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At least 73 records · Page 4

Oak Ridge National Laboratory Pilot Demonstration of an Attestation and Anomaly Detection Framework using Distributed Ledger Technology for Power Grid Infrastructure

This report summarizes the design and pilot demonstration of a framework called Grid Guard that was created to provide increased data and device trustworthiness to electric grid devices by leveraging distributed ledger technology (DLT), specifically blockchain. Grid Guard contains a combination of core cryptographic methods such as the secure hash algorithm (SHA), and asymmetric cryptography, private permissioned blockchain, baselining configuration data, consensus algorithm (Raft) and the Hyperledger Fabric (HLF) framework. The system implements a low energy, fast, and robust enhancement to system trustworthiness within and across electric grid systems such as substations, control centers and metering infrastructures. Blockchain is a distributed database structured that provides a practically unalterable (immutable) timeline of stored transactions. By relying on hashing and the Raft consensus algorithm, if an entity tries to illegitimately alter a record at one instance of the database the other ledger nodes are not altered. They work to cross-reference each other and easily locate any incorrectly added data and remove it. The bulk raw data is stored in an off-chain storage (outside of the blockchain ledger) and a hash of this baseline data is stored in the Blockchain ledger via hashing windows of time-series and configuration data, after aggregation and filtering. The bulk off-chain data repository is then considered to be trust-anchored using the hashes stored in the blockchain. To secure the electric grid testbed devices and data, device configuration baselines were compared to those baselines that had been previously stored in the ledger. Statistical baselines for device configurations, network communication patterns, and high-speed sensor data are calculated and then stored off-chain and hashes stored in the ledger. Measurements such as three-phase voltage and current, frequency, breaker status, protection scheme settings, network configuration settings (and other device configuration artifacts) and network traffic features (packet interarrival times) are compared every minute or other selected time windows. During phase 1 of the Grid Guard DLT project different DLT technologies were studies, and an assessment was performed on DLT technology vulnerabilities, uses, and key characteristics. DLT consensus protocols were studies (e.g., RAFT, named after Reliable, Replicated, Redundant, And Fault-Tolerant). Also, cryptography, public, private and permissioned or permissionless systems were assessed. Grid Guard implements a permissioned private DLT. Consensus algorithm selection and choice of DLT implementation depended heavily on the use-case. For this use-case, parameters were selected to measure performance and existing tools for assessment. Benchmarking was performed theoretically and practically. During phase 2 hashed transactions/blocks were inserted into the ledger every second. During phase 2 of the Grid Guard DLT project, a prototype framework was developed and demonstrated for attestation of critical substation devices and data using precision timing systems that use PTP and IRIG-B protocols) on a testbed of operational devices that emulated a distribution substation, control center, and power metering infrastructure using real Operational Technology (OT). The testbed includes OT devices such as protective relays, human machine interfaces (HMI), and power meters. To determine when to collect and compare system and network baselines, an initial examination of an anomaly detection capability to identify malicious manipulation of data streams was conducted. The resulting anomaly detection was demonstrated in a set of experiments and leveraged to trigger device artifact attestation checks. Attestation checks occur against device configuration baselines when compared with the immutable blockchain-stored baselines, which provided a cryptographically supported means by which to store baselines. The electrical substation-grid testbed was created to test the Grid Guard framework. The testbed emulates the operations of a portion of a power grid and SCADA systems as closely as possible. The testbed integrates real protocols, mainly IEC 61850 standard protocols, such as the Sampled Value (SV) and the GOOSE protocols. The testbed also supports DNP3 and other layer 2 and layer 3 protocols such as Telnet, SSH, SFTP/FTP and other proprietary protocols needed to connect to industrial control system equipment. The testbed emulates real power conditions using the OpalRT hardware-in-the-loop (HIL) device which can create fault situations that cannot be easily tested on real systems. The electrical substation-grid testbed was created using real measurement, communication, and protection devices that electrical utilities commonly use.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Cybersecurity Anomaly Detection in SCADA-Assisted OT Networks Using Ensemble-Based State Prediction Model

The cybersecurity threats of power system gradually grow due to the increased sophisticated interactions between Information Technology (IT) and Operational Technology (OT) networks. False data injection attack (FDIA) that aims to compromise the Supervisory Control and Data Acquisition (SCADA) measurement and disturb the system operation is one of such cyber threats. Such attacks can potentially lead to significant operational issues at the control centers and substations, and hence, result in severe physical consequences. To avoid catastrophic failure across the power grid resulting from these attacks, it is essential to arm the OT network with real-time vulnerability assessment tools. To this end, this paper outlines various drawbacks of the Purdue architecture model to defend against cyberattacks in the OT network. Furthermore, a novel ensemble-based state prediction model is proposed to detect cybersecurity anomalies in SCADA assisted OT networks. The proposed model uses control center level generation and load forecasts, scheduled, and forced outages, power flow solutions, and the substation level historical data. The hypothesis of the proposed scheme relies on the fact that additional control center and substation data can hardly be accessed and compromised by attackers. One of the vital features of the proposed scheme is an hour-ahead prediction of the operational feasibility of the SCADA measurement range at the control center and substation in real time helps in detecting anomalies in measurements across both substation and the control center.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Gauche Ethyl Alcohol: Laboratory Assignments and Interstellar Identification

Ethyl alcohol (ethanol) is known to possess a pair of closely spaced excited torsional substates (gauche+, gauche-) at an energy of approximately 57 K above the ground (trans) torsional substate. We report an extended analysis of some gauche - gauche+ Q-branch ((Delta)J = 0) transitions with a three-substate fixed frame axis method (FFAM) Hamiltonian. Our approach accounts for complex trans-gauche interactions for the first time. In addition, we are able to obtain intensities for perturbed rotational transitions, and to determine the trans to gauche+ separation to be 1185399.1 MHz. A complete ground state rotational-torsional partition function accounting for the previously neglected gauche substates is presented. Based on our analysis, a total of 14 U lines obtained towards Orion KL can now be assigned to gauche substates of ethanol. Analysis of these lines yields a rotational temperature of 223 K and a total (trans + gauche) column density of 7.0 x 10(exp 15)/sq cm. The column density is in reasonable agreement with the recent value of 2-3 x 10(exp 15)/sq cm based on observations of trans-ethanol by Ohishi et al., although there is some disparity in the rotational temperatures. Eight additional U lines in the literature are assigned to transitions of gauche ethanol.

Pearson, J. C.↗

The Millimeter- and Submillimeter-Wave Spectrum of Gauche-Ethyl Alcohol

We report an investigation of the rotational-torsional spectrum of the gauche rotational isomers of ethyl alcohol in the 51-505 GHz frequency region. Over a thousand transitions between rotational levels in the gauche substates of the ground OH torsional state have been measured and assigned. These transitions involve rotational quantum numbers J and K(sub a) up to 30 and 15, respectively, and are of two types: alpha-type transitions between levels in either the gauche+ or the gauche-substate, and c-type transitions between rotational levels in the different substates. The majority of these transitions have been fit satisfactorily using a two-state Hamiltonian based on the Fixed Framework Axis Method (FFAM). The rotation, distortion, and interaction constants have been determined along with the energy difference between the two gauche substates. The derived constants can be used to predict many more transitions accurately for astronomical purposes. The J and K(sub a) region where the two-state analysis can be used has been determined. The basis for a three-state analysis including the trans substate is presented and the applicability of the FFAM approach is discussed.

Pearson, J. C.↗

Rolling Root Mean Square Based Multimodal Anomaly Detection for Real Time Monitoring of Smart Grid

Reliable real-time monitoring is valuable for maintaining the operational integrity of modern electrical smart grids. Deployment of heterogeneous sensing technologies in substations has enabled high-resolution, multichannel waveform monitoring, but also introduces challenges for anomaly detection due to noise, baseline drift, and modality-dependent signal characteristics. In this work, we present a computationally efficient unsupervised method for multimodal event detection based on Rolling Root Mean Square based Event Detection (RRMSED). The method is developed using in-house, field deployed sensors collecting data at a utility substation. The sensing system comprises voltage and current sensors, triaxial accelerometers, and magnetometers, collectively capturing electrical, vibrational, and magnetic waveform measurements at high temporal resolution. RRMSED operates by extracting rolling RMS energy features and their first-order temporal differences from consecutive waveform segments for each channel and then applying channel-specific statistical thresholds learned from historical data. A persistence-based exceedance logic is employed to robustly identify transient events while suppressing impulsive noise, and to provide precise temporal localization with high resolution. The framework is designed for continuous server-side operation and can be deployed in real time without requiring complex models. Experiments on simulated waveform data with known ground truth demonstrate low false positive (FP) and false negative (FN) rates. Application to real substation data shows RRMSED to identify events that are not captured by conventional monitoring indicators including fast transient detection algorithm currently deployed in the system. These results indicate that rolling RMS based features provide an effective and practical basis for real-time multimodal event detection in smart-grid substations.

Mukherjee, Subrata [ORNL] (ORCID:0000000309930338)↗

SDN-Based Dynamic Cybersecurity Framework of IEC-61850 Communications in Smart Grid

In recent years, critical infrastructure and power grids have experienced a series of cyber-attacks, leading to temporary, widespread blackouts of considerable magnitude. Since most substations are unmanned and have limited physical security protection, cyber breaches into power grid substations present a risk. Nowadays, the susceptibility of SDN architecture to cyber-attacks has exhibited a notable increase in recent years, as indicated by research findings. This suggests a growing concern regarding the potential for cybersecurity breaches within the SDN framework. In this paper, we propose a hybrid intrusion detection system (IDS)-integrated SDN architecture for detecting and preventing the injection of malicious IEC 61850-based generic object-oriented system event (GOOSE) messages in a digital substation. Additionally, this program locates the fault’s location and, as a form of mitigation, disables a certain port. Furthermore, implementation examples are demonstrated and verified using a hardware-in-the-loop (HIL) testbed that mimics the functioning of a digital substation.

Liu, Chen-Ching [Virginia Tech] (ORCID:00000002894↗

Alerga: Alert Aggregation and Reasoning in GOOSE Simulation Pipeline

IEC 61850 specifies the Generic Object Oriented Substation Event (GOOSE) protocol as one option for low latency communication of substation-related events. Due to its strict timing requirements, GOOSE lacks any form of encryption or authentication and has only minimal integrity guarantees. These absences render the protocol vulnerable to a variety of communication anomalies, including adversarial action. In particular, an adversary with access to the substation network can launch man in the middle (MITM) attacks. We propose Alerga, a set of tools to allow operators to mitigate some of the risks of the protocol while retaining its strengths. To that end, we have developed first a GOOSE simulation pipeline including data generation, anomaly detection, alert handling, causal reasoning and data visualization components. The simulator is designed to be modular, allowing operators to swap components to better fit their network capabilities. The volume of alert traffic on a substation network threatens operators with alert fatigue. In order to combat this, we secondly present a novel form of alert aggregation and processing, offering operators a condensed view of any threats to the system. Thirdly, to facilitate the handling of these threats, our causal reasoning system traces the alerts back to their most likely cause, generating an initial hypothesis for operators to investigate.

alert aggregation↗

Flexible Resource Scheduler for FAST-DERMS (FRS-FASTDERMS) v0.9

The Flexible Resource Scheduler is a hierarchical controller that manages the distributed energy resources in a distribution substation or distribution feeder to provide a firm commitment of power flow at the substation or feeder head to be scheduled in transmission-level markets as an aggregated demand resource. It is the reference controller for the FAST-DERMS Architecture, developed in tandem with the architecture under the DOE FAST-DERMS project. It is comprised of a day-ahead stochastic optimization, which schedules substation power flow and reserves, a intra-hour MPC, which generates dispatch base points for DER, and a real-time PID controller maintaining that dispatches DER to maintain the substation power around the base points. The repository also includes a representative aggregator controller, and all of the necessary components to run a simulation using PNNL's GridAPPS-D software with the controller.

MacDonald, Jason [Lawrence Berkeley National Labor↗

Federated Architecture for Secure and Transactive Distributed Energy Resource Management Solutions (FAST-DERMS)

This document provides system-level specifications for a federated architecture for secure and transactive distributed energy resource management solutions (FAST-DERMS), presents a solution, and describes operational concepts for the proposed solution. FAST-DERMS enables the provision of reliable, resilient, and secure transmission and distribution (T&D) grid services through the scalable aggregation and near-real-time management of utility-scale and small-scale distributed energy resources (DERs). We first present the principles and objectives of FAST-DERMS. Then, after discussing important system concepts, we present the specifications for FAST-DERMS and a solution that employs a distributed and federated control methodology in which the DERs connected to a single point of common coupling with the rest of the system, such as individual substations, are optimized coordinately to provide system-level grid services. FAST-DERMS aims to aggregate and coordinate the operations of DERs to support T&D grid operations. The key optimization and control component of this FAST-DERMS reference implementation is a flexible resource scheduler (FRS) that aggregates the DERs within a substation service area. These FRSs operate at the substation level and perform constrained economic dispatch of DERs, either directly or through a transactive market or aggregator, as shown in Figure ES-1. An FRS Coordinator at the distribution system operator (DSO) level aggregates distribution substations operated by FRSs and interfaces with the transmission system operator (TSO) to provide transmission services. FAST-DERMS also allows for the integration of the FRS Coordinator with an existing distribution utility management system that could be employed by the DSO to enhance distribution grid operations.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Autonomous Tools for Attack Surface Reduction (Final Report)

The electric power grid is a complex critical infrastructure that forms the lifeline of modern society, and its secure and reliable operation is of paramount importance to national security and economic wellbeing. However, recent findings documented in authoritative sources indicate the threat of cyber-based attacks growing in numbers and sophistication. However, securing the grid against stealthy cyberattacks is a challenging task due to legacy nature of the infrastructure coupled with dynamic nature of threat landscape and ever-growing sophistication of the adversaries. Additionally, the grid’s attack surface continues to grow with the increased dependence on digital communications and control that now extends to each consumer through smart meters and distributed energy resources. Unfortunately, this expansive surface increases the grid’s vulnerability and further exposes critical control systems in both substations and control centers. To respond to this emerging need, we had successfully assembled an interdisciplinary team with academic- industry partnership to successfully conduct research, development, evaluation, demonstration, and commercialization of attack surface reduction tools, whose goal was to significantly reduce the cyber attack surface in the North American power grid. Our proposed project was a synergistic collaborative effort leveraging the synergistic expertise of the team members across power systems, cyber security and CPS security, testbeds, field deployments and demonstration, and successful commercialization. The following are the specific tasks that have been successfully completed two phases (2016-2020). Phase I: Task 1: Developed and implemented a robust Project Management and Data Management Plan, coupled with a well thought out Risk Mitigation Plan. Task 2.1: Developed a comprehensive framework that continually assesses and autonomously reduces the attack surface for the power grid control environment spanning across substations, control center and the SCADA network to significantly reduce the risks of cyber attacks. Task 2.2: Developed attack surface analysis techniques, metrics, and tools that assess the attack surface at multiple levels including the control center, substations, and the SCADA network. Task 2.3: Developed attack surface reduction techniques and tools that dynamically reduce attack surface and hence increase attacker’s cost without interfering in the critical functions of the system. Task 2.4: Prototyped, implemented, and quantitatively evaluated/validated the techniques and tools on a realistic industrial CPS security testbed environment by leveraging the unique resources of the team. Task 3: Developed Commercialization plan to transition the developed tools into power system industry stakeholders for a broader adoption by leveraging the expertise of our industrial members. Phase II: Task 4: Successfully completed field demonstration, verification, and evaluation of the effectiveness of the attack surface analysis and reduction techniques on a realistic utility testbed environment. This also involved the development of realistic scenarios, sound metrics, data sets, evaluation criteria, and documentation. Technology integration & Field demonstration: The project had significantly advanced the state-of-the-art research and practice in improving the cybersecurity of our nation’s power grid infrastructure against cyber threats. In particular, the proposed, designed, and deployed attack surface analysis and reduction algorithms and tools have contributed to significantly reducing the exposure and risk of the devices, substations, and the integrated SCADA/EMS/ DMS grid environment to cyber threat. Strong demonstration and evaluation techniques have verified the feasibility of the developed techniques on realistic cyber-physical testbeds and utility partner's real grid environment, and collaborative research and evaluation of attack surface reduction techniques (for wide-are monitoring and control) within a vendor (GE) EMS platform. The Attack Host Analyzer (AHA) tool that was developed through this project was made available through GitHub.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Reference floating wind array designs for three representative regions

This work presents the systematic development of three open-source reference floating wind array designs. The designs are tailored to representative site conditions for three regions of the United States: Humboldt Bay off the coast of California, the Gulf of Maine, and the Gulf of America. We adopted existing reference designs for the individual 15 MW turbines, semisubmersible floating platforms, substations, mooring systems, and power cables – integrating and adapting them as needed for each location. We adapted existing dynamic cable designs to use larger conductor sizes to meet the arrays' power transmission requirements, and we set up redundant mooring systems for each substation. The layout of each array is a uniform-grid design optimized to approximately minimize the levelized cost of energy (LCOE) within a square lease area while satisfying spatial constraints. These constraints ensure adequate clearances between adjacent turbines and between underwater components during the layout optimization to prevent clashing and ensure that all components reside within the lease boundaries. Substations are included to allow accounting for intra-array cable costs. They are placed within the uniform grid to maintain the navigability of the arrays. For each feasible layout considered, annual energy production and cable routing costs are calculated and updated in the LCOE objective function. After the optimization, we refined the cable routing with a mix of algorithmic and manual methods to ensure that the cables avoid mooring system components and approach the substation with adequate clearances. We confirmed the suitability of each reference array's layout by comparing the wake losses at each wind heading angle to the wind rose, observing that the optimized layouts largely avoid wake losses in the predominant wind directions. These reference arrays provide open-source baseline designs to enable future research and innovation of floating wind technology at the array scale.

17 WIND ENERGY↗

An extension of the high-resolution millimeter- and submillimeter-wave spectrum of methanol to high angular momentum quantum numbers

The high-resolution laboratory millimeter- and submillimeter-wave spectra of C-12H(3)OH and C-13H(3)OH have been extended to include transitions involving significantly higher angular momentum quantum numbers than studied previously. For C-12H(3)OH, the data set now includes 549 A torsional substate transitions and 524 E torsional substate transitions through J is not greater than 24, exclusive of blends. For C-13H(3)OH the data set now includes 453 A torsional substate transitions and 440 E torsional substate transitions through J is not greater than 24, exclusive of blends. The extended internal axis method Hamiltonian has been used to analyze the transitions to experimental accuracy. The molecular constants determined by this approach have been used to predict accurately the frequencies of many transitions through J = 25 not measured in the laboratory.

Anderson, Todd↗

National Maglev initiative: California line electric utility power system requirements

The electrical utility power system requirements were determined for a Maglev line from San Diego to San Francisco and Sacramento with a maximum capacity of 12,000 passengers an hour in each direction at a speed of 300 miles per hour, or one train every 30 seconds in each direction. Basically the Maglev line requires one 50-MVA substation every 12.5 miles. The need for new power lines to serve these substations and their voltage levels are based not only on equipment loading criteria but also on limitations due to voltage flicker and harmonics created by the Maglev system. The resulting power system requirements and their costs depend mostly on the geographical area, urban or suburban with 'strong' power systems, or mountains and rural areas with 'weak' power systems. A reliability evaluation indicated that emergency power sources, such as a 10-MW battery at each substation, were not justified if sufficient redundancy is provided in the design of the substations and the power lines serving them. With a cost of $5.6 M per mile, the power system requirements, including the 12-kV DC cables and the inverters along the Maglev line, were found to be the second largest cost component of the Maglev system, after the cost of the guideway system ($9.1 M per mile), out of a total cost of $23 M per mile.

Save, Phil↗

The Millimeter- and Submillimeter-Wave Spectrum of Gauche-Ethyl Alcohol

We report an investigation of the rotational-torsional spectrum of the gauche rotational isomers of ethyl alcohol in the 51е05 GHz frequency region. Over a thousand transitions between rotational levels in the gauche substates of the ground OH torsional state have been measured and assigned. These transitions involve rotational quantum numbers J and Ka up to 30 and 15, respectively, and are of two types: a-type transitions between levels in either the gauche+ or the gaucheРsubstate, and c-type transitions between rotational levels in the different substates. The majority of these transitions have been fit satisfactorily using a two-state Hamiltonian based on the fixed framework axis method (FFAM). The rotation, distortion, and interaction constants have been determined along with the energy difference between the two gauche substates. The derived constants can be used to predict many more transitions accurately for astronomical purposes. The J and Ka region where the two-state analysis can be used has been determined. The basis for a three-state analysis including the trans substate is presented and the applicability of the FFAM approach is discussed.!

rotational-torsional↗

Electrical Infrastructure Cost Model for Marine Energy Systems

The National Renewable Energy Laboratory's Electrical Infrastructure Cost Model is an Excel-based tool designed to estimate the electrical infrastructure costs of marine energy components and subsystems. It incorporates data collected from offshore wind projects, utility projects, and other relevant sources to provide accurate and comprehensive cost projections. With its user-friendly interface, the model allows users to input various parameters related to the system array, electrical cables, and substations. By leveraging industry data, cost trends, and technological advancements, the model generates outputs that include system array sizing, electrical cable specifications and costs, substation specifications and costs, and total electrical infrastructure costs. One of the notable strengths of the model is its flexibility in covering multiple-orders-of-magnitude scaled systems, accommodating projects ranging from proof-of-concept or pilot-scale installations to large-scale offshore systems. By collecting data largely from offshore wind reports and utility projects, the model incorporates real-world conditions and accounts for industry-specific factors. It incorporates cost trends and sizing relationships to deliver cost estimations for electrical infrastructure components, such as electrical cables and substation equipment.

16 TIDAL AND WAVE POWER↗

Generalized Power Flow Model of an Extra High-Power Multi-Terminal HVdc Transmission Grid with Parallel-Connected and Voltage-Stacked Converters

To increase power transfer capacity of high-voltage direct current (HVdc) transmission, a new extra high-power HVdc architecture with multiple standard modular multilevel converters (MMCs) per substation has recently been introduced. This paper proposes a power flow model for a multi-terminal HVdc (MTdc) grid with this innovative substation architecture. The proposed MTdc model can be integrated seamlessly with existing ac-dc power flow algorithms with minimal modifications. The model is applicable to various MTdc grid types and topologies, different numbers of dc buses, dc lines, and MMCs per substation, along with diverse control parameters. In addition, it accurately captures both balanced and unbalanced operations of the MTdc grid. The proposed model is verified using a 5-terminal bipole MTdc grid that spans 4 areas in the Eastern Interconnection system of the USA. The numerical solutions obtained from unified and sequential ac-dc power flow algorithms under different operating conditions closely match the time-domain simulation results in PSCAD, validating the accuracy and versatility of the proposed MTdc power flow model.

Nguyen, Quan H.↗

Distributed Intrusion Detection System using Semantic-based Rules for SCADA in Smart Grid

Cyber-physical system (CPS) security for the smart grid enables secure communication for the SCADA and wide-area measurement system data. Power utilities world-wide use various SCADA protocols, namely DNP3, Modbus, and IEC 61850, for the data exchanges across substation field devices, remote terminal units (RTUs), and control center applications. Adversaries may exploit compromised SCADA protocols for the reconnaissance, data exfiltration, vulnerability assessment, and injection of stealthy cyberattacks to affect power system operation. In this paper, we propose an efficient algorithm to generate robust rule sets. We integrate the rule sets into an intrusion detection system (IDS), which continuously monitors the DNP3 data traffic at a substation network and detects intrusions and anomalies in real-time. To enable CPS-aware wide-area situational awareness, we integrated the methodology into an open-source distributed-IDS (D-IDS) framework. The D-IDS facilitates central monitoring of the detected anomalies from the geographically distributed substations and to the control center. The proposed algorithm provides an optimal solution to detect network intrusions and abnormal behavior. Different types of IDS rules based on packet payload, packet flow, and time threshold are generated. Further, IDS testing and evaluation is performed with a set of rules in different sequences. The detection time is measured for different IDS rules, and the results are plotted. All the experiments are conducted at Power Cyber Lab, Iowa State University, for multiple power grid models. After successful testing and evaluation, knowledge and implementation are transferred to field deployment.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Bus Clustering for Distribution Grid Topology Identification

Recovering the distribution grid topology is essential to perform several distribution system operator functions. Many algorithms that address the topology recovery problem have already been proposed in the literature. Most are based on a priori information regarding which buses are fed by which substation; however, this information might not be available because frequent grid reconfigurations change the distribution grid portion connected to each substation. This paper addresses the problem of assigning every substation the set of buses that it is feeding, given field data. First, the aforementioned task is cast as a nonconvex optimization problem. Second, a relaxed version of the optimization problem is solved via the alternating direction method of multipliers. Finally, the performance of our approach is validated through numerical simulations of realistic scenarios using a standard IEEE benchmark feeder.

bus clustering↗