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This presentation covers the motivation for this research, optimization under the uncertainty problem formulation, a two-turbine case, the Princess Amalia Wind Farm case, and conclusions and next steps.
Traditionally, distribution system state estimations (DSSE) are challenged by the lack of measurements at both primary and secondary sides of the system. The widely available cable television (CATV) voltage sensors installed in low-voltage (LV) networks bring opportunities to achieve higher quality DSSE covering a broader area of the distribution network. This study proposes a medium-/low-voltage (MV/LV) joint distribution system state estimation approach using the untapped CATV measurements. It aims at addressing the need for system situational awareness at the grid edge while improving the estimation accuracy at both the primary and secondary sides compared to its disjointed counterpart. Linearized measurement functions and boundary condition uncertainty propagation rules are derived to ensure the computational efficiency and accuracy of the joint state estimator. Numerical experiments are conducted on an IEEE test feeder to demonstrate the efficacy of the proposed method and the value of CATV measurements.
Algebraic modeling languages (AMLs) have drastically simplified the implementation of algebraic optimization problems. However, there are still many classes of optimization problems that are not easily represented in most AMLs. These classes of problems are typically reformulated before implementation, which requires significant effort and time from the modeler and obscures the original problem structure or context. In this work we demonstrate how the Pyomo AML can be used to represent complex optimization problems using high-level modeling constructs. We focus on the operation of dynamic systems under uncertainty and demonstrate the combination of Pyomo extensions for dynamic optimization and stochastic programming. We use a dynamic semibatch reactor model and a large-scale bubbling fluidized bed adsorber model as test cases.
Uncertainty analysis is a critical requirement in reactor simulation as it is used to quantify the reliability of best-estimate calculation. A comprehensive uncertainty analysis should characterize all sources of uncertainties in a computationally-feasible and scientifically-defendable manner. Here we employ a well-established reduced order modeling (ROM) based uncertainty quantification methodology to propagate uncertainties throughout neutronic calculations. ROM relies on recent advances in randomized data mining techniques applied to large data streams. In our proposed implementation, the nuclear data uncertainties are first propagated from multi-group level through lattice physics calculation to generate few-group parameter uncertainties, described using a vector of mean values and a covariance matrix. Employing an ROM-based compression of the covariance matrix, the few-group uncertainties are then propagated through downstream core simulation in a computationally efficient manner. This straightforward approach, albeit efficient as compared to brute force forward and/or adjoint-based methods, often employs a number of assumptions that have been unquestioned in the literature of neutronic uncertainty analysis. This manuscript argues that these assumptions could introduce another source of uncertainty referred to as modeling uncertainties, whose magnitude needs to be quantified in tandem with nuclear data uncertainties. Thus, our primary goal is to explore the interactions between these two uncertainty sources in order to assess whether modeling uncertainties have an impact on parameter uncertainties. To explore this endeavor, the impact of a number of modeling assumptions on core attributes uncertainties is quantified. The study employs a CANDU reactor model, with Serpent and NEWT as lattice physics solvers and NESTLE-C as core simulator. The modeling assumptions investigated include those related with the uncertainty propagation method employed, e.g., deterministic vs. stochastic, the few-group energy structure employed to represent the cross-sections, the resonance treatment in lattice physics calculation, the reference values for the cross-section, and the number of samples employed to render ROM compression. Results indicate that some of the modeling assumptions could have a non-negligible impact on the core responses propagated uncertainties, highlighting the need for a more comprehensive approach to combine parameter and modeling uncertainties.
We use a simple one-zone galactic chemical evolution model to quantify the uncertainties generated by the input parameters in numerical predictions for a galaxy with properties similar to those of the Milky Way. We compiled several studies from the literature to gather the current constraints for our simulations regarding the typical value and uncertainty of the following seven basic parameters: the lower and upper mass limits of the stellar initial mass function (IMF), the slope of the high-mass end of the stellar IMF, the slope of the delay-time distribution function of Type Ia supernovae (SNe Ia), the number of SNe Ia per M {sub ⊙} formed, the total stellar mass formed, and the final mass of gas. We derived a probability distribution function to express the range of likely values for every parameter, which were then included in a Monte Carlo code to run several hundred simulations with randomly selected input parameters. This approach enables us to analyze the predicted chemical evolution of 16 elements in a statistical manner by identifying the most probable solutions, along with their 68% and 95% confidence levels. Our results show that the overall uncertainties are shaped by several input parameters that individually contribute at different metallicities, and thus at different galactic ages. The level of uncertainty then depends on the metallicity and is different from one element to another. Among the seven input parameters considered in this work, the slope of the IMF and the number of SNe Ia are currently the two main sources of uncertainty. The thicknesses of the uncertainty bands bounded by the 68% and 95% confidence levels are generally within 0.3 and 0.6 dex, respectively. When looking at the evolution of individual elements as a function of galactic age instead of metallicity, those same thicknesses range from 0.1 to 0.6 dex for the 68% confidence levels and from 0.3 to 1.0 dex for the 95% confidence levels. The uncertainty in our chemical evolution model does not include uncertainties relating to stellar yields, star formation and merger histories, and modeling assumptions.
We propose herein a probabilistic framework for assessing the consistency of an experimental dataset, i.e., whether the stated experimental conditions are consistent with the measurements provided. In case the dataset is inconsistent, our framework allows one to hypothesize and test sources of inconsistencies. This is crucial in model validation efforts. The framework relies on Bayesian inference to estimate experimental settings deemed uncertain, from measurements deemed accurate. The quality of the inferred variables is gauged by its ability to reproduce held-out experimental measurements. We test the correctness of the framework on three double-cone experiments conducted in the CUBRC Inc.'s LENS-I shock tunnel, which have also been numerically simulated successfully. Thereafter, we use the framework to investigate two double-cone experiments (executed in the LENS-XX shock tunnel) which have encountered difficulties when used in model validation exercises. We detect an inconsistency with one of the LENS-XX experiments. In addition, we hypothesize two causes for our inability to simulate LEXS-XX experiments accurately and test them using our framework. We find that there is no single cause that explains all the discrepancies between model predictions and experimental data, but different causes explain different discrepancies, to larger or smaller extent. We end by proposing that uncertainty quantification methods be used more widely to understand experiments and characterize facilities, and we cite three different methods to do so, the third of which we present in this paper.
Abstract not provided.
Calculations of wind farm annual energy production (AEP) on operational data are essential for a variety of financial transactions during the life of wind plants. The AEP estimate is associated with an uncertainty value, which is calculated by combining contributions connected to on-site measurements, long-term reference measurements, losses, regression, windiness adjustment, and wind resource interannual variability. Although very limited documentation on the topic exists, the conventional approach currently used by the wind energy community to assess the uncertainty connected to the operational AEP estimate assume that the different uncertainty components are uncorrelated and therefore calculates the overall uncertainty with a sum of squares approach. In this analysis, we contrast the traditional technique to estimate the overall AEP uncertainty by ignoring the correlation between its different components with a novel Monte Carlo based approach, which can instead take into account the correlation between different uncertainty categories. We consider monthly operational data from 472 wind farms from the Energy Information Administration (EIA) 923 database to assess the difference between the two approaches. Long-term wind speed data needed for the AEP assessment are taken from three reanalysis products: the Modern-Era Retrospective analysis for Research and Applications v2 (MERRA-2), the European Reanalysis Interim (ERA-interim), and the National Centers for Environmental Prediction v2 (NCEP-2). The results of the Monte Carlo approach show that three pairs of AEP uncertainty components do show a statistically significant correlation: the uncertainty connected with wind resource inter-annual variability is positively correlated with the one related to the windiness correction and negatively correlated with the one due to the regression, and the wind measurement uncertainty is positively correlated with the regression uncertainty. All these correlations, which are found between uncertainty components which are not only part of an operational analysis, but also of a wind resource assessment, are currently ignored in the conventional techniques used as industry standard. We further investigate the causes of these correlations, in terms of common dependencies of different uncertainty components on wind resource variability, number of data points, and quality of the regression between wind speed and energy production data. Next, we quantify the error in the current industry standard technique, in terms of the percentage difference in total uncertainty calculated with the two considered approaches, for all the analyzed wind farms. We find a mean absolute percentage difference of about 6%, with the largest differences being greater than 20%. The data clearly confirm that ignoring the actual correlation between the uncertainty components can lead to large errors in the assessment of the operational AEP uncertainty, and the proposed Monte Carlo approach should be preferred.
Not provided.
Detector response functions (DRFs) are often used for inverse analysis. We compute the DRF of a sodium iodide (NaI) nuclear material holdup field detector using the code named g03 developed by the Center for Engineering Applications of Radioisotopes (CEAR) at NC State University. Three measurement campaigns were performed in order to validate the DRF’s constructed by g03: on-axis detection of calibration sources, off-axis measurements of a highly enriched uranium (HEU) disk, and on-axis measurements of the HEU disk with steel plates inserted between the source and the detector to provide attenuation. Furthermore, this work quantifies the uncertainty of the Monte Carlo simulations used in and with g03, as well as the uncertainties associated with each semi-empirical model employed in the full DRF representation. Overall, for the calibration source measurements, the response computed by the DRF for the prediction of the full-energy peak region of responses was good, i.e. within two standard deviations of the experimental response. In contrast, the DRF tended to overestimate the Compton continuum by about 45–65% due to inadequate tuning of the electron range multiplier fit variable that empirically represents physics associated with electron transport that is not modeled explicitly in g03. For the HEU disk measurements, computed DRF responses tended to significantly underestimate (more than 20%) the secondary full-energy peaks (any peak of lower energy than the highest-energy peak computed) due to scattering in the detector collimator and aluminum can, which is not included in the g03 model. We ran a sufficiently large number of histories to ensure for all of the Monte Carlo simulations that the statistical uncertainties were lower than their experimental counterpart’s Poisson uncertainties. The uncertainties associated with least-squares fits to the experimental data tended to have parameter relative standard deviations lower than the peak channel relative standard deviation in most cases and good reduced chi-square values. The highest sources of uncertainty were identified as the energy calibration polynomial factor (due to limited source availability and NaI resolution) and the Ba-133 peak fit (only a very weak source was available), which were 20% and 10%, respectively.
Tristructural isotropic (TRISO) particle fuel is one of the most promising fuel concepts enabling high temperature and high burnup reactor operation. One dominant source of radioactivity released from the TRISO particles is silver (Ag), which is subject to a high release fraction and long decay life compared to other fission products. Previous modeling efforts using the fuel performance code BISON indicated nonnegligible uncertainties in modeling the diffusion process of fission products in TRISO compared to the Advanced Gas Reactor experiments. The overall uncertainties observed when modeling the fission product diffusion can result from uncertainties in model parameters, noisy experimental measurements, and deficiencies in the developed models. The three types of underlying uncertainties have not yet been properly quantified in open literature. Here, this paper presents the Bayesian uncertainty quantification (UQ) using massively parallelizable Markov chain Monte Carlo samplers. The uncertainties due to model parameters, model inadequacy, and experimental measurement noise are quantified, with the σ term used to represent the sum of the model inadequacy and measurement noise uncertainties. It is worth noting that this is the first time the σ term is inferred for nuclear fuel experiments, as compared to using prescribed values for uncertainty quantification in previous work. The parallelizable Markov chain Monte Carlo samplers efficiently infer the model parameters and the σ term, giving insight into physical parameters like diffusion coefficients and the combined model discrepancy and measurement noise. A subsequent forward uncertainty quantification (UQ) is also performed based on the calibration results to generate more accurate predictions of the Ag release. The model inadequacy plus experimental noise is the most dominant source of uncertainty compared to the parametric uncertainty. All the UQ analyses presented in this work are based on the second series of the irradiation experiments in the Advanced Gas Reactor program.
A golden standard in science is to repeat an experiment a statistically significant number of times, recording data using the same set of detectors and the same data analysis methodology. In such case experimental error includes both the range of true values generated by repetitions of the experiment, and measurement uncertainty caused by the detector. They are independent. It is a huge and too frequently used simplification, to assume that one can measure multiple repetitions of an identical experiment, resulting in identical true experimental value. Repetitions, as similar is it is experimentally achievable result in a range of the true values rather than in a single value. When modern, very sensitive and well calibrated measurement systems are used, this range is not negligible, and sometimes dominates, in comparison to the measurement uncertainty. Range of true values depends on the physics of the experiment, while measurement uncertainty depends on the measurement method (properties of the detector not of the experiment). When data from one–of–a kind experiment are analyzed, only the measurement uncertainty is reported. It gives no information about the range, in which the true values of experiment would spread if the experiment was repeated. A frequently used approximation, that if a physical quantity is measured as a function of time, only measurement of this quantity, produces uncertainty is also in some real experiments fare to strong. Example: In reaction history time measurement uncertainty propagated to alpha dominated under certain conditions over the flux measurement uncertainty propagated to alpha. Reliability of a data point is in general independent from its measurement uncertainty. However, in practice reliable measurement methods frequently have high measurement uncertainty, while low reliability methods are applied to limit measurement uncertainty. Comparison of reliable data with high measurement uncertainty to not so reliable data measured with low uncertainty is discussed – in different scenarios different data analysis methods are applicable.
With substantially increasing penetration levels of wind power, electric power system flexibility is needed to address the variability and uncertainty of wind power output. Thus, it has become an urgent issue to obtain an optimal trade-off between economics and reliability, and to price system uncertainties. This paper proposes a new electricity market-clearing mechanism based on locational marginal prices (LMPs) for pricing uncertain generation and load. The uncertainty contained locational marginal price (U-LMP) is derived from a distributionally robust chance-constrained optimal power flow (DRCC-OPF) model in which only the first-order and second-order moments of the uncertain sources' probability distribution are needed. Compared with traditional LMPs, the proposed U-LMP formulation includes two new uncertainty components: transmission line overload uncertainty price and generation violation uncertainty price. These LMP uncertainty components are the price signals reflecting the system costs as a result of wind generation and demand uncertainty at different locations. Finally, using parametric case studies, the relationship among uncertainty levels, system generation cost, and LMP uncertainty components are established. Case studies performed on the PJM 5-bus and IEEE 118-bus systems verify the proposed U-LMP method.
Abstract. The financing of a wind farm directly relates to the preconstruction energy yield assessments which estimate the annual energy production for the farm. The accuracy and the precision of the preconstruction energy estimates can dictate the profitability of the wind project. Historically, the wind industry tended to overpredict the annual energy production of wind farms. Experts have been dedicated to eliminating such prediction errors in the past decade, and recently the reported average energy prediction bias is declining. Herein, we present a literature review of the energy yield assessment errors across the global wind energy industry. We identify a long-term trend of reduction in the overprediction bias, whereas the uncertainty associated with the prediction error is prominent. We also summarize the recent advancements of the wind resource assessment process that justify the bias reduction, including improvements in modeling and measurement techniques. Additionally, because the energy losses and uncertainties substantially influence the prediction error, we document and examine the estimated and observed loss and uncertainty values from the literature, according to the proposed framework in the International Electrotechnical Commission 61400-15 wind resource assessment standard. From our findings, we highlight opportunities for the industry to move forward, such as the validation and reduction of prediction uncertainty and the prevention of energy losses caused by wake effect and environmental events. Overall, this study provides a summary of how the wind energy industry has been quantifying and reducing prediction errors, energy losses, and production uncertainties. Finally, for this work to be as reproducible as possible, we include all of the data used in the analysis in appendices to the article.