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Maximum likelihood identification using an array processor

Maximum likelihood estimation (MLE) is a method used to calculate the parameters of a dynamic system. It can be applied to a large class of problems and has good statistical properties. The main disadvantage of the MLE method is the amount of computation required. This paper describes how the computation time can be reduced significantly by using an array processor. The estimation of the parameters of a dynamic model of the Space Station is used as an example to evaluate the method.

Sridhar, Banavar↗

Identification of atypical flight patterns

Method and system for analyzing aircraft data, including multiple selected flight parameters for a selected phase of a selected flight, and for determining when the selected phase of the selected flight is atypical, when compared with corresponding data for the same phase for other similar flights. A flight signature is computed using continuous-valued and discrete-valued flight parameters for the selected flight parameters and is optionally compared with a statistical distribution of other observed flight signatures, yielding atypicality scores for the same phase for other similar flights. A cluster analysis is optionally applied to the flight signatures to define an optimal collection of clusters. A level of atypicality for a selected flight is estimated, based upon an index associated with the cluster analysis.

Statler, Irving C.↗

Aircraft System Identification from Multisine Inputs and Frequency Responses

A frequency-domain approach is described for estimating parameters, such as stability and control derivatives, in aircraft flight dynamic models from measured input and output data. The approach uses orthogonal phase-optimized multisines for moving the aircraft control effectors, Fourier analysis for computing multiple-input multiple-output frequency responses, and a maximum likelihood estimator called frequency response error (FRE) for determining values and uncertainties for the model parameters. The approach is demonstrated using flight test data for two subscale airplanes: the T-2 generic transport model and the X-56A aeroelastic demonstrator. Results and comparisons with the output-error method indicated that the approach produced accurate estimates of stability and control derivatives and their uncertainties from flight test data.

Grauer, Jared A.↗

On-orbit parametric identification methodology

On-orbit system identification (ID) of large space systems is essential for various reasons. For example, the complex composite structure of such systems cannot be ground-tested; their structural dynamic characteristics must be known accurately in order to accomplish active control. Furthermore, such capability can be used to characterize/identify various disturbances. The identification process is consisted of four principal elements: (1) modeling, (2) the estimation algorithm, (3) input system, and (4) measurement system. These elements are highly correlated and all togerher determine the success of the identification problem. Accurate modeling of large space systems is the most important element of the identification process. Large flexible structures are non-linear and infinite dimensional systems with highly coupled parameters and low frequency packed modes. In addition, these systems are subject to stochastic and time-varying disturbances, they have structural parameters which can vary due to on-orbit assembly deployment, and operations. These systems are generally; however, represented by constant coefficient, finite order differential equations. The non-linearities, coupling and noise effects are also often neglected. Moreover, identification experiment designs which lead to highly complex optimization problems usually require the simultaneous choice of ID algorithm, sensor, and actuator type and placement. On-orbit bandwidth and power restrictions on excitation, limited data window, and restrictions on sensor/actuator type, placement and number, has led to practical questions of implementations.

Hadaegh, Fred Y.↗

Real-Time Adaptive Drag Minimization Wind Tunnel Investigation of a Flexible Wing with Variable Camber Continuous Trailing Edge Flap System

This paper reports the results of a recently completed real-time adaptive drag minimization wind tunnel investigation of a highly flexible wing wind tunnel model equipped with the Variable Camber Continuous Trailing Flap (VCCTEF) technology at the University of Washington Aeronautical Laboratory (UWAL). The wind tunnel investigation is funded by NASA SBIR Phase II contract with Scientific Systems Company, Inc. (SSCI) and University of Washington (UW) as a subcontractor. The wind tunnel model is a sub-scale Common Research Model (CRM) wing constructed of foam core and fiberglass skin and is aeroelastically scaled to achieve a wing tip deflection of 10% of the wing semi-span which represents a typical wing tip deflection for a modern transport such as Boeing 787. The jig-shape twist of the CRM wing is optimized using a CART3D aero-structural model to achieve the minimum induced drag for the design cruise lift coefficient of 0.5. The wing is equipped with two chord wise cambered segments for each of the six span wise flap sections for a total of 12 individual flap segments that comprise the VCCTEF system. Each of the 12 flap segments is actively controlled by an electric servo-actuator. The real-time adaptive drag optimization strategy includes an on-board aerodynamic model identification, a model excitation, and a real-time drag optimization. The on-board aerodynamic model is constructed parametrically as a function of the angle of attack and flap positions to model the lift and drag coefficients of the wing. The lift coefficient models include a linear model and a second-order model. The drag coefficient models include a quadratic model and a higher-order up to 6th-order model to accurately model the drag coefficient at high angles of attack. The onboard aerodynamic model identification includes a recursive least-squares (RLS) algorithm and a batch least-squares (BLS) algorithm designed to estimate the model parameters. The model excitation method is designed to sample the input set that comprises the angle of attack and the flap positions. Three model excitation methods are developed: random excitation method, sweep method, and iterative angle-of-attack seeking method. The real-time drag optimization includes a generic algorithm developed by SSCI and several optimization methods developed by NASA which include a second-order gradient Newton-Raphson optimization method, an iterative gradient optimization method, a pseudo-inverse optimization method, an analytical optimization method, and an iterative refinement optimization method. The first wind tunnel test entry took place in September 2017. This test revealed major hardware issues and required further redesign of the flap servo mechanisms. The second test entry took place in April 2018. However, the test was not successful due to the issues with the onboard aerodynamic model identification RLS algorithm which incorrectly identified model parameters. This test also provides an experimental comparison study between the VCCTEF and a variable camber discrete trailing edge flap (VCDTEF) without the elastomer transition mechanisms. The experimental result confirms the benefit of the VCCTEF which produces lower drag by 5% than the VCDTEF. The third and final test entry took place in June 2018 after the issues with the RLS algorithm have been identified and corrected. Additional improvements were implemented. These include the BLS algorithm, the iterative angle-of-attack seeking method, the iterative gradient optimization method, and the pseudo-inverse optimization method. The test objectives were successfully demonstrated as the real-time drag optimization identifies several optimal solutions at off-design lift coefficients. The iterative gradient optimization method is found to achieve up to 4.7% drag reduction for the off-design lift coefficient of 0.7. The pseudo-inverse optimization method which does not require the drag coefficient model is found to be quite effective in reducing drag. Up to 9.4% drag reduction for the off-design lift coefficient of 0.7 is achieved with the pseudo-inverse optimization method. The wind tunnel investigation demonstrates the potential of real-time drag optimization technology. Several new capabilities are developed that could enable future adaptive wing technologies for flexible wings equipped with drag control devices such as the VCCTEF.

Drag Optimization↗

Modal Analysis and Model Correlation of the Mir Space Station

This paper will discuss on-orbit dynamic tests, modal analysis, and model refinement studies performed as part of the Mir Structural Dynamics Experiment (MiSDE). Mir is the Russian permanently manned Space Station whose construction first started in 1986. The MiSDE was sponsored by the NASA International Space Station (ISS) Phase 1 Office and was part of the Shuttle-Mir Risk Mitigation Experiment (RME). One of the main objectives for MiSDE is to demonstrate the feasibility of performing on-orbit modal testing on large space structures to extract modal parameters that will be used to correlate mathematical models. The experiment was performed over a one-year span on the Mir-alone and Mir with a Shuttle docked. A total of 45 test sessions were performed including: Shuttle and Mir thruster firings, Shuttle-Mir and Progress-Mir dockings, crew exercise and pushoffs, and ambient noise during night-to-day and day-to-night orbital transitions. Test data were recorded with a variety of existing and new instrumentation systems that included: the MiSDE Mir Auxiliary Sensor Unit (MASU), the Space Acceleration Measurement System (SAMS), the Russian Mir Structural Dynamic Measurement System (SDMS), the Mir and Shuttle Inertial Measurement Units (IMUs), and the Shuttle payload bay video cameras. Modal analysis was performed on the collected test data to extract modal parameters, i.e. frequencies, damping factors, and mode shapes. A special time-domain modal identification procedure was used on free-decay structural responses. The results from this study show that modal testing and analysis of large space structures is feasible within operational constraints. Model refinements were performed on both the Mir alone and the Shuttle-Mir mated configurations. The design sensitivity approach was used for refinement, which adjusts structural properties in order to match analytical and test modal parameters. To verify the refinement results, the analytical responses calculated using original and refined math models were compared with the measured responses. The results from this study show that the refined models predict more accurately the dynamics of the actual structure. The MiSDE test and analysis results provided the information and experience on test design, flight testing, and data analysis for the ISS and other future spacecraft, which are critical to the verification of analytical models and structural loads.

Kim, Hyoung M.↗

A Nonlinear Dual-Adaptive Control Strategy for Identification and Control of Flexible Structures

A technique is presented for obtaining a control law to regulate the modal dynamics and identify the modal parameters of a flexible structure. The method is based on using a min-max performance index to derive a control law which may be considered to be a best compromise between optimum one step control and identification inputs. Features of the approach are demonstrated by a computer simulation of the controlled modal response of a flexible beam.

Thau, F. E.↗

A refined assessment of nuclear data target accuracy requirements for ALFRED

The interest in target accuracy assessment has been recently renewed within the OECD/NEA Working Party on International Nuclear Data Evaluation Cooperation with an update exercise, thanks to the invaluable initiative of Massimo Salvatores. This work, moving from evaluations on the main core integral parameters of the Advanced Lead-cooled Fast Reactor European Demonstrator (ALFRED), and the identification of the associated target accuracies needed for improving its design, approaches the retrieval of target accuracy requirements for nuclear data, as the inverse problem of uncertainty quantification. The preliminary results obtained in a previous work are here refined by explicitly taking into account the total contribution due to correlations among variables in the optimization constraint, while its various components are evaluated individually. Moreover, three different sets of cost parameters are considered to introduce a bias in the solution in order to take in due account the relative difficulties in the execution of new differential experiments as needed for achieving the proposed target accuracies. By this, the obtained results are deemed usefully informative, and proposed for the update of a High Priority List which identifies the isotopes-reaction couples of most interest for future refinement experiments, especially when integrated with further analogous information collected on other advanced nuclear systems. Among the cross-sections whose refinement contributes the most to the reduction of the multiplication factor, the fission of Pu{sup 239} was found, which needs to be fixed below 1% in the range of interest for ALFRED (2 keV-4 MeV). Another contribution for the amelioration of the multiplication factor calculation accuracy, is due to the capture channel of Pu{sup 239}, for which the initial high uncertainty (around 15%) can be significantly reduced resorting to easily practicable experiments. The same occurs for the inelastic of Pb{sup 207}, for which the initial uncertainty value of around 50% can be drastically reduced up to target values between 4% and 7%.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Practical Understanding of Cancer Model Identifiability in Clinical Applications

Mathematical models are a core component in the foundation of cancer theory and have been developed as clinical tools in precision medicine. Modeling studies for clinical applications often assume an individual’s characteristics can be represented as parameters in a model and are used to explain, predict, and optimize treatment outcomes. However, this approach relies on the identifiability of the underlying mathematical models. In this study, we build on the framework of an observing-system simulation experiment to study the identifiability of several models of cancer growth, focusing on the prognostic parameters of each model. Our results demonstrate that the frequency of data collection, the types of data, such as cancer proxy, and the accuracy of measurements all play crucial roles in determining the identifiability of the model. We also found that highly accurate data can allow for reasonably accurate estimates of some parameters, which may be the key to achieving model identifiability in practice. As more complex models required more data for identification, our results support the idea of using models with a clear mechanism that tracks disease progression in clinical settings. For such a model, the subset of model parameters associated with disease progression naturally minimizes the required data for model identifiability.

59 BASIC BIOLOGICAL SCIENCES↗

Recent System Identification Research at NASA Langley Research Center

This talk summarizes some of the recent advances in system identification at NASA Langley Research Center. Efforts discussed were applied to aeroelastic models, aircraft with redundant inputs and feedback control active, and aircraft flying in turbulence. Topics mentioned include experiment design with orthogonal multisine inputs, frequency response estimation, maximum likelihood parameter estimation, and parameter estimation considering process noise.

NASA LaRC↗

IM3 Open Source Data Center Atlas

IM3 Open Source Data Center Atlas Description This dataset contains locations of existing data center facilities in the United States. Data center locations were derived from OpenStreetMap (OSM), a crowd-sourced database. Data points from OSM are processed in various ways to determine additional variables provided in the data including: facility area (square feet), associated US county, and US state. This dataset can be used to identify areas of concentrated data center development and inform government and private sector planning strategies for future buildout of data centers and the infrastructure necessary to support it. Usage Notes Validation of OSM-derived data center locations is an ongoing development under the IM3 project, and the database will be updated as new information becomes available. In some instances, both the data center area (e.g., campus) and individual data center buildings are included as overlapping areas in the database. Both values are retained. Data center points, buildings, and campus areas are provided as separate layers in the downloadable data package. Note that data items are not necessarily complete across layers. That is, a specific data center may only be present as a single point geometry in the "point" layer while other data centers are represented in both the campus and building layers. In some cases, data center campuses and/or buildings straddle a county boundary line. Mappings to both counties are retained in the database as separate rows. These data rows will have the same data center id information, but each will have different county information. Crowd-sourced data, by nature, relies on individuals and communities to provide information. As a result, some data may be missing where it has not yet been reported. As we collect information on additional data center locations and as OSM receives additional contributions, the database will be updated to capture additional data points not yet shown. Technical Information Data is available for download under the following formats: GeoPackage (GPKG) CSV Geospatial data is provided in the WGS84 (EPSG:4326) coordinate reference system. The GeoPackage download contains the following layers. See usage notes for more information. "point" "building" "campus" The "point" layer includes all data from OSM that had POINT geometry type (i.e., individual coordinates). The "building" layer includes all OSM data that did not have POINT geometry and where the building tag in the OSM export was neither equal to "no" or null. Data that did not meet the "point" or "building" qualification was assumed to be a facility campus and included in the "campus" layer. The dataset contains the following parameters. Variables provided by OSM are labeled with (OSM-provided). id - unique identification number (OSM-provided with prefix of "node/", "relation/" and similar attributes removed) state - name of US state state_abb - two letter US state abbreviation state_id - state ID number county - name of US county county_id - county ID number ref - reference numbers or codes (OSM-provided) operator - the name of the company, corporation, or person in charge facility (OSM-provided) name - name of facility (OSM-provided) sqft - surface area of facility polygon, measured in square feet. Only available for "building" and "campus" layers lat - latitude of data centroid point lon - longitude of data centroid point type – represented spatial information. One of "point", "building", or "campus". geometry – POLYGON geometry of area footprint (in "campus" and "building" layers) or POINT geometry of locations (in "point" layer). This parameter is not included in the csv download. Attribution Data center locations were derived from OpenStreetMap, which is made available at openstreetmap.org under the Open Database License (ODbL). US state and county boundary information was collected from the US Census Bureau for the year 2024, which is made publicly available at https://www.census.gov/geographies/mapping-files.html Acknowledgment IM3 is a multi-institutional effort led by Pacific Northwest National Laboratory and supported by the U.S. Department of Energy's Office of Science as part of research in MultiSector Dynamics, Earth and Environmental Systems Modeling Program. License The IM3 Open Source Data Center Atlas is made available under the Open Database License: http://opendatacommons.org/licenses/odbl/1.0/. Disclaimer This material was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor the United States Department of Energy, nor the Contractor, nor any or their employees, nor any jurisdiction or organization that has cooperated in the development of these materials, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness or any information, apparatus, product, software, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or Battelle Memorial Institute. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. PACIFIC NORTHWEST NATIONAL LABORATORYoperated byBATTELLEfor theUNITED STATES DEPARTMENT OF ENERGYunder Contract DE-AC05-76RL01830

Mongird, Kendall [Pacific Northwest National Labor↗

IM3 Open Source Data Center Atlas

IM3 Open Source Data Center Atlas Description This dataset contains locations of existing data center facilities in the United States. Data center locations were derived from OpenStreetMap (OSM), a crowd-sourced database. Data points from OSM are processed in various ways to determine additional variables provided in the data including: facility area (square feet), associated US county, and US state. This dataset can be used to identify areas of concentrated data center development and inform government and private sector planning strategies for future buildout of data centers and the infrastructure necessary to support it. Usage Notes Validation of OSM-derived data center locations is an ongoing development under the IM3 project, and the database will be updated as new information becomes available. In some instances, both the data center area (e.g., campus) and individual data center buildings are included as overlapping areas in the database. Both values are retained. Data center points, buildings, and campus areas are provided as separate layers in the downloadable data package. Note that data items are not necessarily complete across layers. That is, a specific data center may only be present as a single point geometry in the "point" layer while other data centers are represented in both the campus and building layers. In some cases, data center campuses and/or buildings straddle a county boundary line. Mappings to both counties are retained in the database as separate rows. These data rows will have the same data center id information, but each will have different county information. Crowd-sourced data, by nature, relies on individuals and communities to provide information. As a result, some data may be missing where it has not yet been reported. As we collect information on additional data center locations and as OSM receives additional contributions, the database will be updated to capture additional data points not yet shown. Data items will occasionally be removed from OSM if they are misidentified, if they no longer exist, if they are duplicates of another item, or similar. For that reason, updated versions of this database may not contain all data center locations included in previous versions. Technical Information Data is available for download under the following formats: GeoPackage (GPKG) CSV Geospatial data is provided in the WGS84 (EPSG:4326) coordinate reference system. The GeoPackage download contains the following layers. See usage notes for more information. "point" "building" "campus" The "point" layer includes all data from OSM that had POINT geometry type (i.e., individual coordinates). The "building" layer includes all OSM data that did not have POINT geometry and where the building tag in the OSM export was neither equal to "no" or null. Data that did not meet the "point" or "building" qualification was assumed to be a facility campus and included in the "campus" layer. The dataset contains the following parameters. Variables provided by OSM are labeled with (OSM-provided). id - unique identification number (OSM-provided with prefix of "node/", "relation/" and similar attributes removed) state - name of US state state_abb - two letter US state abbreviation state_id - state ID number county - name of US county county_id - county ID number ref - reference numbers or codes (OSM-provided) operator - the name of the company, corporation, or person in charge facility (OSM-provided) name - name of facility (OSM-provided) sqft - surface area of facility polygon, measured in square feet. Only available for "building" and "campus" layers lat - latitude of data centroid point lon - longitude of data centroid point type – represented spatial information. One of "point", "building", or "campus". geometry – POLYGON geometry of area footprint (in "campus" and "building" layers) or POINT geometry of locations (in "point" layer). This parameter is not included in the csv download. Attribution Data center locations were derived from OpenStreetMap, which is made available at openstreetmap.org under the Open Database License (ODbL). US state and county boundary information was collected from the US Census Bureau for the year 2024, which is made publicly available at https://www.census.gov/geographies/mapping-files.html Acknowledgment IM3 is a multi-institutional effort led by Pacific Northwest National Laboratory and supported by the U.S. Department of Energy's Office of Science as part of research in MultiSector Dynamics, Earth and Environmental Systems Modeling Program. License The IM3 Open Source Data Center Atlas is made available under the Open Database License: http://opendatacommons.org/licenses/odbl/1.0/. Disclaimer This material was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor the United States Department of Energy, nor the Contractor, nor any or their employees, nor any jurisdiction or organization that has cooperated in the development of these materials, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness or any information, apparatus, product, software, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or Battelle Memorial Institute. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. PACIFIC NORTHWEST NATIONAL LABORATORYoperated byBATTELLEfor theUNITED STATES DEPARTMENT OF ENERGYunder Contract DE-AC05-76RL01830

Mongird, Kendall [Pacific Northwest National Labor↗

Identification of a typical flight patterns

Method and system for analyzing aircraft data, including multiple selected flight parameters for a selected phase of a selected flight, and for determining when the selected phase of the selected flight is atypical, when compared with corresponding data for the same phase for other similar flights. A flight signature is computed using continuous- valued and discrete-valued flight parameters for the selected flight parameters and is optionally compared with a statistical distribution of other observed flight signatures, yielding a typicality scores for the same phase for other similar flights. A cluster analysis is optionally applied to the flight signatures to define an optimal collection of clusters. A level of atypicality for a selected flight is estimated, based upon an index associated with the cluster analysis.

Irving C Statler↗

Updating High-Order Aeroservoelastic Models from Low-Order System Identification Results

Estimating aircraft models from test data requires several simplifying assumptions that introduce biases into the parameter estimates. In this paper, these biases are defined and a method for estimating the biases is discussed. Having an estimate of the bias allows the parameters estimated from test to be integrated into a high-order model. The Integrated Adaptive Wing Technology Maturation (IAWTM) wind tunnel model is discussed and the bias is demonstrated for one of the testing configurations. The methodology was able to estimate these biases and apply corrections to high-order aeroelastic models to improve the fit to test data. The consideration of the biases allows more meaningful comparisons and avoids the erroneous differences between pretest predictions and the fitted model.

Jeffrey Ouellette↗

Updating High-Order Aeroservoelastic Models from Low-Order System Identification Results

Estimating aircraft models from test data requires several simplifying assumptions that introduce biases into the parameter estimates. In this paper, these biases are defined and a method for estimating the biases is discussed. Having an estimate of the bias allows the parameters estimated from test to be integrated into a high-order model. The Integrated Adaptive Wing Technology Maturation (IAWTM) wind tunnel model is discussed and the bias is demonstrated for one of the testing configurations. The methodology was able to estimate these biases and apply corrections to high-order aeroelastic models to improve the fit to test data. The consideration of the biases allows more meaningful comparisons and avoids the erroneous differences between pretest predictions and the fitted model.

Jeffrey Ouellette↗

Robust Adaptive Control for Large-scale Inverter-based Resources with Partial and Complete Loss of Inverters

This article proposes an approach to address the current and the aggregated active power control challenge for large-scale inverter-based resources subjected to partially or completely loss of inverters and grid voltage variations. To address this problem, a distributed active power mechanism is proposed which generates desired inverters current. Then an adaptive mechanism distributes the voltage control input automatically between inverters in response to the partial or complete loss of inverters. An L2-gain-based controller is designed for each inverter to track the desired current and rejects the grid voltage disturbance. Here, simulation results show a significant robust tracking for collective active power and current.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Design of a low frequency, density profile reflectometer system for the MAST-U spherical tokamak

Validated and accurate edge profiles (temperature, density, etc.) are vitally important to the Mega Ampere Spherical Tokamak Upgrade (MAST-U) divertor and confinement effort. Density profile reflectometry has the potential to significantly add to the measurement capabilities currently available on MAST-U (e.g., Thomson scattering and Langmuir probes). This work presents the diagnostic requirements, problems, and solutions facing profile reflectometry in spherical tokamaks and MAST-U in particular. Requirements include density measurements near zero electron density in the scrape off layer region, coverage for a broad range of MAST-U plasma parameters, high time (≤10 microseconds) and spatial resolutions (≤1 cm), reliability, and identification of the plasma start frequency.

Instruments & Instrumentation↗

High Impedance Fault Detection Through Quasi-Static State Estimation: A Parameter Error Modeling Approach

This paper presents a model for detecting high impedance faults using parameter error modeling and a two step per-phase weighted-least squares state estimation process. The proposed scheme leverages the use of Phasor Measurement Units and synthetic measurements to identify per-phase power flow and injection measurements which indicate a parameter error through ?2 Hypothesis Testing applied to the composed measurement error. Although current and voltage waveforms are commonly analyzed for high-impedance fault detection, wide area power flow and injection measurements, which are already inherent to the state estimation process, also show promise for real-world high-impedance fault detection applications. The error distributions after detection share the measurement function error spread observed in proven parameter error diagnostics and can be applied to high-impedance fault identification. Further, this error spread across measurement functions related to the fault will be clearly discerned from measurement error. Case studies are performed on the IEEE 33-Bus Distribution System along with the proposed model in Simulink.

Cooper, Austin↗