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Logarithmic Resilience Risk Metrics That Address the Huge Variations in Blackout Cost
Resilience risk metrics must address the customer cost of the largest blackouts of greatest impact. However, there are huge variations in blackout cost in observed distribution utility data that make it impractical to properly estimate the mean large blackout cost and the corresponding risk. These problems are caused by the heavy tail observed in the distribution of customer costs. To solve these problems, we propose resilience metrics that describe large blackout risk using the mean of the logarithm of the cost of large-cost blackouts, the slope index of the heavy tail, and the frequency of large-cost blackouts.
A mechanistic model of a PWR-based nuclear power plant in response to external hazard-induced station blackout accidents
Natural hazard-induced nuclear accidents, such as the Fukushima Daiichi Accident that occurred in Japan in 2011, have significantly increased reactor safety studies in understanding nuclear power plant (NPP) responses to external hazard events such as earthquakes and floods. Natural hazards could cause the loss of offsite power in nuclear power plants, potentially leading to a Station Blackout (SBO) accident that significantly contributes to the overall risk of nuclear power plant accidents. Despite the fact that extensive research has been conducted on the station blackout accident for nuclear power plant, further understanding of these events is needed, particularly in the context of the dynamic nature of external hazards such as external flooding. This paper estimates the progression of station blackout events for a generic pressurized water reactor (PWR) in response to external flooding events. The original RELAP5-3D model of the Westinghouse four-loop design pressurized water reactor was adopted and modified to simulate the external flood-induced station blackout accident, including the short-term and long-term station blackout scenarios. A sensitivity analysis of long-term station blackout, examining reactor operation times and analyzing key parameters over time, was also conducted in this work. The results of the analyses, especially the critical timing parameters of key event sequences, provide useful insights about the time during the external flooding event, which is important for plant operators to make timely decisions to prevent potential core damage. This paper represents significant progress toward developing an integrated risk assessment framework for further identifying and assessing the effects of the critical sources of uncertainties of nuclear power plant under external hazard-induced events.
Distribution of blackouts in the power grid and the Motter and Lai model
Carreras, Dobson, and colleagues have studied empirical data on the sizes of the blackouts in real grids and modeled them with computer simulations using the direct current approximation. They have found that the resulting blackout sizes are distributed as a power law and suggested that this is because the grids are driven to the self-organized critical state. In contrast, more recent studies found that the distribution of cascades is bimodal resulting in either a very small blackout or a very large blackout, engulfing a finite fraction of the system. Here we reconcile the two approaches and investigate how the distribution of the blackouts changes with model parameters, including the tolerance criteria and the dynamic rules of failure of the overloaded lines during the cascade. Finally, we study the same problem for the Motter and Lai model and find similar results, suggesting that the physical laws of flow on the network are not as important as network topology, overload conditions, and dynamic rules of failure.
Code for the manuscript titled "Blackout Diffusion: Generative Diffusion Models in Discrete-State Spaces"
We would like to disclose two scripts, written in Jupyter notebook, in which we implement the "Blackout Diffusion Process" described in the manuscript "Blackout Diffusion: Generative Diffusion Models in Discrete-State Spaces" (LA-UR-23-20509), to be submitted to the International Conference of Machine Learning (ICML). The abstract of the manuscript is append below. == Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used generate samples from Gaussian noise. However, real world data often takes place in discrete-state spaces, which occur in many scientific applications. Here, we develop a theoretical formulation for arbitrary discrete-state Markov processes in the forward diffusion process. We relate the theory to the existing continuous-state Gaussian diffusion and identify the corresponding reverse-time stochastic process and score function in the continuous-time setting, and the reverse-time mapping in the discrete-time setting. As an example of this framework, we introduce "Blackout Diffusion", which learns to produce samples from an empty image instead of from noise. Numerical experiments on the CIFAR-10 dataset confirm the feasibility of generative diffusion modeling in a discrete space. Generalizing from specific (Gaussian) forward processes to a more general framework also sheds light on how to interpret generative diffusion models and their mathematical structure, which we comment on.
Material Interactions in Severe Accidents – Benchmarking the MELCOR V2.2 Eutectics Model for a BWR-3 Mark-I Station Blackout: Part II – Uncertainty Analysis
Single case comparisons between severe accident simulations can provide detailed insights into severe accident model behavior, however, they cannot offer insights into model uncertainty, sensitivity to uncertain parameters, or underlying model biases.Here in this analysis, the single case benchmark comparison of the MELCOR material interaction models for a station blackout (SBO) scenario of a boiling water reactor (BWR) using representative Fukushima Daiichi Unit 1 boundary conditions is expanded to include an uncertainty analysis. As part of this uncertainty analysis, 1200 simulations are performed for each material interaction model (2400 total), with random sampling of 14 uncertain MELCOR input parameters. Input parameters are selected for their impact on models representing core degradation processes. These include candling, fuel rod failure, debris quenching and dryout. The analysis performed here is not a traditional “best-estimate” uncertainty analysis that uses best-estimate parameters or identifies best-estimate figure of merit distributions. Instead, it is an exploratory uncertainty analysis that identifies and interrogates underlying model form biases of the two material interaction models (eutectics and interactive materials models). Uniform distributions are applied to all uncertain parameters to ensure coverage of the model parameter uncertainty space. Key findings from this study include underlying model form biases exhibited by material interaction models, and notable differences in accident progression outcomes between the material interaction models. This uncertainty study extends and confirms the conclusions from the first part of this study, which compared the impact of material interaction modeling on simulation of a short-term station blackout scenario with representative Fukushima Daiichi Unit I boundary conditions. In particular, this study confirms that the eutectics model generally exhibits accelerated degradation and failure of fuel components, the core plate, and the lower head. The eutectics model also has a tendency to exhibit a greater degree of core degradation, greater debris mass formation, and larger debris mass ejection. Finally, the eutectics model exhibits higher maximum temperatures for fuel, cladding, particulate debris, oxidic molten pool, and metallic molten pool components than the interactive materials model; interactive materials model simulations exhibit a soft “limitation” on maximum temperatures that is related to the temperature at which material relocation occurs.
System code evaluation of near-term accident tolerant claddings during pressurized water reactor station blackout accidents
Following the Fukushima Daiichi nuclear accident in 2011, researches on Accident-tolerant fuels (ATFs) are currently of high interest in not only the nuclear industry but also governmental and international organizations. In this work, a quantitative evaluation of the performance of monolithic FeCrAl cladding and Cr-coated Zircaloy cladding has been performed for Pressurized Water Reactor (PWR) Station Blackout (SBO) accidents. A generic PWR model has been built in system thermal-hydraulics code TRACE based on the Surry Nuclear Power Station with counter-current natural circulation modelling capability for hotleg and steam generator U-tube components during the accidents. The base model results are then compared to MELCOR and RELAP simulations to verify the system component implementation in TRACE. Two PWR SBO scenarios were investigated, including: short-term SBO and long-term SBO with early reactor coolant pump (RCP) seal failure. These scenarios are defined to be very similar to the accidents studied in the State-of-the-Art Reactor Consequence Analysis (SOARCA) project. TRACE code is modified to reflect the oxidation kinetics of FeCrAl and Cr-coating. Larson-Miller creep rupture model is also implemented in TARCE using its built-in control systems to simulate the creep rupture of hotlegs. Additionally, the comparison between the TRACE models with and without the counter-current flow modeling resulted in significant difference when comparing ATF cladding to Zircaloy for short term SBO, while it marginal impacted the performance during long term SBO with RCP seal failure. For short term SBO, both ATF cladding underwent hot leg creep rupture ~20 min after Zircaloy cladding. While Zircaloy and Cr-coated cladding had generated significant amount of hydrogen gas (>10 kg) before the creep rupture event, FeCrAl cladding had only generated <0.5 kg of hydrogen gas. For long term SBO with RCP seal failure, significant hydrogen generation and fuel melting was predicted before hot leg creep rupture for the ATF cladding while providing only 10–20 min additional coping time compared to Zircaloy.
April 28th 2025 Iberian Blackout: Analysis of Available Information [Slides]
This slide deck shows the analysis of the data available about 2025 Iberian Blackout. It contains analysis of the oscillations, frequency behavior and available images of voltage behavior.
Bulk Electric System Protection Model Demonstration with 2011 Southwest Blackout in DCAT
Protection equipment modeling is critical to power systems planning and operational studies, it enables more accurate system response when control actions including protection relays and remedial action schemes (RAS) are adequately modeled and assessed. This paper incorporates a generic protection philosophy to the Dynamic Contingency Analysis Tools (DCAT), and demonstrates its effectiveness by modeling 2011 Pacific Southwest Blackout event autonomously.
The application of MAMMOTH for a detailed tightly coupled fuel pin simulation with a station blackout
The accurate calculation of desired quantities to predict fuel behavior in a nuclear reactor requires the solution of inter linked equations representing different physics phenomena. Traditional fuels performance codes often rely on internal empirical models for the pin power density and a simplified boundary condition on the cladding outer surface. These simplifications are performed because of the difficulty of coupling applications or codes on differing domains and mapping the required data. In this work the MAMMOTH application is employed in the demonstration of an approach that more consistent with first principles, in a simulation that couples the neutronics application Rattlesnake, the thermal fluids application RELAP-7 and the fuels performance application BISON. A single fuel pin was modeled based on the dimensions of a fuel rod from a Westinghouse 17*17 optimized PWR fuel assembly. The simulation consisted of a depletion period of 1343 days, representing three full operating cycles, followed by a station blackout (SBO) event. The fuel rod was depleted with a total pin power of 65.81 kW. After 1343 days the fission power was reduced to zero (simulating a reactor shutdown). Decay heat calculations provided the time-varying energy source after this time. For this problem, Rattlesnake, BISON, and RELAP-7 are coupled under MAMMOTH in a tightly coupled approach. Each system solves its physics on a separate mesh and, for RELAP-7 and BISON, on only a subset of the full problem domain. Rattlesnake solves the neutronics over the whole domain, which includes the fuel, cladding, gaps, water, and top and bottom rod holders. Here BISON is applied to the fuel and cladding with a 2-D axisymmetric domain, and RELAP-7 is applied to the flow of the circular outer water channel with a set of 1-D flow equations. For this work, the mesh on the Rattlesnake side is either be 3-D (for low order PN transport or diffusion) or 2-D axisymmetric (for diffusion). BISON has a matching ring structure mesh for the fuel so both the power density and local burnup are transferred accurately from Rattlesnake. At each depletion time step, Rattlesnake calculates a power density, fission density rate, burnup distribution and fast flux based on the current water density and fuel temperature. These are then mapped to the BISON mesh to perform a fuels performance solution. BISON calculates the fuel temperature and cladding surface temperature based upon the current power density and bulk fluid temperature. RELAP-7 then calculates the fluid temperature, water density fraction and water phase velocity based upon the cladding surface temperature. The fuel temperature and the fluid density are then passed back to Rattlesnake for another neutronics calculation. For this paper, sets of results from the detailed calculation are provided for both depletion and the SBO event. We demonstrate that a detailed simulation akin to first principles can be achieved using MAMMOTH and the various MOOSE application on differing domains. (authors)
Electrical Cross-Tie Option and Issues to Cope With Extended Station Blackout
The electrical cross-tie option was proposed to cope with extended station blackout event (Ext-SBO) for Barakah NPP in UAE, the EDG Cross-Tie consider a donor Unit EDG as a power source for an Ext-SBO Unit under specific conditions. The cross-tie option is discussed and the issues related to this option are generated in systematic approach as a part of dependencies between multiple units. The applied approach benefited from the previous classification of the historical occurred events as site risk that has dependencies with an enhancement of the approach by adding the operation dimension to the dependencies risk.
Integral Effect Test of ATLAS Facility on Multiple Failure in a Prolonged Station Blackout
Since the Fukushima accident, the design extension conditions (DECs) in a nuclear power plant (NPP) have attracted more importance with respect to nuclear reactor safety, and a consensus has been developed such that these high-risk multiple failure accidents should be revisited from the viewpoint of a reinforcement of the 'defense in depth' concept. In particular, a station blackout (SBO) is one of the most important DECs because a loss of the heat sink without an appropriate accident measure might lead to a core uncovery, core damage, and ultimately, a core meltdown under high pressure. SBO has been recognized to be one of the risk-contributing sequences when combined with additional failure of components such as a reactor coolant pump (RCP) seal leakage or a steam generator tube rupture (SGTR). The RCP seal failure could occur due to a loss of continuous cooling through the seal during SBO. The SGTR during SBO can be a potentially important risk due to the release of the fission product with bypassing the containment boundary. The objective of this study is to experimentally simulate and analyze a prolonged SBO scenario in a thermal hydraulic integral effect test facility, ATLAS. As test items in OECD-ATLAS project, two tests for the SBO condition were conducted with additional failures, that is, a RCP seal failure (A2.1 test) and a SGTR (A2.2 test). In those tests, both the effect of the additional failure on reactor safety and the natural circulation characteristics during prolonged SBO conditions could be investigated. The present test can provide physical insight into the system response during the prolonged SBO scenario combined with the multiple failure.
Feedback Control Approaches for Restoration of Power Grids from Blackouts
The automated restoration of power systems with variable energy resources is a timely problem to tackle. Automated restoration advice can support operators in deciding on strategic actions to restore power grids from a blackout with a mix of conventional and renewable generation resources. To this end, this paper frames the restoration process of power grids with solar resources as a nonlinear dynamic model with algebraic constraints in discrete time which is steered by feedback control loops. We discuss two feedback-control strategies based on greedy and reinforcement learning algorithms, and contrast their performance with restoration plans generated by a mixed-integer linear program. We found that the reinforcement learning algorithm infers restoration actions faster than the greedy one. However, the tuning process of the reinforcement learning parameters is slower than for the greedy one.
Branch-and-Bound algorithm applied to uncertainty quantification of a Boiling Water Reactor Station Blackout
Evaluation of the impacts of uncertainty and sensitivity in modeling presents a significant set of challenges in particular to high fidelity modeling. Computational costs and validation of models creates a need for cost effective decision making with regards to experiment design. Experiments designed to validate computation models can be used to reduce uncertainty in the physical model. In some cases, large uncertainty in a particular aspect of the model may or may not have a large impact on the final results. For example, modeling of a relief valve may result in large uncertainty, however, the actual effects on final peak clad temperature in a reactor transient may be small and the large uncertainty with respect to valve modeling may be considered acceptable. Additionally, the ability to determine the adequacy of a model and the validation supporting it should be considered within a risk informed framework. Low fidelity modeling with large uncertainty may be considered adequate if the uncertainty is considered acceptable with respect to risk. In other words, models that are used to evaluate the probability of failure should be evaluated more rigorously with the intent of increasing safety margin. Probabilistic risk assessment (PRA) techniques have traditionally been used to identify accident conditions and transients. Traditional classical event tree methods utilize analysts’ knowledge and experience to identify the important timing of events in coordination with thermal-hydraulic modeling. These methods lack the capability to evaluate complex dynamic systems. In these systems, time and energy scales associated with transient events may vary as a function of transition times and energies to arrive at a different physical state. Dynamic PRA (DPRA) methods provide a more rigorous analysis of complex dynamic systems. Unfortunately DPRA methods introduce issues associated with combinatorial explosion of states. This study presents a methodology to address combinatorial explosion using a Branch-and-Bound algorithm applied to Dynamic Event Trees (DET), which utilize LENDIT (L – Length, E – Energy, N – Number, D – Distribution, I – Information, and T – Time) as well as a set theory to describe system, state, resource, and response (S2R2) sets to create bounding functions for the DET. The optimization of the DET in identifying high probability failure branches is extended to create a Phenomenological Identification and Ranking Table (PIRT) methodology to evaluate modeling parameters important to safety of those failure branches that have a high probability of failure. The PIRT can then be used as a tool to identify and evaluate the need for experimental validation of models that have the potential to reduce risk. Finally, in order to demonstrate this methodology, a Boiling Water Reactor (BWR) Station Blackout (SBO) case study is presented.
Effect of ATF Cr-coated-Zircaloy on BWR In-vessel Accident Progression during a Station Blackout
The deposition of protective coatings on nuclear fuel cladding has been considered as a near-term Accident Tolerant Fuel (ATF) concept that will reduce the high-temperature oxidation rate and enhance accident tolerance of the cladding while providing additional benefits during normal and transient. In this study, the performance of the proposed ATF concept of Cr-coated-Zircaloy is assessed using a generic Boiling Water Reactor MELCOR plant model considering a Short-term Station Blackout (STSBO) scenario. Simulation results indicate that the use of Cr-coated-Zircaloy as cladding and canister material mitigates the core degradation process as compared to the traditional Zircaloy cladding and canister design. The onset of fuel degradation and collapse is delayed by over thirty minutes, and the extent of fuel degradation is reduced. Specifically, the gross in-vessel hydrogen generation decreased by almost a factor of three. Although the eutectic reaction between Cr-coating and Zircaloy could cause an early failure of the coating, the improvement in the delay of fuel degradation is still notable. In addition, a thicker coating is found helpful to obtain additional coping time and to decrease hydrogen generation. In addition to the eutectic formation that may compromise Cr-coated Zr, a different failure mode is identified for the Cr-coated-Zr when compared to Zircaloy; i.e., a complete melt of base material leads to component collapse before the coating is oxidized and consumed. These findings can help the industry focus on productive areas of research and development for accident-tolerant fuel concepts and enhancement of core safety margins.
Assessment of Pump Coastdown and Reactor Protection Scram Delays during Station Blackout Conditions
This report presents an assessment of the impact of pump coastdown time and reactor protection scram delays for the Versatile Test Reactor (VTR) during Protected Station Blackout (PSBO) conditions. While previous simulations for the VTR assumed centrifugal pumps in the primary system, the current pre-conceptual design uses electromagnetic (EM) pumps. Because there is uncertainty as to what the parameters of the EM pump design will be, this report focuses on the impact of the flow coastdown and the reactor protection scram delay, not on the needs of the pump design. PSBO transient simulations were performed using the SAS4A/SASSYS-1 fast reactor safety analysis code (version 5.2.3). The model used in the simulations is based on the FY18 SAS4A/SASSYS-1 model. A change to the model was made to replace the centrifugal pump model with an electromagnetic pump model with a motor generator as a coastdown mechanism. The results of the PSBO transient simulations were assessed against the criteria used in Reference 2 with an additional 50°C for conservatism to account for uncertainties. The results show that as the delay before scramming the rods increases, the moment of inertia of the coastdown mechanism must increase to satisfy the criteria. By increasing the moment of inertia to extend the flow coastdown, temperatures can be kept below the desired limits with reactor protection scram delays between 3 and 10 seconds.
Orchestrating the Restoration of Wind-Dominant Grids from Blackouts (Final Report of Award No. DE-SC0021410)
This is the final report of Award No. DE-SC0021410: “Orchestrating the Restoration of Wind-Dominant Grids from Blackouts.” It: (1) summarizes the technical/scientific accomplishments, (2) lists the publications containing scientific details of the accomplishments, (3) reports several dissemination activities, (4) names new research grants as consequence of this project, (5) lists the project team funded by the project, and (6) concludes the project.
THE APPLICATION OF MAMMOTH FOR A DETAILED TIGHTLY COUPLED FUEL PIN SIMULATION WITH A STATION BLACKOUT
Accurate calculation of desired quantities to predict fuel behavior requires the solution of interlinked equations representing different physics. Traditional fuels performance codes often rely on internal empirical models for the pin power density and a simplified boundary condition on the cladding edge. These simplifications are performed because of the difficulty of coupling applications or codes on differing domains and mapping the required data. To demonstrate an approach closer to first principles, the neutronics application Rattlesnake and the thermal hydraulics application RELAP-7 were coupled to the fuels performance application BISON under the master application MAMMOTH. A single fuel pin was modeled based on the dimensions of a Westinghouse 17x17 fuel rod. The simulation consisted of a depletion period of 1343 days, roughly equal to three full operating cycles, followed by a station blackout (SBO) event. The fuel rod was depleted for 1343 days for a near constant total power loading of 65.81 kW. After 1343 days the fission power was reduced to zero (simulating a reactor shut-down). Decay heat calculations provided the time-varying energy source after this time. For this problem, Rattlesnake, BISON, and RELAP-7 are coupled under MAMMOTH in a split operator approach. Each system solves its physics on a separate mesh and, for RELAP-7 and BISON, on only a subset of the full problem domain. Rattlesnake solves the neutronics over the whole domain that includes the fuel, cladding, gaps, water, and top and bottom rod holders. Here BISON is applied to the fuel and cladding with a 2D axi-symmetric domain, and RELAP-7 is applied to the flow of the circular outer water channel with a set of 1D flow equations. The mesh on the Rattlesnake side can either be 3D (for low order transport) or 2D (for diffusion). BISON has a matching ring structure mesh for the fuel so both the power density and local burn up are copied accurately from Rattlesnake. At each depletion time step, Rattlesnake calculates a power density, fission density rate, burn-up distribution and fast flux based on the current water density and fuel temperature. These are then mapped to the BISON mesh for a fuels performance solve. BISON calculates the fuel temperature and cladding surface temperature based upon the current power density and bulk fluid temperature. RELAP-7 then calculates the fluid temperature, water density fraction and water phase velocity based upon the cladding surface temperature. The fuel temperature and the fluid density are then passed back to Rattlesnake for another neutronics calculation. Six Picard or fixed-point style iterations are preformed in this manner to obtain consistent tightly coupled and stable results. For this paper a set of results from the detailed calculation are provided for both during depletion and the SBO event. We demonstrate that a detailed calculation closer to first principles can be done under MAMMOTH between different applications on differing domains.