability and predictability—remaining relatively constant on a daily basis and available 24/7. However, there are currently few commercial devices capable of harnessing the energy from flowing water. This project aims to bridge that gap by designing and evaluating a novel hydrokinetic turbine concept that can efficiently harvest energy from both rivers and tidal streams. The RAFT (Reconfigurable Array of High-Efficiency Ducted Turbines) concept introduces a duct surrounding the turbine rotor and creates an array of small 5-kW units. The duct serves two primary purposes: (1) it enhances hydrodynamic efficiency by accelerating flow to the rotor, and (2) it functions as a structural component, facilitating the formation of modular arrays that lower costs. This project focuses on demonstrating this concept and validating these benefits through simulations and scaled prototype testing. The project team includes 8 faculty members and over 20 students from 3 universities, organized into three core areas: hydrodynamics, electrical systems, and structural analysis, with additional teams dedicated to system integration, environmental assessment and risk management, and tech-to-market strategy. The team successfully demonstrated the increased hydrodynamic efficiency of a ducted turbine compared to an unducted version using high-fidelity simulations and prototype tests. Moreover, design optimization efforts led to surpassing the SHARKS program's goal of 60% reduction of the levelized cost of energy with a significant margin.

13 HYDRO ENERGY↗
DOE OSTI2021

Blockchain-Enabled Cyber-Secure Microgrid Control Using Consensus Algorithm

This paper proposes a distributed control method based on a consensus algorithm for distributed energy resources (DERs) using blockchain as a secure communication medium for cyber resilience. Each DER communicates with a local blockchain server that is maintained by the distributed ledger technology to allow for securely sharing local measurements among neighbouring assets to achieve the global control objectives, i.e., voltage and frequency regulation as well as accurate power sharing among the DERs, including collective grid-forming capability. To prove that the distributed control can retain system stability under a blockchain-induced variable communication delay, Lyapunov function-based stability analysis is carried out. This paper demonstrates the concept on an 11-bus test case developed in MATLAB Simulink, which has been modified from the IEEE 9-bus test case, to study dynamic operations of the five inverter-based DERs working with a blockchain-induced variable delay. The results validate the superior performance of the proposed control method, compared to heavily compromised operations of the other test cases without the security measure, affected by heavy communication delays and communication interruptions.

blockchains↗
DOE OSTI2021

Cybersecurity Certification Recommendations for Interconnected Grid Edge Devices and Inverter Based Resources

Escalating deployment of PV and grid-edge devices on the distribution grid has increased the sustainability and efficiency of the electric grid. However, the increasing number of distributed energy resources (DERs) deployed creates a heightened cyber-physical interdependency on the distribution grid and thus creates more vectors for cyber-attacks to exploit through information and communication technology (ICT) systems and networks. For example, control signal packets can be modified, intercepted, or corrupted due to vulnerabilities in communication protocols used by microgrid controllers and grid edge devices for power control. Therefore, to mitigate and prevent cyber-attacks on grid edge devices and the inverter-based resources connected to the distribution grid, the U.S. Department of Solar Energy Technologies Office (SETO) awarded funding to the National Renewable Energy Laboratory and Sandia National Laboratory (SNL) to research, develop, and harmonize cybersecurity standards for Photovoltaic (PV) systems and for other kinds of DERs. To help develop a standard for DER cybersecurity, NREL established certification recommendations and test cases, in consensus with the solar industry and UL, for ensuring intrinsic design security for DERs. These recommendations were developed to bolster the cybersecure functionalities such as TLS, MAC, CRL, session resumption/renegotiation, and password, system, and service security management within the DER devices. The proposed test cases verify authentication, authorization, confidentiality, and data integrity for data and communications of DERs that use Transmission Control Protocol/Internet Protocol (TCP/IP). They were also developed to protect DER communications from eavesdropping, replay, man-in-the-middle, denial of service (DoS), spoofing through security certificates, least-privilege violation, and brute-force credentials. This report, which has been validated and reviewed by UL, expands upon those test cases to provide DER cybersecurity certification recommendations which increase DER resiliency and help to mitigate cyber-attacks. UL's collaboration with NREL and approval of this document will accelerate the adoption of a UL standard for DER cybersecurity.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Blockchain-Enabled Cyber-Secure Microgrid Control Using Consensus Algorithm: Preprint

This paper proposes a distributed control method based on a consensus algorithm for distributed energy resources (DERs) using blockchain as a secure communication medium for cyber resilience. Each DER communicates with a local blockchain server that is maintained by the distributed ledger technology to allow for securely sharing local measurements among neighboring assets to achieve the global control objectives, i.e., voltage and frequency regulation as well as accurate power sharing among the DERs, including collective grid-forming capability. To prove that the distributed control can retain system stability under a blockchain-induced variable communication delay, Lyapunov function-based stability analysis is carried out. This paper demonstrates the concept on an 11-bus test case developed in MATLAB Simulink, which has been modified from the IEEE 9-bus test case, to study dynamic operations of the five inverter-based DERs working with a blockchain-induced variable delay. The results validate the superior performance of the proposed control method, compared to heavily compromised operations of the other test cases without the security measure, affected by heavy communication delays and communication interruptions.

blockchain↗
DOE OSTI2025

Comparison of Sequence Component-Based Fault Detection and Relay Coordination Algorithms in Inverter-Based Networks

Protection of inverter-based microgrids using sequence component-based relaying schemes is a promising solution. These methods offer several advantages, including lower computational requirements, compatibility with commercial relay systems, and cost-effectiveness compared to communication-based approaches. This article investigate the performance of various sequence component based schemes with the objective of identifying the algorithms that provide the best fault detection and relay coordination, solely relying on local voltages and current at relay terminals. Positive, negative and zero sequence impedance, admittance and power detection algorithms were tested on modified IEEE 13 bus test network for various shunt faults (LG, LL, LLG, LLL). Hardware-in-the-loop validation was achieved using the Typhoon real-time simulator, interfacing with a SEL 751 relay. This research demonstrates that while several algorithms are capable of detecting faults with sufficient accuracy, only a few are effective in achieving proper coordination. Validation results indicate that the negative sequence power approach provides the best performance in both fault detection and coordination.

Patel, Deepika [ORNL] (ORCID:0000000341099994)↗
DOE OSTI2021

A Multi-Site Networked Hardware-in-Loop Platform for Evaluation of Interoperability and Distributed Intelligence at Grid-Edge

Electric power systems have experienced large increases in the number of intelligent, connected and controllable devices being deployed, leading to a high degree of distributed intelligence at the grid-edge. These devices, both utility-owned and consumer-owned, include but are not limited to: renewable generation sources, energy storage, remote switches, voltage regulators, and smart controllable loads such as electric vehicles. These new devices provide significant potential for increased operational flexibility that can be leveraged to achieve system reconfiguration, resiliency improvements, power quality improvements, and distribution system automation. However, there are two significant challenges that must be addressed before these assets can be leveraged for operations: interoperability and system level validation prior to deployment. Because of the complexity of distributed control systems, and their interactions with legacy centralized controls, a purely simulations-based approach for pre-deployment validation is not sufficient. It requires hardware-in-loop testing to emulate the operational hardware devices and evaluate their performance. Additionally, securely integrating multiple test facilities at utility operators and vendors might enable rapid scale-up of evaluation platforms, and remove the need for multiple expensive standalone installations. Presented in this paper, is the development of a multi-site evaluation platform that employs Advanced Distribution Management Systems (ADMS), distributed control devices, real-time hardware-in-loop assets, secure communication links, and protocol adapters. This platform uses standards-based approaches and open-source tools, and hence can serve as a template for other researchers and institutions to implement their multi-site evaluation frameworks for pre-deployment testing.

Essakiappan, Somasundaram↗