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DOE OSTI2023

Demonstrating Computational Equivalence Between Continuous and Discrete Adjoint Methods by Calculating Time-Dependent Adjoint Solutions with Neutron Diffusion Models

The continuous adjoint method and the discrete adjoint method are two alternative approaches used to calculate adjoint solutions for adjoint systems. The continuous adjoint method derives adjoint equations analytically from continuous forward equations and then solves the adjoint equations either analytically or numerically in a discretized form whereas the discrete adjoint method calculates the adjoint solutions directly from the discretized forward equations. With regard to the methodology development and calculation procedure, distinct differences are well recognized between the two methods. For certain reasons, both methods are exclusively preferred and commonly used by different computational communities, but limited studies clarify the connections between the two adjoint methods from either of the communities. Herein, this paper demonstrates the computational equivalence between the continuous and discrete adjoint methods by investigating time-dependent adjoint solutions to the two-group neutron diffusion model in nuclear reactor analysis problems using both methods. Adjoint solutions can be used to estimate system parameters for reactor safety analysis. Appropriate final state conditions for the adjoint systems are specified in both of the methods, and the conditions are clarified with proper physical explanations. With the help of an event-based case study on neutron diffusion models, the accuracy of the time-dependent adjoint fluxes obtained from both methods is verified, and the pros and cons of both adjoint methods are examined. More importantly, the computational equivalence of both methods is demonstrated when they are applied to multigroup neutron diffusion systems. The advantage of calculating time-dependent adjoint fluxes by directly solving time-dependent adjoint systems rather than taking steady-state approximations as in common practice is also demonstrated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2019

OPERATIONAL TOPOLOGY ESTIMATION OF THREE PHASE UNBALANCED POWER DISTRIBUTION SYSTEMS WITH OUTAGES

Distribution grid, in general, is constructionally loopy but a radially operated network. Opening and closing of suitable tie-switches allows transition from one radial topology to another. Tie-switches ensure reliability and provide restoration paths when faults (outages) occur. The estimation of the system's current operational topology is a precursor to implementing any optimal control actions (during normal operation) or restorative actions (during outage condition). The existing literature in topology detection suffers with several limitations including: (1) computationally intensive nonlinear formulations that are not scalable for large distribution systems, (2) methods requiring exhaustive search for the correct topology by enumerating the complete topological search space, and (3) approaches requiring large volumes of time-series measurements and are not applicable for estimating continuously changing operational topology. Furthermore, the existing literature on distribution grid topology estimation cannot be extended to estimate the operational topology during outage conditions. For operational topology estimation during outages, our objective is to estimate both energized radial feeder and the outaged sections. Starting with a radial topology, these methods identify outaged feeder sections and hence, are inapplicable when the current radial operational topology is not known. In this work, we present a mathematical programming approach to estimate the operational topology of a three-phase unbalanced power distribution system under both outage and normal operating conditions. The aforementioned limitations of existing literature were countered by modeling the problem as a mixed-integer linear programming (MILP) problem which minimizes the errors in available measurements while satisfying the power flow and structural constraints of the system. Specically, a minimum weighted least absolute value estimator is proposed that uses the instantaneous line flow measurements, historical/ forecasted load data, and ping measurements from a limited set of smart meters and solves an MILP to identify the operational topology based on a linearized three-phase unbalanced power flow model. The proposed approach is tested on IEEE 123-bus feeder and 1069 bus multi-feeder test system and the numerical results prove the applicability of the proposed method to large three phase unbalanced grids with high errors in measurements. It is observed that the approach performs well even at high percentages of measurement errors.

GANDLURU NAGA, ANANDINI↗

DOE OSTI2022

Discovering causal structure with reproducing-kernel Hilbert space ε -machines

We merge computational mechanics’ definition of causal states (predictively equivalent histories) with reproducing-kernel Hilbert space (RKHS) representation inference. The result is a widely applicable method that infers causal structure directly from observations of a system’s behaviors whether they are over discrete or continuous events or time. A structural representation—a finite- or infinite-state kernel ϵ-machine—is extracted by a reduced-dimension transform that gives an efficient representation of causal states and their topology. In this way, the system dynamics are represented by a stochastic (ordinary or partial) differential equation that acts on causal states. We introduce an algorithm to estimate the associated evolution operator. Paralleling the Fokker–Planck equation, it efficiently evolves causal-state distributions and makes predictions in the original data space via an RKHS functional mapping. We demonstrate these techniques, together with their predictive abilities, on discrete-time, discrete-value infinite Markov-order processes generated by finite-state hidden Markov models with (i) finite or (ii) uncountably infinite causal states and (iii) continuous-time, continuous-value processes generated by thermally driven chaotic flows. The method robustly estimates causal structure in the presence of varying external and measurement noise levels and for very high-dimensional data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Estimating Highway Volumes Using Vehicle Probe Data - Proof of Concept: Preprint

This paper examines the feasibility of using sampled commercial probe data in combination with validated continuous counter data to accurately estimate vehicle volume across the entire roadway network, for any hour during the year. Currently either real time or archived volume data for roadways at specific times are extremely sparse. Most volume data are average annual daily traffic (AADT) measures derived from the Highway Performance Monitoring System (HPMS). Although methods to factor the AADT to hourly averages for typical day of week exist, actual volume data is limited to a sparse collection of locations in which volumes are continuously recorded. This paper explores the use of commercial probe data to generate accurate volume measures that span the highway network providing ubiquitous coverage in space, and specific point-in-time measures for a specific date and time. The paper examines the need for the data, fundamental accuracy limitations based on a basic statistical model that take into account the sampling nature of probe data, and early results from a proof of concept exercise revealing the potential of probe type data calibrated with public continuous count data to meet end user expectations in terms of accuracy of volume estimates.

25 ENERGY STORAGE↗

DOE OSTI2014

Cadmium exposure and neuropsychological development in school children in southwestern Spain

This study assessed the association between cadmium exposure and neuropsychological development in children from a region with high industrial and mining activities in southwestern Spain. We conducted a cross-sectional study with 261 children aged 6–9 years between January and March 2012. Cadmium exposure was measured in urine and hair of children, and neuropsychological development was assessed with the Wechsler Intelligence Scale for Children-Fourth Edition (WISC-IV) and with three computerized tests from the Behavioral Assessment and Research System (BARS): Reaction Time Test (RTT), Continuous Performance Test (CPT) and Selective Attention Test (SAT). Multivariate linear regression models, adjusted for potential confounders, were used to estimate the association between neuropsychological development and cadmium exposure measured in urine and hair samples. Geometric means of urine and hair cadmium levels were 0.75 μg/g creatinine and 0.01 μg/g, respectively. We observed that doubling of levels of cadmium in urine was associated with a reduction of two points (95% CI: −3.8 to −0.4) in the Full-Scale intelligence quotient (IQ) in boys. By domains, association was statistically significant for Verbal Comprehension (β=−2.0; p=0.04) and close to the significance level for Perceptual Reasoning (β=−1.8; p=0.06). Among girls, only Verbal Comprehension showed suggestive associations with cadmium exposure (β=−1.7; p=0.06). Cadmium exposure is associated with cognitive delays in boys in our region. Our results provide additional evidence of the neurotoxic effect of low-level postnatal cadmium exposure among children, and support the hypothesis of differences between sexes in the neurotoxic effect of metals on children. - Highlights: • This study associates Cd exposure and neuropsychological development in children. • Cd exposure was associated with cognitive delay in boys, but not in girls. • Intellectual quotient of boys decreased two points for a doubling of urine Cd levels. • Verbal Comprehension and Perceptual Reasoning were the most affected domains in boys. • Results support the sex-related differences in the neurotoxicity of metals in children.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2018

Experimental Investigation of Hydrodynamic Response of an Ocean Uranium Extraction Machine Attached to a Floating Wind Turbine

With conventional sources of uranium forecasted to be depleted within a century, developing methods to cost-effectively harvest uranium from seawater, which is estimated to contain 1000 times more uranium than on land, are crucial to the continued viability of nuclear power generation. Studies have shown that coupling a uranium harvester system with an existing offshore structure, such as a floating wind turbine (FWT), could greatly reduce the cost of harvesting uranium from seawater as it eliminates the need for dedicated moorings and increases the overall energy-gathering ability of the offshore wind farm. This study explores the hydrodynamic effects of adding a uranium harvester to an offshore floating wind turbine. The experimentally determined hydrodynamic responses of two designs of a Symbiotic Machine for Ocean uRanium Extraction (SMORE) are compared with that of an unmodified FWT. Both SMORE designs utilize adsorbent filament that is enclosed in a hard permeable shell to decouple the mechanical and chemical requirements of the device. In this work, it was found that both SMORE designs do not significantly shift the resonant peaks of the FWT.

42 ENGINEERING↗

DOE OSTI2015

COHERENT NETWORK ANALYSIS FOR CONTINUOUS GRAVITATIONAL WAVE SIGNALS IN A PULSAR TIMING ARRAY: PULSAR PHASES AS EXTRINSIC PARAMETERS

Supermassive black hole binaries are one of the primary targets of gravitational wave (GW) searches using pulsar timing arrays (PTAs). GW signals from such systems are well represented by parameterized models, allowing the standard Generalized Likelihood Ratio Test (GLRT) to be used for their detection and estimation. However, there is a dichotomy in how the GLRT can be implemented for PTAs: there are two possible ways in which one can split the set of signal parameters for semi-analytical and numerical extremization. The straightforward extension of the method used for continuous signals in ground-based GW searches, where the so-called pulsar phase parameters are maximized numerically, was addressed in an earlier paper. In this paper, we report the first study of the performance of the second approach where the pulsar phases are maximized semi-analytically. This approach is scalable since the number of parameters left over for numerical optimization does not depend on the size of the PTA. Our results show that for the same array size (9 pulsars), the new method performs somewhat worse in parameter estimation, but not in detection, than the previous method where the pulsar phases were maximized numerically. The origin of the performance discrepancy is likely to be in the ill-posedness that is intrinsic to any network analysis method. However, the scalability of the new method allows the ill-posedness to be mitigated by simply adding more pulsars to the array. This is shown explicitly by taking a larger array of pulsars.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

TH-AB-202-12: The First Clinical Implementation of a Real-Time Six Degree of Freedom Tracking System During Radiation Therapy

Purpose: In current practice, imaging is typically performed prior to treatment; the cancer target motion during treatment is unknown. We present the first clinical implementation of real time Kilovoltage Intrafraction Monitoring (KIM) system which tracks the cancer target translational and rotational motions during treatment. Methods: KIM technology: KIM estimates the 3D position of the target tumour based on segmented 2D positions of the three implanted fiducials in each of the kV images (125 kV, 10 mA at 11 fps) taken continuously during the treatment arc. The 2D-3D target estimation is based on a probability distribution function, obtained during pre-treatment CBCT. Rotations about each axis with the centroid of the markers as the pivot were calculated using the iterative closest point algorithm in real time. Patient: A patient with prostate adenocarcinoma undergoing stereotactic body radiotherapy (SBRT) with 36.25 Gy delivered in 5 fractions (Varian TrueBeam, 6X, VMAT) was enrolled in the study. The trial complies with Australian ethical and regulatory standards. Results: Of the 5 fractions of treatment the patient received, KIM was utilised successfully in 4 fractions with 3 couch shifts due to large persistent prostate movements (>2mm for more than 5 seconds). KIM translational accuracy and precision in comparison with post treatment kV-MV triangulation are 0.28±0.59 mm, −0.19±0.25 mm and 0.23±0.69 mm in the Left-Right, Superior-Inferior and Anterior-Posterior directions, respectively. KIM rotational accuracy as compared with triangulation is: 0.429°±2.22°, −0.44°±4.7° and 0.06°±1.08° in the roll, pitch and yaw direction, respectively. Conclusion: The first six degree of freedom KIM system was successfully implemented clinically. The presented KIM system has sub-millimeters accuracy and precision in all three translational axes, and less than 1° of mean error in all three rotational axes. Acknowledgement: This work is supported by Cancer Australia grants APPXXX, APPYYY.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2025

Towards a Robust Adaptive Digital Twin for Fusion Applications

The development of a digital twin system for fusion applications is essential for enhancing the prediction, analysis, and optimization of complex plasma processes. Machine learning (ML), particularly deep learning has demonstrated strong capabilities in modeling such highly nonlinear and intricate systems. However, two critical challenges limit the deployment of deep learning-based digital twins: Uncertainty Quantification (UQ) and data drift. UQ is vital for ensuring trustworthy predictions, especially in decision-support scenarios. Additionally, data-driven models are often sensitive to changes in the underlying data distribution, such as shot-to-shot variations in fusion experiments, which can lead to performance degradation over time. To address these challenges, we are developing an uncertainty-aware, adaptive digital twin framework. Our approach incorporates deep learning models enhanced with Gaussian Process approximations for predictive uncertainty estimation, coupled with an online learning mechanism that enables continuous model adaptation to new experimental data. This adaptive capability allows the data driven models to respond effectively to evolving plasma behaviors and equipment conditions. Specifically, to mitigate the effects of shot-to-shot drift, our system updates itself incrementally as new data becomes available, improving both robustness and fidelity. Our vision is to evolve this data driven model into a self-sustaining digital twin system that leverages UQ based feedback to continuously refine itself and potentially support real-time decision making. This presentation will cover a brief background on uncertainty quantification for ML, our ongoing effort on development of UQ capabilities for ML, our data science pipeline from data collection to model development and analysis and online learning framework for modeling coil deflection at DIII-D. I will also briefly touch upon opportunities and challenges in development of digital twin framework.

Sammuli, Brian [General Atomics]↗

DOE OSTI2019

Analytic Estimation Method of Forced Oscillation Amplitude Under Stochastic Continuous Disturbances

This paper proposes an analytic method for the amplitude estimation of the forced oscillation under stochastic continuous disturbances (SCDs). There is considerable interest in the integration of intermittent renewable energy resources into a power system, which leads to the power system in an environment with SCDs. Thus, the forced oscillation issues under SCDs are of concern. In this paper, the SCDs are described as continuous-time stochastic processes, and then the systems under SCDs are modeled by stochastic differential algebraic equations. Furthermore, by employing stochastic theory, an efficient analytic method for calculating the statistics of system states during the forced oscillation is proposed. Moreover, a novel forced oscillation phenomenon, which presents system states oscillate with stationary distributions under SCDs, is clearly characterized and theoretically explained. Based on the proposed analytic method, a scheme is put forth to estimate amplitudes of system states during forced oscillation under SCDs. Finally, compared to Monte Carlo simulation, the proposed scheme has two significant advantages. First, the proposed scheme offers a fast and effective solution for engineering applications. Second, the impact mechanism of SCDs on forced oscillation in power system is clearer, by the proposed scheme.

42 ENGINEERING↗

DOE OSTI2016

Photometric and period investigation of the late F-type overcontact binary II UMa

II UMa is a late F-type (F5) contact binary with a close-in tertiary and a distant visual companion. According to the four-color (B V R{sub c}I{sub c}) light curves’ solutions of II UMa, it is a high fill-out (f = 86.6%) and low-mass ratio (q = 0.172) contact binary system, which indicates that it is at the late evolutionary stage of late-type tidal-locked binary stars. The masses of the primary star and secondary star are calculated to be M{sub 1}=1.99M{sub ⊙} and M{sub 2}=0.34M{sub ⊙}. The primary star has evolved from the zero-age main sequence, but it still appeared before the terminal-age main sequence, and the secondary star is even more evolved. Considering the mass ratio (M{sub 3}/M{sub 1}=0.67) obtained by spectroscopic observations, the mass of the close-in tertiary is estimated to be M{sub 3}=1.34M{sub ⊙}. The period variations of the binary system are investigated for the first time. According to the observed–calculated (O−C) curve analysis, a continuous period increase at a rate of dP/dt=4.88×10{sup −7} day yr{sup −1} is determined. The parabolic variation in the O−C curve may be part of a cyclic period of change, or the combined period of change of a parabolic variation and a cyclic one. More instances of minimum light are needed to confirm this. The presence of the tertiary component may play an important role in the formation and evolution of this binary system by drawing angular momentum from the central system during the pre-contact stage.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Calcined Polyethyleneimine Coated Optical Fibers for Distributed pH Monitoring at High Pressures and Temperatures

In the oil and gas, CO2 sequestration, H2 subsurface storage, and geothermal energy sectors, subsurface pH measurements are critical for monitoring the geochemical conditions and estimating potential corrosion rates of wellbore systems. Real-time pH measurements in these conditions are vital for detecting and predicting corrosion deterioration of wellbore components that may jeopardize the safety and continued operation of wellbore systems. Building off of earlier TiO2 based pH sensors and the known pH sensitivity of amine-based polymers, a coating based on the secondary amine polymer polyethyleneimine (PEI) was developed. The sensor coating was treated with a high temperature (500 °C) calcination procedure in air to convert it into a more stable oxidized coating capable of withstanding hot aqueous solutions without dissolving while retaining linear pH sensitivity from pH values between 2 and 11. The sensor performance was measured using optical transmission measurements in solutions of various pHs and using optical backscatter reflectometry for distributed pH sensing demonstration in wellbore-relevant pressures (up to 1000 psi) and temperatures (80 °C). A calibration curve with strong differentiation between acidic and alkaline pH was developed for both transmission-based and distributed pH measurements, using fixed wavelength transmission and integrated linear amplitude of backscattered light for distributed measurements.

Shumski, Alexander↗

DOE OSTI2024

Calcined Polyethyleneimine-Coated Optical Fibers for Distributed pH Monitoring at High Pressures and Temperatures

In the oil and gas, CO2 sequestration, H2 subsurface storage, and geothermal energy sectors, subsurface pH measurements are critical for monitoring the geochemical conditions and estimating potential corrosion rates of wellbore systems. Real-time pH measurements in these conditions are vital for detecting and predicting corrosion deterioration of wellbore components that may jeopardize the safety and continued operation of wellbore systems. Previous tests using metal oxide-based coatings (TiO2) provided strong responses at elevated temperatures and moderate pressure stability but provided poor differentiation between acidic and alkaline solutions. Building off the pH responsiveness of the TiO2 surface and known pH sensitivity of amine-based polymers, a coating based on the secondary amine polymer polyethyleneimine (PEI) was developed. As the polymer itself is highly water soluble and easily removed by aqueous solutions, the sensor coating was treated with a high temperature (500 °C) calcination procedure in air to convert it into a more stable oxidized coating capable of withstanding hot aqueous solutions without dissolving while retaining linear pH sensitivity from pH values between 2 and 11. The sensor performance was measured using optical transmission measurements in solutions of various pHs and using optical backscatter reflectometry for distributed pH sensing demonstration in wellbore-relevant pressures (up to 1,000 psi) and temperatures (80 °C).

Shumski, Alexander↗

DOE OSTI2018

Understanding activity engagement across weekdays and weekend days: A multivariate multiple discrete-continuous modeling approach

This paper is motivated by the increasing recognition that modeling activity-travel demand for a single day of the week, as is done in virtually all travel forecasting models, may be inadequate in capturing underlying processes that govern activity-travel scheduling behavior. The considerable variability in daily travel suggests that there are important complementary relationships and competing tradeoffs involved in scheduling and allocating time to various activities across days of the week. Both limited survey data availability and methodological challenges in modeling week-long activity-travel schedules have precluded the development of multi-day activity-travel demand models. With passive and technology-based data collection methods increasingly in vogue, the collection of multi-day travel data may become increasingly commonplace in the years ahead. This paper addresses the methodological challenge associated with modeling multi-day activity-travel demand by formulating a multivariate multiple discrete-continuous probit (MDCP) model system. The comprehensive framework ties together two MDCP model components, one corresponding to weekday time allocation and the other to weekend activity-time allocation. By tying the two MDCP components together, the model system also captures relationships in activity-time allocation between weekdays on the one hand and weekend days on the other. Model estimation on a week-long travel diary data set from the United Kingdom shows that there are significant inter-relationships between weekdays and weekend days in activity-travel scheduling behavior. In conclusion, the model system presented in this paper may serve as a higher-level multi-day activity scheduler in conjunction with existing daily activity-based travel models.

30 DIRECT ENERGY CONVERSION↗

DOE OSTI2024

Single-shot Quantum Signal Processing Interferometry

Quantum systems of infinite dimension, such as bosonic oscillators, provide vast resources for quantum sensing. Yet, a general theory on how to manipulate such bosonic modes for sensing beyond parameter estimation is unknown. We present a general algorithmic framework, quantum signal processing interferometry (QSPI), for quantum sensing at the fundamental limits of quantum mechanics by generalizing Ramsey-type interferometry. Our QSPI sensing protocol relies on performing nonlinear polynomial transformations on the oscillator's quadrature operators by generalizing quantum signal processing (QSP) from qubits to hybrid qubit-oscillator systems. We use our QSPI sensing framework to make efficient binary decisions on a displacement channel in the single-shot limit. Theoretical analysis suggests the sensing accuracy, given a single-shot qubit measurement, scales inversely with the sensing time or circuit depth of the algorithm. We further concatenate a series of such binary decisions to perform parameter estimation in a bit-by-bit fashion. Numerical simulations are performed to support these statements. Our QSPI protocol offers a unified framework for quantum sensing using continuous-variable bosonic systems beyond parameter estimation and establishes a promising avenue toward efficient and scalable quantum control and quantum sensing schemes beyond the NISQ era.

Physics↗

DOE OSTI2021

Estimating and Forecasting Time-Varying Groundwater Recharge in Fractured Rock: A State-Space Formulation with Preferential and Diffuse Flow to the Water Table

Rapid infiltration following precipitation may result in groundwater contamination from surface contaminants or pathogens. In fractured rock, contaminants can migrate rapidly to points of groundwater withdrawals. In contrast to the temporal availability of groundwater quality chemical indicators, meteorological and groundwater level observations are available in real-time to estimate time-varying recharge, which can act as a surrogate to identify periods of rapid infiltration that may indicate contamination susceptibility. Estimating recharge using methods, such as base-flow recession, unsaturated infiltration models, or Water-Table Fluctuations (WTF), cannot capitalize on currently available technologies and telecommunication infrastructure to conduct real-time recharge estimation at scales relevant to characterizing rapid infiltration. We present a linear, physics-based State-Space (SS) model of one-dimensional infiltration to estimate recharge, which includes preferential and diffuse-flow to the water table. The model can take advantage of real-time data for water-table altitude, precipitation, and evapotranspiration. Model parameters are calibrated over an observation period, and the Kalman Filter (KF) is subsequently applied to continuously update the observed (water-table altitude) and unobserved (groundwater recharge) system states and predict future states as new data become available. The SS/KF algorithm is demonstrated at the Masser Groundwater Recharge Site in Pennsylvania, USA and comparisons are made with recharge estimates from WTF methods. Model results indicate that the frequency of observations (daily versus sub-daily) dictates the allocation between preferential and diffuse flow. Additionally, because infiltration processes encompass many nonlinearities, model parameters estimated from observation periods need to be updated at least seasonally to account for changing recharge conditions.

groundwater, Recharge, infiltration, recursive est↗

DOE OSTI2020

Ubiquitous Traffic Volume Estimation through Machine-Learning Procedure

Traffic volume data is one of the most important metrics for accurate assessment of the performance of a transportation system. Quality volume data is required to effectively assess extent of delay and congestion, detect real-time perturbations to the network, and understand traffic patterns during major weather events. Traffic volume on freeways are typically collected through continuous count stations installed by state DOTs, while there is lack of traffic volume observability on off-freeway roads. The National Renewable Energy Laboratory (NREL), in Collaboration with the I-95 Corridor Coalition and the University of Maryland, extended its research into estimating volumes anywhere anytime from industry probe based data for off-freeway roads. NREL combined vehicle probe count data with several other data sets (speed, whether, roadway geometry, time-of-day, day-of-week, etc.) to estimate hourly volumes as well as AADTs. The research validated and demonstrated the machine learning model, namely XGBoost, using data collected from Pennsylvania, North Carolina, and Tennessee.

47 OTHER INSTRUMENTATION↗

DOE OSTI2021

Pulsar-Calibrated Timing Source for Synchronized Sampling

The Global Positioning System (GPS) is critical to the real-time synchronized sampling of phasor measurement units (PMUs). Unfortunately, GPS signals are occasionally unstable due to several factors such as weak satellite signal and GPS spoofing, thereby leaving the PMU with a degraded sampling performance. In this letter, a novel Pulsar-calibrated Timing Source (PTS) is proposed as the alternative timing source for synchronized sampling. Further, the PTS can generate the timing signal with a 1 μs drift error within 91 holdover minutes to ensure continuity of sampling accuracy. Experimental tests are conducted and the results reveal the reliability and accuracy of the PTS for PMU synchronization.

42 ENGINEERING↗