Optimal mitigation planning for highly disruptive contingencies to a transmission-level power system requires optimization with dynamic power system constraints, due to the key role of dynamics in system stability to major perturbations. We formulate a generalized disjunctive program to determine optimal grid component hardening choices for protecting against major failures, with differential algebraic constraints representing system dynamics (specifically, differential equations representing generator and load behavior and algebraic equations representing instantaneous power balance over the transmission system). We optionally allow stochastic optimal pre-positioning across all considered failure scenarios, and optimal emergency control within each scenario. This novel formulation allows, for the first time, analyzing the resilience interdependencies of mitigation planning, preventive control, and emergency control. Using all three strategies in concert is particularly effective at maintaining robust power system operation under severe contingencies, as we demonstrate on the Western System Coordinating Council (WSCC) 9-bus test system using synthetic multi-device outage scenarios. Towards integrating our modeling framework with real threats and more realistic power systems, we explore applying hybrid dynamics to power systems. Our work is applied to basic RL circuits with the ultimate goal of using the methodology to model protective tripping schemes in the grid. Finally, we survey mitigation techniques for HEMP threats and describe a GIS application developed to create threat scenarios in a grid with geographic detail.
Quantifying the sensitivity - how a quantity of interest (QoI) varies with respect to a parameter – and response – the representation of a QoI as a function of a parameter - of a computer model of a parametric dynamical system is an important and challenging problem. Traditional methods fail in this context since sensitive dependence on initial conditions implies that the sensitivity and response of a QoI may be ill-conditioned or not well-defined. If a chaotic model has an ergodic attractor, then ergodic averages of QoIs are well-defined quantities and their sensitivity can be used to characterize model sensitivity. The response theorem gives sufficient conditions such that the local forward sensitivity – the derivative with respect to a given parameter - of an ergodic average of a QoI is well-defined. We describe a method based on ergodic and response theory for computing the sensitivity and response of a given QoI with respect to a given parameter in a chaotic model with an ergodic and hyperbolic attractor. This method does not require computation of ensembles of the model with perturbed parameter values. The method is demonstrated and some of the computations are validated on the Lorenz 63 and Lorenz 96 models.
Th e U.S. Strategic Petroleum Reserve (SPR) is a crude oil storage system administered by the U.S. Department of Energy. The reserve consists of 60 active storage caverns located in underground salt domes spread across four sites in Louisiana and Texas, near the Gulf of Mexico. Beginning in 2016, the SPR started executing C ongressionally mandated oil sales. The configuration of the reserve, with a total capacity of greater than 700 million barrels ( MMB ) , re quires that unsaturated water (referred to herein as ?raw? water) is injected into the storage caverns to displace oil for sales , exchanges, and drawdowns . As such, oil sales will produce cavern growth to the extent that raw water contacts the salt cavern walls and dissolves (leaches) the surrounding salt before reaching brine saturation. SPR injected a total of over 45 MMB of raw water into twenty - six caverns as part of oil sales in CY21 . Leaching effects were monitored in these caverns to understand how the sales operations may impact the long - term integrity of the caverns. While frequent sonars are the most direct means to monitor changes in cavern shape, they can be resource intensive for the number of caverns involved in sales and exchanges. An interm ediate option is to model the leaching effects and see if any concerning features develop. The leaching effects were modeled here using the Sandia Solution Mining Code , SANSMIC . The modeling results indicate that leaching - induced features do not raise co ncern for the majority of the caverns, 15 of 26. Eleven caverns, BH - 107, BH - 110, BH - 112, BH - 113, BM - 109, WH - 11, WH - 112, WH - 114, BC - 17, BC - 18, and BC - 19 have features that may grow with additional leaching and should be monitored as leaching continues in th ose caverns. Additionally, BH - 114, BM - 4, and BM - 106 were identified in previous leaching reports for recommendation of monitoring. Nine caverns had pre - and post - leach sonars that were compared with SANSMIC results. Overall, SANSMIC was able to capture the leaching well. A deviation in the SANSMIC and sonar cavern shapes was observed near the cavern floor in caverns with significant floor rise, a process not captured by SANSMIC. These results validate that SANSMIC continues to serve as a useful tool for mon itoring changes in cavern shape due to leaching effects related to sales and exchanges.
Modeling real-world phenomena to any degree of accuracy is a challenge that the scientific research community has navigated since its foundation. Lack of information and limited computational and observational resources necessitate modeling assumptions which, when invalid, lead to model-form error (MFE). The work reported herein explored a novel method to represent model-form uncertainty (MFU) that combines Bayesian statistics with the emerging field of universal differential equations (UDEs). The fundamental principle behind UDEs is simple: use known equational forms that govern a dynamical system when you have them; then incorporate data-driven approaches – in this case neural networks (NNs) – embedded within the governing equations to learn the interacting terms that were underrepresented. Utilizing epidemiology as our motivating exemplar, this report will highlight the challenges of modeling novel infectious diseases while introducing ways to incorporate NN approximations to MFE. Prior to embarking on a Bayesian calibration, we first explored methods to augment the standard (non-Bayesian) UDE training procedure to account for uncertainty and increase robustness of training. In addition, it is often the case that uncertainty in observations is significant; this may be due to randomness or lack of precision in the measurement process. This uncertainty typically manifests as “noisy” observations which deviate from a true underlying signal. To account for such variability, the NN approximation to MFE is endowed with a probabilistic representation and is updated using available observational data in a Bayesian framework. By representing the MFU explicitly and deploying an embedded, data-driven model, this approach enables an agile, expressive, and interpretable method for representing MFU. In this report we will provide evidence that Bayesian UDEs show promise as a novel framework for any science-based, data-driven MFU representation; while emphasizing that significant advances must be made in the calibration of Bayesian NNs to ensure a robust calibration procedure.
Particle heat exchangers are a critical enabling technology for next generation concentrating solar power (CSP) plants that use supercritical carbon dioxide (sCO2) as a working fluid. This report covers the design, manufacturing and testing of a prototype particle-to-sCO2 heat exchanger targeting thermal performance levels required to meet commercial scale cost targets. In addition, the the design and assembly of integrated particle and sCO2 flow loops for heat exchanger performance testing are detailed. The prototype heat exchanger was tested to particle inlet temperatures of 500 °C at 17 MPa which resulted in overall heat transfer coefficients of approximately 300 W/m2-K at the design point and cases using high approach temperature with peak values as high as 400 W/m2-K
Prediction of flow, transport, and deformation in fractured and porous media is critical to improving our scientific understanding of coupled thermal-hydrological-mechanical processes related to subsurface energy storage and recovery, nonproliferation, and nuclear waste storage. Especially, earth rock response to changes in pressure and stress has remained a critically challenging task. In this work, we advance computational capabilities for coupled processes in fractured and porous media using Sandia Sierra Multiphysics software through verification and validation problems such as poro-elasticity, elasto-plasticity and thermo-poroelasticity. We apply Sierra software for geologic carbon storage, fluid injection/extraction, and enhanced geothermal systems. We also significantly improve machine learning approaches through latent space and self-supervised learning. Additionally, we develop new experimental technique for evaluating dynamics of compacted soils at an intermediate scale. Overall, this project will enable us to systematically measure and control the earth system response to changes in stress and pressure due to subsurface energy activities.
This SAND report documents CIS Late Start LDRD Project 22-0311, "Differential geometric approaches to momentum-based formulations for fluids". The project primarily developed geometric mechanics formulations for momentum-based descriptions of nonrelativistic fluids, utilizing a differential geometry/exterior calculus treatment of momentum and a space+time splitting. Specifically, the full suite of geometric mechanics formulations (variational/Lagrangian, Lie-Poisson Hamiltonian and Curl-Form Hamiltonian) were developed in terms of exterior calculus using vector-bundle valued differential forms. This was done for a fairly general version of semi-direct product theory sufficient to cover a wide range of both neutral and charged fluid models, including compressible Euler, magnetohydrodynamics and Euler-Maxwell. As a secondary goal, this project also explored the connection between geometric mechanics formulations and the more traditional Godunov form (a hyperbolic system of conservation laws). Unfortunately, this stage did not produce anything particularly interesting, due to unforeseen technical difficulties. There are two publications related to this work currently in preparation, and this work will be presented at SIAM CSE 23, at which the PI is organizing a mini-symposium on geometric mechanics formulations and structure-preserving discretizations for fluids. The logical next step is to utilize the exterior calculus based understanding of momentum coupled with geometric mechanics formulations to develop (novel) structure-preserving discretizations of momentum. This is the main subject of a successful FY23 CIS LDRD "Structure-preserving discretizations for momentum-based formulations of fluids".