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At least 91 records · Page 5

Mitigating the Impacts of Uncertain Geomagnetic Disturbances on Electric Grids: A Distributionally Robust Optimization Approach

Severe geomagnetic disturbances (GMDs) increase the magnitude of the electric field on the Earth’s surface (E-field) and drive geomagnetically-induced currents (GICs) along the transmission lines in electric grids. These additional currents can pose severe risks, such as current distortions, transformer saturation and increased reactive power losses, each of which can lead to system unreliability. Today several mitigation actions (e.g., changing grid topology) exist that can reduce the harmful GIC effects on the grids. Making such decisions can be challenging, however, because the magnitude and direction of the E-field are uncertain and non-stationary. In this paper, we model uncertain E-fields using the distributionally robust optimization (DRO) approach that determines optimal transmission grid operations such that the worst-case expectation of the system cost is minimized. We also capture the effect of GICs on the nonlinear AC power flow equations. For solution approaches, we develop an accelerated column-and-constraint generation (CCG) algorithm by exploiting a special structure of the support set of uncertain parameters representing the E-field. Extensive numerical experiments based on “epri-21” and “uiuc-150” systems, designed for GMD studies, demonstrate (i) the computational performance of the accelerated CCG algorithm, (ii) the superior performance of distributionally robust grid operations that satisfy nonlinear, nonconvex AC power flow equations and GIC constraints, in comparison with standard stochastic programming-based methods during the out-of-sample testing.

42 ENGINEERING↗

Restoration Strategy for Active Distribution Systems Considering Endogenous Uncertainty in Cold Load Pickup

Cold load pickup (CLPU) phenomenon is identified as the persistent power inrush upon a sudden load pickup after an outage. Under the active distribution system (ADS) paradigm, where distributed energy resources (DERs) are extensively installed, the decreased outage duration can induce a strong interdependence between CLPU pattern and load pickup decisions. In this paper, we propose a novel modelling technique to tractably capture the decision-dependent uncertainty (DDU) inherent in the CLPU process. Subsequently, a two-stage stochastic decision-dependent service restoration (SDDSR) model is constructed, where first stage searches for the optimal switching sequences to decide step-wise network topology, and the second stage optimizes the detailed generation schedule of DERs as well as the energization of switchable loads. Further, to tackle the computational burdens introduced by mixed-integer recourse, the progressive hedging algorithm (PHA) is utilized to decompose the original model into scenario-wise subproblems that can be solved in parallel. The numerical test on modified IEEE 123-node test feeders has verified the efficiency of our proposed SDDSR model and provided fresh insights into the monetary and secure values of DDU quantification.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Uncertainty Quantification for Capacity Expansion Planning

This report quantifies the uncertainty in output decisions from a Capacity Expansion Planning (CEP) model. The need to understand how uncertainties within CEP models and modeling assumptions affect Quantities of Interest (QoIs) such as expansion and operating costs, as well as expansion decisions remains an ongoing challenge in scientific research and industrial operations. This area of research is particularly important for models which seek to capture how large networks will evolve and operate under increased sources of variable generation, i.e., higher penetration of renewable technologies such as solar and wind generators. Uncertainty quantification (UQ) of CEP models which estimate expansion costs and decisions, and production cost models which estimate operating costs and dispatch decisions, is a key focus of research at NREL. The Regional Energy Deployment System (ReEDS) represents a state-of-the-art CEP model and considers a range of possible grid evolutions in an attempt to identify key drivers, ramifications, and decisions which contribute to better informed investment and policy decisions. However, research to quantify how uncertainties and model assumptions, such as unit commitment (UC), within ReEDS may be affecting its outputs remains challenging due to to size and complexity of the model

24 POWER TRANSMISSION AND DISTRIBUTION↗

A Multistage Stochastic Transmission Expansion Algorithm for Wide-Area Planning under Uncertainty

The overall objective for this project was to develop and demonstrate a set of methods for solving the transmission investment problem for a large network considering many possible scenarios of future conditions and multiple decision points when investments can be made. Project sub-objectives achieved this goal through a succession of extending the methods to apply to problems with increasing complexity or additional features, including the number of decision points, whether generation and transmission are co-optimized, and whether AC or DC power flow is used. A transmission model was developed for the Western Electric Coordinating Council (WECC) region, the high-voltage transmission system that serves the western third of the continental U.S. Using a dataset provided by WECC and by researchers from John Hopkins University, we have validated and demonstrated the model and used it to compare the new method for solving multi-stage stochastic transmission planning to several state-of-the-art techniques. The project has resulted in several key outcomes and achievements: The covariance-based method for choosing a small set of hours to represent short-term variability has superior performance in terms of accuracy to existing methods, including K-means clustering and Importance Sampling; The combined partitioning method for long-term uncertainty with the nested clustering approach for choosing representative hours for each long-term group has superior accuracy for equivalent computational effort compared with existing methods; Using the partitioning/clustering method combined with Sample Average Approximation provides both statistical bounds on the quality of the solution and at the same time, a complete investment plan for all contingencies in the full uncertainty set; no existing methods can provide both at the same time; The method is demonstrated to work well for choosing both transmission and generation investments; A variant on the method allows for both scenario selection and simultaneous correction for the error from the DC power flow approximation to provide a tractable method for AC power flow-based transmission planning under uncertainty; The method applied to the WECC case study demonstrates the additional value to the system operator and the consumer of identifying flexible investment options in the near-term decisions. In particular, the case study exhibits significant option value in postponing some transmission additions that appear useful but in some long-term system states create new congestion problems.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Resilience Development for Electric Energy Delivery Sytems (ResDEEDS): A Tool for Power System Resilience Planning (Rev. 1)

The INL Resilience Framework is built to be customized to a particular system’s characteristics, resilience goals, and hazards that it is likely to face. The challenge with a framework that is built to be customized is that it requires more effort from the user to understand the framework and apply it correctly to a particular system. The goal of the web application described here is to automate the framework application as much as possible. Inputs from users are standardized into a common format, but the modeling platform used is a modular framework built to adapt to any system. Baseline effects from common hazards are programmed with stochastic variables to allow for quick exploration of hazard impacts, but can be customized down to component-level impact if a user desires a high level of detail and specificity.

17 WIND ENERGY↗

Residuals-based distributionally robust optimization with covariate information

We consider data-driven approaches that integrate a machine learning prediction model within distributionally robust optimization (DRO) given limited joint observations of uncertain parameters and covariates. Our framework is flexible in the sense that it can accommodate a variety of regression setups and DRO ambiguity sets. We investigate asymptotic and finite sample properties of solutions obtained using Wasserstein, sample robust optimization, and phi-divergence-based ambiguity sets within our DRO formulations, and explore cross-validation approaches for sizing these ambiguity sets. Through numerical experiments, we validate our theoretical results, study the effectiveness of our approaches for sizing ambiguity sets, and illustrate the benefits of our DRO formulations in the limited data regime even when the prediction model is misspecified.

97 MATHEMATICS AND COMPUTING↗

Assignment of Freight Traffic in a Large-scale Intermodal Network under Uncertainty

This paper presents a methodology for freight traffic assignment in a large-scale road-rail intermodal network under uncertainty. Network uncertainties caused by natural disasters have dramatically increased in recent years. Several of these disasters (e.g., Hurricane Sandy, Mississippi River Flooding, and Hurricane Harvey) severely disrupted the U.S. freight transportation network, and consequently, the supply chain. To account for these network uncertainties, a stochastic freight traffic assignment model is formulated. An algorithmic framework, involving the sample average approximation and gradient projection algorithm, is proposed to solve this challenging problem. The developed methodology is tested on the U.S. intermodal network with freight flow data from the Freight Analysis Framework. The experiments consider three types of natural disasters that have different risks and impacts on transportation networks: earthquakes, hurricanes, and floods. It is found that for all disaster scenarios, freight ton-miles are higher compared to the base case without uncertainty. The increase in freight ton-miles is the highest under the flooding scenario; this is because there are more states in the flood-risk areas, and they are scattered throughout the U.S.

42 ENGINEERING↗

mpi-sppy: Optimization Under Uncertainty for Pyomo

We introduce a new Pyomo extension for optimization under uncertainty, mpi-sppy. This extension allows for the mixing of, and sharing of information between, various algorithmic approaches for optimization under uncertainty. We will discuss the underlying architecture and assess the performance and scalability of mpi-sppy on various systems, including HPC clusters.

27 ARPA - Advanced Research Projects Agency-Energy↗

Data and Multistage Optimization for the New Grid

Three essential capabilities for using exascale computing resources on next generation power grid applications are: generating large renewable energy datasets, modeling damage and operations during and after extreme events, and employing multi-stage optimization for infrastructure planning. Powerscenarios, developed as part of the ExaSGD project, addresses these capabilities by enabling users to build synthetic wind farms for large test systems using numerical weather prediction-based data sources. We share examples of using Powerscenarios to build out wind farms on the ACTIVSg2000 test system, to enable simulated operations and emergency asset allocation during a hurricane strike, and to compute multi-stage infrastructure buildouts.

economic dispatch↗

Evolution of Scenario Generation Capabilities in the ExaSGD Project

High-fidelity renewable energy scenarios and rare-event high-impact contingencies are essential for modeling operations and infrastructure expansion of the next generation power grids using exascale computing resources. As the ExaSGD project progressed, our capabilities for generating scenarios for modeling wind power output at multiple wind farms significantly improved, evolving from the use of independent random perturbations to importance sampling-based techniques capturing representative spatial-temporal relations. Contingency generation also improved, evolving from standard N-1 techniques to probabilistic models of infrastructure damage resulting from extreme weather events. We review the developments in the realistic intermittent-energy scenario forecasting and extreme-event contingency creation as the ExaSGD project progressed and discuss the future work in these areas.

economic dispatch↗

A shared-mobility-based framework for evacuation planning and operations under forecast uncertainty

To meet evacuation needs from carless populations who need personalized assistance to evacuate safely, in this article we propose a ridesharing-based evacuation program that recruits volunteer drivers before a disaster strikes, and then matches volunteer drivers with evacuees once demand is realized. Here we optimize resource planning and evacuation operations under uncertain spatiotemporal demand, and construct a two-stage stochastic mixed-integer program to ensure high demand fulfillment rates. We consider three formulations to improve the number of evacuees served, by minimizing an expected penalty cost, imposing a probabilistic constraint, and enforcing a constraint on the conditional value at risk of the total number of unserved evacuees, respectively. We discuss the benefits and disadvantages of the different risk measures used in the three formulations, given certain carless population sizes and the variety of evacuation modes available. We also develop a heuristic approach to provide quick, dynamic and conservative solutions. We demonstrate the performance of our approaches using five different networks of varying sizes based on regions of Charleston County, South Carolina, an area that experienced a mandatory evacuation order during Hurricane Florence, and utilize real demographic data and hourly traffic count data to estimate the demand distribution.

97 MATHEMATICS AND COMPUTING↗

Patchy snapshots of nuclear chain reactions

Stochastic fluctuations of the neutron population within a nuclear reactor are typically prevented by operating the core at a sufficiently high power. This regime, where the evolution of the neutron density is essentially deterministic, is key for automatic protection and safety systems to safely detect unwanted power excursions during an accident, and to rapidly initiate a reactor trip procedure in case it is needed. Recent works, supported by numerical simulations, have however reported that, for large reactors, the branching nature of the fission reactions might induce strongly non-Poissonian patterns in the neutron spatial distribution, and that stochastic fluctuations might still persist at reactor powers close to operating conditions (startup phase). An international program conducted by LANL, IRSN and CEA was therefore setup to experimentally detect and characterize such fluctuations and correlations. An experiment took place in 2017 at the Reactor Critical Facility (RCF) of the Rensselaer Polytechnic Institute (USA). In this paper we will report the main findings of this experimental program, supported by stochastic models and by the development of a dedicated high-fidelity Monte Carlo simulation code. We will in particular describe and explain the strong patchiness in neutron power distributions measured at the RCF, as well as a peculiar ‘blinking’ behavior of the core, and discuss the consequences of these findings on nuclear safety.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Demand response event simulator and risk-aware bidding tool for industrial customers

Incentive Based Demand Response (IBDR) program participation delivers financial benefits to the consumers and resiliency benefits to the electricity grid. Effectively participating in these programs as an industrial consumer requires bidding strategies that balance financial risk with operational constraints. Existing bidding tools tend not to fully incorporate stochastic IBDR event modeling, program specific baseline and payment/penalty calculations, or demand reduction process control schemes that account for the cascading impacts of shutdown in complex facilities. Here, this work presents an IBDR event simulator and risk-aware bidding framework tool integrating three key components: a flexible, parameterized demand response event generator that rigorously accounts for program structures and stochasticity, a demand response operational simulation model that generates explicit control strategies for load reduction, and a Monte Carlo simulator to evaluate financial risk for varied capacity bids. A case study at a wastewater treatment plant participating in PG&E's Capacity Bidding Program demonstrates the framework's utility. In the peak capacity price month of August, optimal bidding by the wastewater treatment plant nets a mean IBDR benefit of $101,000 (67% of the August electricity bill) with 0.4% probability of a financial loss. This framework enables industrial operators to make informed bidding decisions, negotiate better program terms with demand response load aggregators, and analyze energy flexibility investments at their facilities. Ultimately, this work reduces participation barriers in IBDR programs and supports the broader goal of enhancing grid reliability and renewable energy integration.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Strategic Placement and Sizing of Distributed Generation for Resilience Enhancement of Distribution Grids With Microgrid Formation

The rise in frequency and severity of extreme weather events highlights the need for resilient power distribution networks. Microgrids can help improve the resilience of distribution grids by providing continuous power supply using local distribution generation (DG) when the distribution grid fails. In this paper, we propose an approach for optimal placement and sizing of DG to form multiple microgrids throughout the distribution network by restoration actions such as switching operations in case of distribution grid outages caused by extreme weather events. Considering the randomness of damaged distribution lines, the DG placement and sizing problem is formulated as a two-stage stochastic mixed-integer program, with the first stage determining the placement and size of DG, and the second stage focusing on minimizing the amount of load shedding through network restoration and microgrid formations for each scenario. Due to the large number of scenarios, the sample average approximation (SAA) method is employed to solve the problem. The results of case studies on a modified IEEE 33 bus distribution grid demonstrate the effectiveness of the proposed DG placement and sizing strategy in improving the resilience of distribution grids by allowing the formation of multiple microgrids. In addition, the robustness and accuracy of the SAA method are validated through various case studies.

Distributed generation planning↗

From zonal to nodal capacity expansion planning: Spatial aggregation impacts on a realistic test-case

Solving power system capacity expansion planning (CEP) problems at realistic spatial resolutions is computationally challenging. Thus, a common practice is to solve CEP over zonal models with low spatial resolution rather than over full-scale nodal power networks. Due to improvements in solving large-scale stochastic mixed integer programs, these computational limitations are becoming less relevant, and the assumption that zonal models are realistic and useful approximations of nodal CEP is worth revisiting. Here, this work is the first to conduct a systematic computational study on the assumption that spatial aggregation can reasonably be used for ISO-scale CEP. By considering a realistic, large-scale test network based on the state of California with over 8000 buses, we find that well-designed small spatial aggregations can yield good approximations but that coarser zonal models may result in large distortions of investment decisions, e.g., capacity under-investment of up to 41% for the lowest resolution model considered.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Multistage distributionally robust mixed-integer programming with decision-dependent moment-based ambiguity sets

We study multistage distributionally robust mixed-integer programs under endogenous uncertainty, where the probability distribution of stage-wise uncertainty depends on the decisions made in previous stages. We first consider two ambiguity sets defined by decision-dependent bounds on the first and second moments of uncertain parameters and by mean and covariance matrix that exactly match decision-dependent empirical ones, respectively. For both sets, we show that the subproblem in each stage can be recast as a mixed-integer linear program (MILP). Moreover, we extend the general moment-based ambiguity set in to the multistage decision-dependent setting, and derive mixed-integer semidefinite programming (MISDP) reformulations of stage-wise subproblems. We develop methods for attaining lower and upper bounds of the optimal objective value of the multistage MISDPs, and approximate them using a series of MILPs. We deploy the Stochastic Dual Dynamic integer Programming (SDDiP) method for solving the problem under the three ambiguity sets with risk-neutral or risk-averse objective functions, and conduct numerical studies on multistage facility-location instances having diverse sizes under different parameter and uncertainty settings. Furthermore, our results show that the SDDiP quickly finds optimal solutions for moderate-sized instances under the first two ambiguity sets, and also finds good approximate bounds for the multistage MISDPs derived under the third ambiguity set. We also demonstrate the efficacy of incorporating decision-dependent distributional ambiguity in multistage decision-making processes.

97 MATHEMATICS AND COMPUTING↗