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Integrated Analysis Of Static Distributed Systems
Integrated approach encompasses modeling, identification of parameters, estimation of states, and control. Applies to models specified in part by possibly interconnected elliptic partial differential equations for deflections of structures under static loads. Appropriate for systems in which time-dependent effects negligibleand where control forces applied without exciting significiant dynamic behavior.
Joint state and parameter estimation
Recent results are described concerning the problem of state reconstruction for a class of nonlinear distributed systems. The methods are then applied to the problem of joint state and parameter estimation. An example with the wave equation is presented.
Improved Line Outage Detection in Transmission Systems with Few PMUs
Unlike transmission systems, distribution systems historically lack enough measurements, making their real-time monitoring almost impossible. Recent deployment of diverse types of devices such as phasor measurement units (PMUs), smart meters, solar inverters and weather information sensors opens up new ways of monitoring these systems, with the assistance of customized machine learning (ML) applications. The paper describes a grid-model-informed machine learning (ML) tool which integrates heterogeneous data streams and creates synchronous measurement snapshots to be used by a hybrid robust state estimator (SE) which provides not only accurate state estimates but also real-time feedback for ML model refinement. Improved monitoring performance due to the use of developed computational framework is experimentally observed by simulated scenarios on an electric utility’s distribution system.
On the Path to SunShot. Emerging Issues and Challenges in Integrating Solar with the Distribution System
This report analyzes distribution-integration challenges, solutions, and research needs in the context of distributed generation from PV (DGPV) deployment to date and the much higher levels of deployment expected with achievement of the U.S. Department of Energy's SunShot targets. Recent analyses have improved estimates of the DGPV hosting capacities of distribution systems. This report uses these results to statistically estimate the minimum DGPV hosting capacity for the contiguous United States using traditional inverters of approximately 170 GW without distribution system modifications. This hosting capacity roughly doubles if advanced inverters are used to manage local voltage and additional minor, low-cost changes could further increase these levels substantially. Key to achieving these deployment levels at minimum cost is siting DGPV based on local hosting capacities, suggesting opportunities for regulatory, incentive, and interconnection innovation. Already, pre-computed hosting capacity is beginning to expedite DGPV interconnection requests and installations in select regions; however, realizing SunShot-scale deployment will require further improvements to DGPV interconnection processes, standards and codes, and compensation mechanisms so they embrace the contributions of DGPV to system-wide operations. SunShot-scale DGPV deployment will also require unprecedented coordination of the distribution and transmission systems. This includes harnessing DGPV's ability to relieve congestion and reduce system losses by generating closer to loads; minimizing system operating costs and reserve deployments through improved DGPV visibility; developing communication and control architectures that incorporate DGPV into system operations; providing frequency response, transient stability, and synthesized inertia with DGPV in the event of large-scale system disturbances; and potentially managing reactive power requirements due to large-scale deployment of advanced inverter functions. Finally, additional local and system-level value could be provided by integrating DGPV with energy storage and 'virtual storage,' which exploits improved management of electric vehicle charging, building energy systems, and other large loads. Together, continued innovation across this rich distribution landscape can enable the very-high deployment levels envisioned by SunShot.
Scaled Implementation of Smart Charge Management for Electric Vehicles
Smart charge management (SCM) has become a critical strategy for mitigating potential grid impacts and reducing electricity costs for all customers. This study will evaluate the economics of implementing light-duty EV SCM at scale across the United States. This work will enhance distribution system analysis by estimating SCM implementation costs, exploring viable business cases, and developing a framework for national-level applications. The primary methodology involves leveraging detailed grid modeling from a specific service territory and using spatial extrapolation techniques to generalize findings to other regions. The analysis will develop key metrics to quantify the costs and benefits of SCM, including implementation costs relative to strategy and scale, the cost of distribution system upgrades with and without SCM, and the percentage of peak-load reduction. The objective is to produce a comprehensive report and a parameterized framework that enables utilities to self-assess the value of SCM in their own service territories. This will support the development of cost-effective charging strategies, accelerate the energization of new EV chargers, and facilitate the seamless integration of EVs into the nation's power grid.
Investigating Low-Altitude Constellations of Ad-Hoc Lunar PNT System for Distributed Spacecraft Autonomy
In this study, we examine a low-altitude Lunar Position, Navigation, and Timing (LPNT) constellations and the localization performance of Centralized Extended Kalman Filter (CEKF) and Decentralized Extended Kalman Filter (DEKF) algorithms. The primary investigation involves a 100-node swarm operating at a 100 km altitude, in contrast to previous studies that examined a 21-node asset in a frozen-orbit at 5,500 km. The autonomous operation of large-scale swarm is based on two-way Inter-Satellite Link (ISL) measurements, which involve pseudoranges and relative velocities among swarm nodes. We perform a numerical assessment of the two filtering approaches, utilizing ‘fully sampled’ measurements from all available assets as well as ‘two ISL’ measurements where each spacecraft is restricted to only two antennas. This research includes an analysis of CEKF under 2-ISL constraints and evaluates the performance of DEKF in a 100-node swarm, which has not been explored in previous studies. In addition, we examine the impact of increasing the sampling frequency for DEKF, showing that the update cycle can be shortened from a 10-minute interval. A novel approach for ‘2-ISL limited’ DEKF will also be introduced, using a matching formulation that exhaustively enumerates all potential matches. This study provides valuable insights into large-scale distributed swarm operations, considering various filter configurations, sampling frequencies, matching strategies, and scalability of CEKF and DEKF for low-altitude LPNT applications. The Lunar PNT technology plays a key role in providing reliable and robust navigation services on the Moon's surface and the South pole, where the primary Lunar missions are planned. To support upcoming Lunar missions, including small satellites from NASA's Commercial Lunar Payload Services program, the Lunar PNT system must be adaptable to smaller platforms like CubeSats. Driven by the growing involvement of public and private exploration partnerships, the traditional low Earth orbit missions are shifting to beyond geosynchronous orbit [1]. These upcoming missions aim to foster a sustainable and innovative exploration program, in collaboration with commercial and international partners, to facilitate human expansion throughout the solar system and return new knowledge and opportunities to Earth [2]. As part of this trend, there are increasing efforts to utilize science missions in Lunar orbit to develop a non-dedicated and ad-hoc PNT network system. Two traditional approaches, the Deep Space Network (DSN) and the weak signal Global Positioning System (GPS), are established deep-space navigation technologies for missions beyond the geosynchronous orbit. Beginning in 1958, the DSN was developed to communicate with the Explorer 1 spacecraft based on the use of radiometric tracking in spacecraft navigation [3]. The DSN is capable of providing nearly unfettered coverage to spacecraft beyond low-Earth orbit (LEO), however, increased space mission volume has created concerns about future expectations of DSN usage for spacecraft navigation [4]. For cislunar mission applications, the position accuracy using DSN achieves 100 m (3σ) with at least three geometrically diverse ground stations when using radiometric tracking alone [5]. The DSN's dependence on Earth-based ground stations restricts its operational capabilities to periods of Earth visibility. This limitation, coupled with its poor localization performance, renders the DSN unsuitable for future lunar missions that demand continuous tracking and precise positioning. To satisfy the increasing requirements of DSN in Lunar applications, spacecrafts are also required to improve their onboard antenna power and efficiency of the transmission. However, there is an important aggregate cost trade between adding capabilities to every spacecraft and adding to a capacity on the ground that serves multiple spacecraft [6]. A weak GPS system can provide PNT service while the user spacecraft is bound to the Moon, leveraging a single, steerable high gain antenna with the relatively narrow beam which includes all the sources in its field of view [7]. However, the higher the altitude the receiver is above the GPS constellations, the poorer and the weaker are the relative geometry and the received signal powers, respectively, leading to a significant navigation accuracy reduction [8]. The transmitted power becomes weaker with increasing distance from the Earth as well as signals tracked from one of the side lobes of the GPS antenna pattern. As a results, the number of visible satellites and relative geometric condition of the GPS satellites at very high altitude drops dramatically and reduces the navigation solution accuracy. Therefore, the weak GPS system is also not an ideal way to provide PNT service to upcoming Lunar missions when considering its limited geometric condition and the recued navigation accuracy. Another navigation approach on the Moon is being developed, similar to the Global Navigation Satellite System (GNSS) on Earth, aiming to offer navigation service with continuous 24/7 coverage across the entire Lunar surface. For example, lunar communications relay and navigation systems (LCRNS) by NASA and Lunar navigation satellite systems (LNSS) by JAXA are designed to serve as dedicated Position, Navigation, and Timing (PNT) systems for the Moon. However, designing a dedicated LNSS and PNT service involves additional challenges, which are unique to the lunar environment, including limited payload capacity for the CubeSat platform, i.e., the size, weight, and power (SWaP) of the onboard clock, limited lunar ground monitoring stations, and limited financial investment as compared to the legacy Earth-GPS [9]. NASA’s focus on utilizing CubeSat platforms on the Moon leads to an alternative Lunar navigation platform that leverages the existing Lunar science and exploration assets. The small satellites used in Lunar missions can be used to create a low-cost, autonomous, ad-hoc, and on-demand mission-centric Lunar PNT swarm capable of providing PNT services to these low-cost lunar missions [10]. As upcoming Lunar missions will often operate at low-altitude about 30 km to 100 km for scientific observations and mapping purposes, the low-altitude orbital constellations could be employed to create an ad-hoc Lunar PNT system. However, several issues must be addressed, such as the instability of these orbits, which often require maintenance or are only suitable for short-duration missions, operating for fewer than 90 days. Additionally, at an altitude of 100 km, the satellites have a limited period during which they are above the horizon and capable of providing PNT service to users. The implementation of a non-dedicated, ad-hoc Lunar navigation constellation facilitates on-demand PNT services. A preliminary study of ad-hoc Lunar PNT system was conducted using 21 spacecraft in 5,5000 km altitude frozen orbits to test its feasibility and a basic performance of orbital asset localization among ad-hoc Lunar constellations in small satellites format [10]. These swarm assets are designed for autonomous localization with minimal Earth interaction, reducing dependency on bandwidth and ground resources. The design in [10] demonstrated the feasibility of a decentralized PNT approach, specifically employing a DEKF approach for state estimation, which helps minimize onboard operating costs. The DEKF method distributes computation across individual satellites, which lightens the computational load while maintaining accuracy in orbit ephemeris and clock offsets, similar to centralized systems [11]. In a follow-on study [12], each spacecraft was limited to 2 communications antennae, forcing the selection of measurements and scheduling spacecraft activities to perform the measurements. A matching algorithm is implemented to select the best measurements and schedule position estimation updates. The decentralized localization performance is also investigated with increasing levels of network degradation for swarm assets considering the impact of intermittent and permanent communication failure, to demonstrate the robustness and fidelity of the decentralized Lunar PNT service [13]. This study confirmed that the ad-hoc PNT constellations in frozen orbit are highly robust and resilient to communication failures. However, unlike frozen orbit swarm assets, the low-altitude satellites have a limited ground view at an altitude of 100 km, where the ad-hoc Lunar constellation consists of 98 low-altitude satellites, evenly distributed across seven circular polar orbital planes, alongside two satellites in a frozen orbit at an altitude of 5,500 km (Figure 1). Therefore, the number of satellites visible to ground users is significantly limited in low-altitude orbit constellations. As each visibility of a spacecraft remains intact for only a few ticks before it moves out of the field of view, the ground user encounters challenges in maintaining continuous navigation service, resulting in sparse availability and provision of Lunar PNT system. Consequently, service availability is primarily restricted to the Lunar South Pole region (Figure 2). Given these limitations and concerns, the localization performance of low-altitude swarm assets will be assessed in this study. We focus on the investigation of the localization performance of low-altitude swarm assets and ground users near the Lunar South Pole. The overall flow of the Lunar PNT simulation incorporates the DEKF approach of asset localization and the weighted least-squares approach in user localization (Figure 3). The autonomous Lunar PNT simulation is primarily implemented in MATLAB, where the DEKF based on the matching scheduler is implemented with Google’s OR-tools as a model builder and Gurobi optimization tool as a backend solver. The General Mission Analysis Tool (GMAT) is utilized to generate ephemeris data for swarm assets, and accounts for satellite orbital details, mass, and perturbations like solar radiation pressure and drag coefficients. Each ephemeris dataset is produced in the Moon International Celestial Reference Frame (ICRF) inertial coordinate system. For state estimation, the distributed swarm assets rely on two-way Inter-Satellite Link (ISL) measurements, which involve tracking pseudoranges and relative velocities between visible satellites and anchor nodes during each observation. Numerical evaluations of the decentralized localization process are conducted to demonstrate the feasibility of the low-altitude PNT system in providing reliable navigation services. The main approach involves using DEKF and CEKF to localize 100 satellites in low-altitude constellations, where the CEKF is implemented to serve as a baseline for comparing the performance of distributed algorithms. In both cases, we evaluate ‘fully sampled’ measurements from all available assets, and ‘two ISL’ measurements when spacecraft are constrained to have only two antennas. We test four estimation techniques: CEKF fully sampled, CEKF two ISL, DEKF fully sampled, and DEKF two ISL filters. As the DEKF update cycle is comprised of network setup, communication, and computations, a global broadcast network and 2-way ISL network setup will take from 4 to 6 minutes as maximum [12]. In this simulation, the DEKF update cycle is set to 10 minutes, including a 4-minute latency for obtaining and computing the actual measurement updates. We experiment an increased update cycle to demonstrate the feasibility and evaluate the impact on localization performance using various tuning values for measurement noise covariances (Figures 4 and 5). By comparing centralized and decentralized approaches using a matching algorithm, we analyze the influence of cross-correlation factors in the covariance matrix, assuming 100% reliability of all assets and measurements. The increased frequency and the adjustments of tuning parameters reveal distinct error patterns between the two scenarios. The localization accuracy of the swarm assets and ground users is assessed by taking the median error across 100 assets and one ground user (84.9°S, 137.5°E) over 7-day simulation period (Table 1). Since the user localization accuracy is significantly affected by the performance of the swarm assets, it is crucial to maintain high localization accuracy within the swarm. This study will continue to explore decentralized filtering for autonomous LPNT operations, with further investigation of an 'iterative' matching approach which enumerates every valid matching pair, planned for the following month.
Detection of Stealthy False Data Injection Attacks in Unobservable Distribution Networks
In this paper, a composite scheme is proposed for detecting stealthy data manipulation attacks on distribution system which is unobservable with standard least squares based state estimators. This technique has three stages where the process of data imputation, voltage phasor estimation and the bad data detection are carried out in a systematic manner. The proposed approach is then integrated with moving target defense strategies which perturbs the network parameters to reveal stealthy false data injection attacks. The proposed approach is tested is validated on a three-phase, unbalanced 37-node distribution system and its results are presented. It is shown that the proposed approach has the ability to accurately detect the presence of FDI attacks using limited measurements (i.e., the test system is unobservable).
Distributed Pressure Sensing for Enabling Self-Aware Autonomous Aerial Vehicles
Autonomous aerial transportation will be a fixture of future robotic societies, simultaneously requiring more stringent safety requirements and fewer resources for characterization than current commercial air transportation. More robust, adaptable, self-state estimation will be necessary to create such autonomous systems. We present a modular, scalable, distributed pressure sensing skin for aerodynamic state estimation of a large, flexible aerostructure. This skin used a network of 22 nodes that performed in-situ computation and communication of data collected from 74 pressure sensors, which were embedded into the skin panels of an ultra-lightweight 14-foot wingspan made from commutable, lattice-based subcomponents, and tested at NASA Langley Research Center's 14X22 wind tunnel. The density of the pressure sensors allowed for the use of a novel distributed algorithm to generate estimates of the wing lift contribution that were more accurate than the direct integration of the pressure distribution over the wing surface.
Efficient Network Partitioning: Application for Decentralized State Estimation in Power Distribution Grids: Preprint
Increase in the proliferation of DERs requires real-time situational awareness for efficient grid operations. State estimation plays an important role for real time control and management of the power grid. As the sensing infrastructure grows, aggregating and handling high volumes of data at a centralized location is extremely difficult. To address this challenge, this paper first proposes a novel and efficient hierarchical spectral clustering-based network partition algorithm followed by a decentralized compressive sensing (DCS) based state estimation. The applicability of the proposed network partitioning algorithm is tested on IEEE-123 bus, IEEE-8500 node, and a 6204-node distribution network. The results shows that the proposed approach efficiently divides the network into multiple sub-networks with the minimum edge connections among the neighbors. Then, we perform DCS-based state estimation on the 6204-node distribution network after dividing the network into 18 optimal partitions. Simulation results show that DCS-based state estimation recovers the system states with high accuracy and low complexity.
Demonstration of machine-learning-enhanced Bayesian quantum state estimation
Machine learning (ML) has found broad applicability in quantum information science in topics as diverse as experimental design, state classification, and even studies on quantum foundations. Here, we experimentally realize an approach for defining custom prior distributions that are automatically tuned using ML for Bayesian quantum state estimation methods that generally better conform to the physical properties of the underlying system than standard fixed prior distributions. Previously, researchers have looked to Bayesian quantum state tomography for advantages like uncertainty quantification, the return of reliable estimates under any measurement condition, and minimal mean-squared error. However, practical challenges related to long computation times and conceptual issues concerning how to incorporate prior knowledge most suitably can overshadow these benefits. Using both simulated and experimental measurement results, we demonstrate that ML-defined prior distributions reduce net convergence times and provide a natural way to incorporate both implicit and explicit information directly into the prior distribution. These results constitute a promising path toward practical implementations of Bayesian quantum state tomography.
Applications of synchrophasor technologies in power systems
Synchrophasors are time-synchronized electrical measurements that represent both the magnitude and phase angle of the electrical sinusoids. Synchrophasors are measured by fast time-stamped devices called phasor measurement units (PMUs) to constitute the basis of real-time monitoring and control actions in the electric grid. Due to its enhanced situational awareness capabilities, many applications of PMUs are presented in the literature in the past decades. This paper presents a comprehensive summary of synchrophasor technology, its architecture, optimal placement techniques and its applications in electric power transmission and distribution systems. These applications include wide-area situational awareness and monitoring, state estimation, fault location and protective relaying, islanding detection etc. This review also covers some of the existing challenges in its implementation and its potential applications.
Ensuring Solution Uniqueness in Three-Phase Power System State Estimation
This paper is concerned with the issue of potential non-unique solutions in three-phase state estimation. Theory of observability analysis for positive sequence power system state estimation is based on certain assumptions that avoid possibility of multiple solutions. Also, it is shown that observability of a positive sequence network remains independent of the network parameters or the operating state. When extending single-phase observability analysis directly to the three-phase case, this paper considers the possibility of converging to multiple solutions, i.e. solution non-uniqueness, even for cases where state estimator successfully converges. The study illustrates via numerical examples the likelihood of converging to entirely different solutions for certain network parameters. It also examines how the operating state, particularly under unbalanced loading, leads to solution non-uniqueness. The paper then describes an alternative approach to ensure a unique solution in three-phase state estimation. This method aims to accurately and uniquely estimate the state of any unbalanced three-phase system, irrespective of load imbalance, network configuration, existence of synchronous generators or transformers.
Sensitivity-Based Reactive Power Dispatch of DERs to Support Transmission Grid During Emergency
This paper proposes a TSO-DSO framework including DER set-point dispatch using sensitivity analysis. We address all three steps of TSO-DSO integration stating by estimating the capability curve of an unbalanced distribution system and then modeling of capability curve on the transmission side grid and estimating the reactive power needed from DSO during emergencies, and ending by dispatching the requested reactive power from TSO. The proposed interaction framework is tested on an IEEE 37-node distribution network connected to IEEE 9 bus transmission system. The simulation shows that using sensitivity-based dispatch would reduce the number of communication signals between DERs and DSO and that can decrease the risk of communication contingency.
Power system state estimation for a spacecraft power system
An application of the maximum likelihood state estimator to a space-based power system is presented. The state estimator uses current and voltage measurements to generate estimates of node voltages for an electrical power distribution system for the Space Shuttle. Preliminary results on the effect of noisy measurements on estimated parameters are reported. The software used in generating these results is part of an overall package being developed at Louisiana Tech University. Intended applications of this package include the analysis of power systems and real-time parallel processing on the Space Shuttle.
Secure Distributed State Estimation for Networked Microgrids
Distributed state estimation (DSE) allows networked microgrids to achieve global state awareness with conservation of local information privacy by peer-to-peer message exchange implemented with Internet of Things protocols over heterogeneous communications. This paper presents a secure DSE (SDSE) method for networked microgrids to enhance system resiliency by addressing false data injection threat in distributed microgrid agent nodes. Here, the designated SDSE applies a trust-based diffusion algorithm using adaptive combination policy, which allows agents to adapt their combination coefficients to exclude misbehaving nodes from the network. The results demonstrate that proposed SDSE algorithm addresses emerging data integrity and security problems in critical energy delivery infrastructure and SCADA environment.
Considerations for AMI-Based Operations for Distribution Feeders
More than $5 billion in investments in advanced metering infrastructure (AMI) technologies, AMI deployments, as pervasive secondary network voltage monitoring systems, provide opportunities for utility operations and controls. This paper focuses on the considerations for AMI-based tools and techniques as the industry moves toward operationalizing such large data sets. Phase identification is a first such tool. Numerous distribution network analysis, monitoring, and control applications - including volt/volt-ampere reactive control, state estimation, and distribution automation - require accurate phase connectivity information in the system models. The phase connectivity database maintained by utilities is inaccurate because of a significant amount of missing data, restoration activities, and network reconfiguration. Existing phase identification techniques that estimate phase connectivity work well in distribution feeders that have low or no photovoltaic (PV) generation; however, they fail to identify the phases accurately when considerable PV generation is present. This work addresses the phase identification problem in the presence of high PV generation using statistical analysis methods. Further, insights into the AMI data requirements for this application in terms of data window length and resolution are provided using sensitivity analysis performed on an actual distribution feeder model of San Diego Gas & Electric Company. The results of this study show that the phase connectivity, even in the presence of high PV generation, can be accurately identified using statistical analysis of AMI data of 1 day.
Considerations for AMI-Based Operations for Distribution Feeders: Preprint
More than $5 billion in investments in advanced metering infrastructure (AMI) technologies, AMI deployments, as pervasive secondary network voltage monitoring systems, provide opportunities for utility operations and controls. This paper focuses on the considerations for AMI-based tools and techniques as the industry moves toward operationalizing such large data sets. Phase identification is a first such tool. Numerous distribution network analysis, monitoring, and control applications - including volt/volt-ampere reactive control, state estimation, and distribution automation - require accurate phase connectivity information in the system models. The phase connectivity database maintained by utilities is inaccurate because of a significant amount of missing data, restoration activities, and network reconfiguration. Existing phase identification techniques that estimate phase connectivity work well in distribution feeders that have low or no photovoltaic (PV) generation; however, they fail to identify the phases accurately when considerable PV generation is present. This work addresses the phase identification problem in the presence of high PV generation using statistical analysis methods. Further, insights into the AMI data requirements for this application in terms of data window length and resolution are provided using sensitivity analysis performed on an actual distribution feeder model of San Diego Gas & Electric Company. The results of this study show that the phase connectivity, even in the presence of high PV generation, can be accurately identified using statistical analysis of AMI data of 1 day.