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At least 1,261 records · Page 70

Investigation of Stochastic Unit Commitment to Enable Advanced Flexibility Measures for High Shares of Solar PV

As the share of solar photovoltaics (PV) in the power system increases, there is a growing need for flexibility from multiple, possibly interdependent sources to adjust to PV's variability, uncertainty, and diurnal dependence. This paper investigates how stochastic unit commitment leveraging probabilistic solar forecasts can support other flexibility measures under high solar shares. We consider two flexibility measures relevant to day-ahead scheduling: battery energy time-shifting and solar ancillary service provision. Unit commitment and economic dispatch simulations are conducted on a realistic test system based on Texas using day-ahead solar trajectories. The benefits of the two flexibility measures are pronounced when the instantaneous solar share is high, offering cost savings of 10%-20% in the spring. For a Texas-sized system, this translates to hundreds of millions of dollars in cost savings once the installed PV capacity enables instantaneous solar shares regularly exceeding 40%. Using probabilistic forecasts also greatly increases the reliability of upward reserve provision from solar PV, reducing unserved reserves by 50%-100%. Both day-ahead forecast resolution and errors can impact system reliability at high solar shares, but the stochastic formulation has significant value, mitigating reliability impacts on over-forecast days.

ancillary services↗

Transferable predictions of energetic and structural properties for refractory solid solution alloys across chemical compositions

We present a data-efficient approach to train graph neural networks (GNNs) on density functional theory (DFT) data for accurate and transferable predictions of energetic and structural properties of refractory solid solution alloys in the niobium-tantalum-vanadium (Nb-Ta-V) chemical space. We start by training the GNN model only on DFT data that describes refractory binary alloys niobium-tantalum (Nb-Ta), niobium-vanadium (Nb-V), and tantalum-vanadium (Ta-V) to predict formation enthalpy and root mean squared displacement. Once trained, the GNN predictions are tested on DFT data describing refractory ternary alloys Nb-Ta-V. While, unsurprisingly, direct transferability from binary to ternary is not sufficiently accurate, augmenting the training with only 1% of the available ternary data (uniformly distributed across the entire range of chemical compositions) improves significantly the quality of the GNN predictions. For comparison, we assess the transferability in the opposite direction by training GNN models on ternary Nb-Ta-V data and making predictions on binaries Nb-Ta, Nb-V, and Ta-V, which exhibits notably higher predictive errors. The proposed methodology, which favors transferability from lower-component to higher-component alloys, offers an efficient path towards avoiding the curse of dimensionality incurred when collecting DFT data for discovery and design of multi-component disordered alloys.

Density functional theory calculations↗

A unified thermionic and thermionic-field emission (TE–TFE) model for ideal Schottky reverse-bias leakage current

We present a unified thermionic emission (TE) and thermionic-field emission (TFE) model for the ideal reverse-bias leakage current in Schottky junctions. The unified TE–TFE analytical model advances upon previous analytical TFE models by Murphy–Good and Padovani–Stratton, which are the two most widely adopted models by the community, in two major aspects: (i) the applicability of the TFE expression therein is extended to near-zero surface electric fields by an error-function correction, allowing for the calculation of the total current by a nontrivial sum of TE (over-the-barrier current) and TFE (below-the-barrier current) contributions; therefore, an accurate description of the TE-to-TFE transition region is captured analytically for the first time; (ii) image-force lowering is considered with much-simpler correction terms. Comparisons with the reference numerical model show that the unified TE–TFE model has excellent accuracy, as well as a 10 000× reduction in computation time. The unified model is further tested against experimental data from Schottky barrier diodes based on Si, 4H-SiC, GaN, and β-Ga 2 O 3 , revealing accurate extractions of barrier heights and correct descriptions of the ideal reverse leakage characteristics. With the extended applicable range, improved accuracy, and computational efficiency, the unified TE–TFE model is highly valuable for the design and analysis of devices based on Schottky junctions, as well as for potential integration in technology computer-aided design (TCAD) tools.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Evaluation of a pair-based, joint-likelihood association approach for regional infrasound event identification

SUMMARY A Bayesian framework for the association of infrasonic detections is presented and evaluated for analysis at regional propagation scales. A pair-based, joint-likelihood association approach is developed that identifies events by computing the probability that individual detection pairs are attributable to a hypothetical common source and applying hierarchical clustering to identify events from the pair-based analysis. The framework is based on a Bayesian formulation introduced for infrasonic source localization and utilizes the propagation models developed for that application with modifications to improve the numerical efficiency of the analysis. Clustering analysis is completed using hierarchical analysis via weighted linkage for a non-Euclidean distance matrix defined by the negative log-joint-likelihood values. The method is evaluated using regional synthetic data with propagation distances of hundreds of kilometres in order to study the sensitivity of the method to uncertainties and errors in backazimuth and time of arrival. The method is found to be robust and stable for typical uncertainties, able to effectively distinguish noise detections within the data set from those in events, and can be made numerically efficient due to its ease of parallelization.

58 GEOSCIENCES↗

Methods for Measuring and Computing the Reference Temperature in Newton’s Law of Cooling for External Flows

Newton’s law of cooling requires a reference temperature (𝑇 𝑟𝑒𝑓 ) to define the heat-transfer coefficient (ℎ). For external flows with multiple temperatures in the freestream, obtaining 𝑇 𝑟𝑒𝑓 is a challenge. One widely used method, referred to as the adiabatic-wall (AW) method, obtains 𝑇 𝑟𝑒𝑓 by requiring the surface of the solid exposed to convective heat transfer to be adiabatic. Another widely used method, referred to as the linear-extrapolation (LE) method, obtains 𝑇 𝑟𝑒𝑓 by measuring/computing the heat flux ($𝑞^{′′}_𝑠$) on the solid surface at two different surface temperatures (𝑇 𝑠 ) and then linearly extrapolating to $𝑞^{′′}_𝑠$ = 0. A third recently developed method, referred to as the state-space (SS) method, obtains 𝑇 𝑟𝑒𝑓 by probing the temperature space between the highest and lowest in the flow to account for the effects of 𝑇 𝑠 or $𝑞^{′′}_𝑠$ on 𝑇 𝑟𝑒𝑓 . This study examines the foundation and accuracy of these methods via a test problem involving film cooling of a flat plate where $𝑞^{′′}_𝑠$ switches signs on the plate’s surface. Results obtained show that only the SS method could guarantee a unique and physically meaningful 𝑇 𝑟𝑒𝑓 where 𝑇 𝑠 =𝑇 𝑟𝑒𝑓 on a nonadiabatic surface $𝑞^{′′}_𝑠$ = 0. The AW and LE methods both assume 𝑇 𝑟𝑒𝑓 to be independent of 𝑇 𝑠 , which the SS method shows to be incorrect. Though this study also showed the adiabatic-wall temperature, 𝑇 𝐴𝑊 , to be a good approximation of 𝑇 𝑟𝑒𝑓 (<10% relative error), huge errors can occur in ℎ about the solid surface where |𝑇 𝑠 −𝑇 𝐴𝑊 | is near zero because where 𝑇 𝑠 =𝑇 𝐴𝑊 , $𝑞^{′′}_𝑠$ ≠ 0.

Newton's law of cooling↗

Test of nuclear decay rate variation due to an antineutrino flux

Unexplained variations of the decay rate parameter for weak interaction decays such as β ± decay, electron capture, as well as strong interaction α decay have been reported. Because these variations have been presented by a number of groups, at various locations, using various types of detectors, different isotopes, and over extended periods of time, some researchers have interpreted the source of these variations as not from ambient environmental factors such as temperature, pressure, and humidity but via an unexplained fundamental interaction. The state of decay rate parameter variations experiments is reviewed, and the reported results are placed into a common comparable context by defining a phenomenological cross section. After that we make decay parameter measurements as a function of time at the level of 10 -5 in the presences of an antineutrino flux with an on-off cycle time of ≈ 30 days. This level of precision requires a detailed understanding of both systematic and statistical errors; otherwise, systematic errors in the measurement may mimic the decay events of fundamental interactions. The experiment searched for variation of the $^{54}_{25}$Mn, e - capture decay rate parameter and $^{137}_{55}$Cs, β - decay rate parameter both to a level of precision of 1 part in ≈10 5 by comparing the difference between the decay rate in the presence of an antineutrino flux ≈ 3 x 10 12 $\bar{ν}$ cm -2 s -1 and no flux measurements. The experiment was located 6.53 m from the reactor core of the High Flux Isotope Reactor at the Oak Ridge National Laboratory. Two weak interaction decays, one via electron capture and the other via β - decay, were selected because the final state and the time reverse state each contain a neutrino and antineutrino, covering arguments that the antineutrino flux may interact differently or not at all in one of the cases. The $\gamma$ spectra from both decays were collected and analyzed independently. The measured variation in the decay rate parameters are found to be δλ/λ =(0.034 ± 1.38) x10 -5 for $^{54}_{25}$Mn and δλ/λ =(0.67±1.56) x10 -5 for $^{137}_{55}$Cs. These results are consistent with no measurable decay rate parameter variation due to an antineutrino flux, yielding a 68% confidence level upper limit sensitivity for $^{54}_{25}$Mn δλ/λ ≤ 1.31 x 10 -5 or σ ≤ 1.29 x10 -25 cm 2 in cross section and for $^{137}_{55}$Cs δλ/λ ≤ 2.23 x 10 -5 or σ ≤ 5.69 x10 -27 cm 2 . The cross-section upper limit obtained in these null or no observable effect measurements are ≈ 10 4 times more sensitive than past experiments reporting positive results in 54 Mn and 137 Cs. . .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Fast dynamic aperture optimization with forward-reversal integration

A fast dynamic aperture (DA) optimization method for storage rings has been developed through the use of reversal integration. Even if dynamical systems have an exact reversal symmetry, a numerical forward integration differs from its reversal. For a chaotic trajectory, cumulative round-off errors are scaled, which results in an exponential growth on the difference. The exponential effect is a generic chaos indicator which represents the sensitivity of the chaotic motion to its initial condition. The chaos indicator of the charged particle motion can be obtained by comparing the forward integrations of particle trajectories with corresponding reversals, a.k.a. “backward integrations.” The indicator is observable even through short-term particle tracking simulations. Therefore, adopting it as an objective function could speed up optimization. Finally, the DA of the National Synchrotron Light Source II storage ring, and another test diffraction-limited light source ring, were optimized using this method for the purpose of demonstration.

43 PARTICLE ACCELERATORS↗

Heliostat optical error inspection with polarimetric imaging drone

On a Concentrated Solar Power (CSP) field, optical errors have significant impacts on the collection efficiency of heliostats. Fast, cost-effective, labor-efficient, and non-intrusive autonomous field inspection remains a challenge. Approaches using imaging drone, i.e., Unmanned Aerial Vehicle (UAV) system integrated with high resolution visible imaging sensors, have been developed to address these challenges; however, these approaches are often limited by insufficient imaging contrast. Here, in this study, we report a polarimetry-based method with a polarization imaging system integrated on UAV to enhance imaging contrast for in-situ detection of heliostat mirrors without interrupting field operation. We developed an optical model for skylight polarization pattern to simulate the polarization images of heliostat mirrors and obtained optimized waypoints for polarimetric imaging drone flight path to capture images with enhanced contrast. The polarimetric imaging-based method improved the success rate of edge detections in scenarios which were challenging for mirror edge detection with conventional imaging sensors. We have performed field tests to achieve significantly enhanced heliostat edge detection success rate and investigate the feasibility of integrating polarimetric imaging method with existing imaging-based heliostat inspection methods, i.e., Polarimetric Imaging Heliostat Inspection Method (PIHIM). Our preliminary field test results suggest that the PIHIM hold the promise to enable sufficient imaging contrast for real-time autonomous imaging and detection of heliostat field, thus suitable for non-interruptive fast CSP field inspection during its operation.

CSP Field↗

On the computational solution of vector-density based continuum dislocation dynamics models: A comparison of two plastic distortion and stress update algorithms

Continuum dislocation dynamics models of mesoscale plasticity consist of dislocation transport-reaction equations coupled with crystal mechanics equations. The coupling between these two sets of equations is such that dislocation transport gives rise to the evolution of plastic distortion (strain), while the evolution of the latter fixes the stress from which the dislocation velocity field is found via a mobility law. Earlier solutions of these equations employed a staggered solution scheme for the two sets of equations in which the plastic distortion was updated via time integration of its rate, as found from Orowan's law. In this work, we show that such a direct time integration scheme can suffer from accumulation of numerical errors. We introduce an alternative scheme based on field dislocation mechanics that ensures consistency between the plastic distortion and the dislocation content in the crystal. The new scheme is based on calculating the compatible and incompatible parts of the plastic distortion separately, and the incompatible part is calculated from the current dislocation density field. Stress field and dislocation transport calculations were implemented within a finite element based discretization of the governing equations, with the crystal mechanics part solved by a conventional Galerkin method and the dislocation transport equations by the least squares method. A simple test was first performed to show the accuracy of the two schemes for updating the plastic distortion, which shows that the solution method based on field dislocation mechanics is more accurate. This method then was used to simulate an austenitic steel crystal under uniaxial loading and multiple slip conditions. By considering dislocation interactions caused by junctions, a hardening rate similar to discrete dislocation dynamics simulation results was obtained. Finally, the simulations show that dislocations exhibit some self-organized structures as the strain is increased.

36 MATERIALS SCIENCE↗

A study of shock initiation experiments for the explosive PBX 9502 using three reactive burn models

Shock to detonation transition (SDT) experiments are essential in calibrating and validating reactive burn models for explosives. This work investigates the large collection of SDT test data for the explosive PBX 9502 at ambient temperature that was presented by Gustavsen, Sheffield, and Alcon [Journal of Applied Physics, 99, 114907 (2006)]. We first analyze the experimental data and compare two different methods of determining the shock transition time/distance (namely, the bilinear method and the single-curve method). This reveals some of the uncertainty in estimating shock transition points, which contributes to scatter in Pop-plot data. Next, we compare the WSD, AWSD, and SURFplus reactive burn models for a collection of approximately 20 experimental shots using the FLAG hydrocode. Error estimates are used to quantify how well each reactive burn model (and their respective parameter calibrations) performs at predicting the SDT process for a range of loading conditions. Additionally, the importance of mesh resolution and numerical dissipation in SDT simulations will be assessed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Comparing correlation components and approximations in Hartree–Fock and Kohn–Sham theories via an analytical test case study

The asymmetric Hubbard dimer is a model that allows for explicit expressions of the Hartree–Fock (HF) and Kohn–Sham (KS) states as analytical functions of the external potential, Δv, and of the interaction strength, U. We use this unique circumstance to establish a rigorous comparison between the individual contributions to the correlation energies stemming from the two theories in the {U, Δv} parameter space. Within this analysis of the Hubbard dimer, we observe a change in the sign of the HF kinetic correlation energy, compare the indirect repulsion energies, and derive an expression for the “traditional” correlation energy, i.e., the one that corrects the HF estimate, in a pure site-occupation function theory spirit [Eq. (45)]. Next, we test the performances of the Liu–Burke and the Seidl–Perdew–Levy functionals, which model the correlation energy based on its weak- and strong-interaction limit expansions and can be used for both the traditional and the KS correlation energies. Further, our results show that, in the Hubbard dimer setting, they typically work better for the HF reference, despite having been originally devised for KS. These conclusions are somewhat in line with prior assessments of these functionals on various chemical datasets. However, the Hubbard dimer model allows us to show the extent of the error that may occur in using the strong-interaction ingredient for the KS reference in place of the one for the HF reference, as has been carried out in most of the prior assessments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

On the estimation of boundary layer heights: a machine learning approach

Abstract. The planetary boundary layer height (zi) is a key parameter used in atmospheric models for estimating the exchange of heat, momentum, and moisture between the surface and the free troposphere. Near-surface atmospheric and subsurface properties (such as soil temperature, relative humidity, etc.) are known to have an impact on zi. Nevertheless, precise relationships between these surface properties and zi are less well known and not easily discernible from the multi-year dataset. Machine learning approaches, such as random forest (RF), which use a multi-regression framework, help to decipher some of the physical processes linking surface-based characteristics to zi. In this study, a 4-year dataset from 2016 to 2019 at the Southern Great Plains site is used to develop and test a machine learning framework for estimating zi. Parameters derived from Doppler lidars are used in combination with over 20 different surface meteorological measurements as inputs to a RF model. The model is trained using radiosonde-derived zi values spanning the period from 2016 through 2018 and then evaluated using data from 2019. Results from 2019 showed significantly better agreement with the radiosonde compared to estimates derived from a thresholding technique using Doppler lidars only. Noteworthy improvements in daytime zi estimates were observed using the RF model, with a 50 % improvement in mean absolute error and an R2 of greater than 85 % compared to the Tucker method zi. We also explore the effect of zi uncertainty on convective velocity scaling and present preliminary comparisons between the RF model and zi estimates derived from atmospheric models.

54 ENVIRONMENTAL SCIENCES↗

Neural-network learning of SPOD latent dynamics

Here, we aim to reconstruct the latent space dynamics of high dimensional, quasi-stationary systems using model order reduction via the spectral proper orthogonal decomposition (SPOD). The proposed method is based on three fundamental steps: in the first, once that the mean flow field has been subtracted from the realizations (also referred to as snapshots), we compress the data from a high-dimensional representation to a lower dimensional one by constructing the SPOD latent space; in the second, we build the time-dependent coefficients by projecting the snapshots containing the fluctuations onto the SPOD basis and we learn their evolution in time with the aid of recurrent neural networks; in the third, we reconstruct the high-dimensional data from the learnt lower -dimensional representation. The proposed method is demonstrated on two different test cases, namely, a compressible jet flow, and a geophysical problem known as the Madden-Julian Oscillation. An extensive comparison between SPOD and the equivalent POD-based counterpart is provided and differences between the two approaches are highlighted. The numerical results suggest that the proposed model is able to provide low rank predictions of complex statistically stationary data and to provide insights into the evolution of phenomena characterized by specific range of frequencies. The comparison between POD and SPOD surrogate strategies highlights the need for further work on the characterization of the interplay of error between data reduction techniques and neural network forecasts.

97 MATHEMATICS AND COMPUTING↗

Machine learning assisted prediction of the Young’s modulus of compositionally complex alloys

We identify compositionally complex alloys (CCAs) that offer exceptional mechanical properties for elevated temperature applications by employing machine learning (ML) in conjunction with rapid synthesis and testing of alloys for validation to accelerate alloy design. The advantages of this approach are scalability, rapidity, and reasonably accurate predictions. ML tools were implemented to predict Young’s modulus of refractory-based CCAs by employing different ML models. Our results, in conjunction with experimental validation, suggest that average valence electron concentration, the difference in atomic radius, a geometrical parameter λ and melting temperature of the alloys are the key features that determine the Young’s modulus of CCAs and refractory-based CCAs. The Gradient Boosting model provided the best predictive capabilities (mean absolute error of 6.15 GPa) among the models studied. Our approach integrates high-quality validation data from experiments, literature data for training machine-learning models, and feature selection based on physical insights. It opens a new avenue to optimize the desired materials property for different engineering applications.

36 MATERIALS SCIENCE↗

Machine-Learning Assisted Identification of Accurate Battery Lifetime Models with Uncertainty

Reduced-order battery lifetime models, which consist of algebraic expressions for various aging modes, are widely utilized for extrapolating degradation trends from accelerated aging tests to real-world aging scenarios. Identifying models with high accuracy and low uncertainty is crucial for ensuring that model extrapolations are believable, however, it is difficult to compose expressions that accurately predict multivariate data trends; a review of cycling degradation models from literature reveals a wide variety of functional relationships. Here, a machine-learning assisted model identification method is utilized to fit degradation in a stand-out LFP-Gr aging data set, with uncertainty quantified by bootstrap resampling. The model identified in this work results in approximately half the mean absolute error of a human expert model. Models are validated by converting to a state-equation form and comparing predictions against cells aging under varying loads. Parameter uncertainty is carried forward into an energy storage system simulation to estimate the impact of aging model uncertainty on system lifetime. The new model identification method used here reduces life-prediction uncertainty by more than a factor of three (86% ± 5% relative capacity at 10 years for human-expert model, 88.5% ± 1.5% for machine-learning assisted model), empowering more confident estimates of energy storage system lifetime.

25 ENERGY STORAGE↗

Advanced Finite-Volume Numerics and Source Term Assumptions for Kernel and G-Equation Modelling of Propane/Air Flames

Here G-Equation models represent propagating flame fronts with an implicit two-dimensional surface representation (level-set). Level-set methods are fast, as transport source terms for the implicit surface can be solved with finite-volume operators on the finite-volume domain, without having to build the actual surface. However, they include approximations whose practical effects are not properly understood. In this study, we improved the numerics of the FRESCO CFD code’s G-Equation solver and developed a new method to simulate kernel growth using signed distance functions and the analytical sphere-mesh overlap. We analyzed their role for simulating propane/air flames, using three well-established constant-volume configurations: a one-dimensional, freely propagating laminar flame; a disc-shaped, constant-volume swirl combustor; and torch-jet flame development through an orifice from a two-chamber device. We tested the explicit (sub-cycled) vs. implicit formulation for the standard transport operators (advection, diffusion, compressibility). In addition to the accurate flame swept-volume method for chemistry and species source term, we developed a more accurate estimator for the burnt/unburnt split cell composition. Then, we developed a signed-distance-function (SDF) based method which provides a more stable reinitialization of the level-set field at every time-step. We found that simplifying assumptions common to several G-Equation implementations, for straightforward terms such as compressibility and advection, lead to large errors in predicting the propagation of even laminar flames, with deviations up to ~300% in simulated vs. formulated flame speed. Conversely, the enhanced numerics enabled through the SDF field reinitialization and improved chemistry source term improve simulation stability and smooth flame propagation even with significantly larger solver time-steps.

42 ENGINEERING↗

Using neural network ensembles to separate ocean biogeochemical and physical drivers of phytoplankton biogeography in Earth system models

Abstract. Earth system models (ESMs) are useful tools for predicting and understanding past and future aspects of the climate system. However, the biological and physical parameters used in ESMs can have wide variations in their estimates. Even small changes in these parameters can yield unexpected results without a clear explanation of how a particular outcome was reached. The standard method for estimating ESM sensitivity is to compare spatiotemporal distributions of variables from different runs of a single ESM. However, a potential pitfall of this method is that ESM output could match observational patterns because of compensating errors. For example, if a model predicts overly weak upwelling and low nutrient concentrations, it might compensate for this by allowing phytoplankton to have a high sensitivity to nutrients. Recently, we demonstrated that neural network ensembles (NNEs) are capable of extracting relationships between predictor and target variables within ocean biogeochemical models. Being able to view the relationships between variables, along with spatiotemporal distributions, allows for a more mechanistically based examination of ESM outputs. Here, we investigated whether we could apply NNEs to help us determine why different ESMs produce different spatiotemporal distributions of phytoplankton biomass. We tested this using three cases. The first and second case used different runs of the same ESM, except that the physical circulations differed between them in the first case, while the biological equations differed between them in the second. Our results indicated that the NNEs were capable of extracting the relationships between variables for different runs of a single ESM, allowing us to distinguish between differences due to changes in circulation (which do not change relationships) from changes in biogeochemical formulation (which do change relationships). In the third case, we applied NNEs to two different ESMs. The results of the third case highlighted the capability of NNEs to contrast the apparent relationships of different ESMs and some of the challenges it presents. Although applied specifically to the ocean components of an ESM, our study demonstrates that Earth system modelers can use NNEs to separate the contributions of different components of ESMs. Specifically, this allows modelers to compare the apparent relationships across different ESMs and observational datasets.

54 ENVIRONMENTAL SCIENCES↗

Experimental demonstration of a data-driven control system for subcritical nuclear facility

Here this paper presents an experimental demonstration of a data-driven control system (DCS) designed for the MIT Graphite Exponential Pile (MGEP). The DCS aims to regulate the neutron flux profile such that symmetry is preserved. Neutron flux perturbations are introduced into the MGEP to test the DCS's capabilities by the movement of an initiating control rod (ICR). To realize this functionality, a control system that relies on an artificial neural network (ANN) was developed, and then demonstrated on the MGEP. A Helium-3 ( 3 He) neutron detector and dual control rods, including their moving mechanisms, were fabricated. The perturbed flux profile was monitored by the moving neutron detector. The prediction accuracy of the neural network (NN) was examined and the DCS response was presented. Our results show that neural network regression model trained by experimental data can achieve a prediction error of less than 2.5 cm with a 95% confidence interval. The demonstration experiment also shows that a perturbation of the ICR can be captured by the control system and flux symmetry can be maintained within 1% after the response of the responding control rod (RCR).

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗