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A Data-Driven Nonparametric Approach for Probabilistic Load-Margin Assessment Considering Wind Power Penetration

A modern power system is characterized by an increasing penetration of wind power, which results in large uncertainties in its states. These uncertainties must be quantified properly; otherwise, the system security may be threatened. Facing this challenge, here we propose a cost-effective, data-driven approach to assessing a power system's load margin probabilistically. Using actual wind data, a kernel density estimator is applied to infer the nonparametric wind speed distributions, which are further merged into the framework of a vine copula. The latter enables us to simulate complex multivariate and highly dependent model inputs with a variety of bivariate copulae that precisely represent the tail dependence in the correlated samples. Furthermore, to reduce the prohibitive computational time of traditional Monte-Carlo simulations that process a large amount of samples, we propose to use a nonparametric, Gaussian-process-emulator-based reduced-order model to replace the original complicated continuation power-flow model through a Bayesian-learning framework. To accelerate the convergence rate of this Bayesian algorithm, a truncated polynomial chaos surrogate, which serves as a highly efficient, parametric Bayesian prior, is developed. This emulator allows us to execute the time-consuming continuation power-flow solver at the sampled values with a negligible computational cost. Results of simulations that are performed on several test systems reveal the impressive performance of the proposed method in the probabilistic load-margin assessment.

17 WIND ENERGY↗

Interpretable Data-Driven Probabilistic Power System Load Margin Assessment with Uncertain Renewable Energy and Loads

The increasing uncertainties caused by the high-penetration of stochastic renewable generation resources poses a significant threat to the power system voltage stability. To address this issue, this paper proposes a probabilistic deep kernel learning enabled surrogate model to extract the hidden relationship between uncertain sources, i.e., wind power and loads, and load margin for probabilistic load margin assessment (PLMA). Unlike other deep learning approaches, a kernel SHAP provides the sensitivity analysis as well as interpretability of the inputs to outputs influences. This allows identifying the critical factors that affect load margin so that corrective control can be initiated for stability enhancement. Numerical results carried out on the IEEE 118-bus power system demonstrate the accuracy and efficiency of the proposed data-driven PLMA scheme.

deep kernel learning↗

Characteristics of locational uncertainty marginal price for correlated uncertainties of variable renewable generation and demands

With the rapid increase of variable renewable energy sources in power systems, how to manage and price the uncertainty of renewable resources’ power outputs is becoming an urgent issue. Current market designs considering the uncertainties are mainly based on the probabilistic scenario set of demand and renewable energy resources power outputs. This consideration makes market designs vulnerable to three significant challenges when put into practice. First, the accurate probability distribution of renewable generation is hard to obtain in real-time. Second, it is challenging to clear the market timely with many scenarios to guarantee accuracy. Third, generation cost recovery cannot be guaranteed for some scenarios. To overcome these challenges, this paper proposes a locational uncertainty marginal price model to price the uncertainty explicitly based on a scenario-free stochastic market-clearing model. Instead of using the probabilistic scenario set, the uncertainty of renewable energy sources and loads is modeled with distributionally-robust chance constraints. The correlation of uncertainties can be endogenously modeled in both the market-clearing and the locational uncertainty marginal price formation. Furthermore, this paper proves that generation cost recovery, revenue adequacy, and partial market equilibrium can be achieved using the locational uncertainty marginal price model. Numerical results from both the small and large systems simulations validate that the generation cost recovery is maintained no matter the generation participates in uncertainty mitigation or not. The transmission congestion surplus is also allocated appropriately among loads, renewable energy sources, and financial transmission right owners.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Managing Solar Photovoltaic Integration in the Western United States: Resource Adequacy Considerations

This study examines the impact of reserve margin-based reliability assessment, as commonly used in capacity expansion models, on planning resource-adequate power systems under high penetrations of solar photovoltaics (PV). As a generation resource, PV is operationally different from the conventional dispatchable resources for which most capacity expansion models were designed. The question this study attempts to answer is whether large amounts of PV on a system (in this case, the Western Interconnection of North America) would bias the results of conventional reserve margin-based capacity expansion modeling towards an over- or under-provisioning of resource adequacy. This analysis used NREL’s Resource Planning Model (RPM) for capacity expansion modeling and NREL’s Probabilistic Resource Adequacy Suite (PRAS) for resource adequacy assessment. RPM uses a reserve margin requirement to enforce resource adequacy. PRAS, a collection of tools for studying the resource adequacy of power systems and the adequacy contributions of individual resources on a probabilistic basis, was used to compute multiple resource adequacy metrics across a number of simulated scenarios and system representations with differing regional detail. In all cases, including high PV penetrations (up to 33% annual generation from PV, interconnection-wide), RPM was able to produce resource-adequate systems as measured by normalized expected unserved energy and loss-of-load expectation results from PRAS. The accuracy of reserve margin approaches depends heavily on the underlying assumptions informing the capacity credit assigned to variable and energy-limited resources, particularly when such resources are abundant in the modeled system. RPM’s standard methodology for estimating variable and flexible resources’ capacity contributions, which is based on the top 100 hours of net load, did not appear to systematically undervalue or overvalue variable generation relative to a more rigorous equivalent firm capacity assessment using PRAS, although both over- and under-valuations were observed in specific scenarios. In the worst cases, the top 100 hour method underestimated the equivalent firm capacity of PV by two percentage points, and overestimated the equivalent firm capacity of PV by five percentage points. Calculating capacity contributions based on the top 10 hours of net load systematically underestimated equivalent firm capacities at more modest PV penetrations, but was often a better approximation of equivalent firm capacity than the existing 100-hour approach in scenarios with higher PV penetrations.

14 SOLAR ENERGY↗

Data-Driven Probabilistic Anomaly Detection for Electricity Market under Cyber Attacks

Information and communication technologies have been widely used in smart grid for efficient operation. However, these technologies are vulnerable to malicious cyber attacks, which may lead to severe reliability and economic issues. Recently, a variety of data-driven anomaly detection approaches have been explored to detect potential cyber attacks in smart grids. In this paper, we researched on the electricity market data aiming to identify anomalies from the locational marginal prices (LMPs) and provide a new indicator for potential cyber attacks in power grids. Specifically, a novel data-driven probabilistic anomaly detection framework is proposed for electricity market, which consists of three major components: long short-term memory (LSTM) based deterministic electricity price forecasting, probabilistic electricity price forecasting and anomaly detection. This framework is tested on a model-based electricity market simulator under two types of cyber attacks, i.e., load redistribution attack (LRA) and price responsive attack (PRA). Numerical results on the simulated LMPs show that the proposed framework is capable of detecting data anomalies over these attacks.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

ASME Design Code Rule Changes for Nuclear Graphite

The American Society of Mechanical Engineers Boiler Pressure and Vessel Code (ASME BPVC) Section III, Division 5, Article HHA-3000 outlines graphite core component and graphite core assembly design guidelines. Graphite core components are defined as ?components manufactured from graphite that are installed to form a graphite core assembly within the reactor pressure vessel of a high temperature, graphite moderated fission reactor.? (p. 413) Graphites? inherent defect distributions do not allow for deterministic material reliability. Rather, graphite has variable strength distributions which change by grade. Article HHA-3000 outlines two semi-probabilistic methods, the full and simplified assessments, which set design load limit targets for each of three component structural reliability classes. The Design Task Group was officially recognized as a specialized task group within ASME November of 2023, though we?ve been collaborating since 2022. The purpose of the Design Task Group is to correct, clarify, and make HHA-3000 function as intended. The Design Task Group will sunset once we?ve achieved our objectives. The Design Task Group was specifically told to not write new Code. While there may be more precise and more accurate methods to determine reliability targets, the current methods are conservative, relatively simple to implement, and have thus far been considered satisfactory for setting design reliability targets. Much of the ground-work to write proposal files and background documents for records to make the changes needed to achieve our objective have been completed. The Design Task Group has documented much of their work through papers, presentations, and memorandums. Three memorandums in which INL team members had substantial contributions are found in the Appendices: FEA Modeling for the Baseline Program, Evaluating the Effects on Margin of Updating the Threshold and Shape Parameters in the Full Assessment, and Interpretations of the Full and Simplified Assessments in ASME BPVC. Most of the on-going work to achieve the Design Task Group?s objective will be addressing comments on existing records and moving records through the balloting process. The Design Task Group met bi-weekly mostly through the end of FY2023. Since February 2024, the Design Task Group has mostly been completed with solving and documenting the technical issues associated with the assessments. Unless new tasks are identified, the remaining work of the Design Task Group will be political and editorial.

97 MATHEMATICS AND COMPUTING↗

Evaluating design safety margins in the American Society of Mechanical Engineers graphite core components design-by-analysis assessments

Graphite is an important material being used for core components in next-generation high-temperature gas-cooled nuclear reactors. The selection of graphite grade for a specific Designer is a complex task, dependent on reactor conditions, component functionality, and required reliability. The American Society of Mechanical Engineers (ASME) provides two semi-probabilistic design-by-analysis assessments to evaluate graphite core components against design reliability targets. The simplified assessment uses a 2-parameter Weibull distribution to describe the graphite grade’s tensile-strength distribution to establish component stress limits. The full assessment uses the 3-parameter Weibull distribution and a modified Weakest-Link Theory approach to calculate a component design probability of failure. The paper defines recommended assessment rules, which are the as-written simplified assessment and the full assessment with parameter lower bounds, the modulus update with threshold reduction, and the 2027 grouping rules. Code rules are applied to three grades: 2114, IG-110, and NBG-18. The baseline margin calculation is developed using the experimental tensile dogbone specimen. Percent margin is defined as the percent reduction in the median experimental load to obtain the allowable load per ASME assessments. Under the recommended rules, the SRC–1 margin in the simplified assessment ranged from 40.2 % to 52.7 % among the grades in this study and from 36.1 % to 49.8 % in the full assessment. The full assessment only decreases the margins by 2.5–4.5 % for the SRC-1 components and 0–1.5 % for the SRC-2 components for this baseline case. Margin is inversely related to material median strength (i.e., the strongest grade, 2114, has the lowest margin).

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗