Uncertain and negative evidence in continuous time Bayesian networks
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This paper presents a novel bidding curve design algorithm tailored for hybrid power plants (HPPs) to participate in the wholesale electricity market. Utilizing forecasts for photovoltaic (PV) generation and available battery power, our algorithm strategically computes the bidding curve to maximize HPP profit while adeptly managing the inherent uncertainty associated with PV power generation. In addition, the introduction of the penalty cost in HPP bidding curves provides the system operator a tool to effectively manage the system-level uncertainty that caused by HPPs. Numerical analysis through Monte Carlo simulations confirms that our bidding curve methodology outperforms the benchmark across various scenarios.
Presented here is a modular methodology for time-domain stochastic seismic wave propagation analysis. Presented methodology is designed to analyse uncertain seismic motions as an input, propagating through uncertain material. Traditional approach for uncertain wave propagation relies on models that include deep bedrock, local soil site, and their random process and random field information. Such models can become quite large and computationally intractable. The modular approach proposed herein features two step approach that allows separate consideration of the deep bedrock and local site along with corresponding random field information. In this work, the first step considers an auxiliary stochastic motions problem in the bedrock. Stochastic local site response can then be simulated in a reduced domain within certain depth from the surface. Application of uncertain seismic motions at depth, for local uncertain site response is done using stochastic effective forces developed through the Domain Reduction Method. By using Hermite polynomial chaos expansion to represent the non-Gaussian random field of material parameters and non-stationary random process of seismic motion, the proposed modular methodology is formulated using intrusive stochastic Galerkin approach, as seen in the Stochastic Elastic–Plastic Finite Element Method (SEPFEM). Developed modular methodology is illustrated using a 1-D stochastic seismic wave propagation analysis with three cases, and simulation results are also verified with results from conventional approach.
Robust stabilization of uncertain systems has been extensively investigated and the stability test for the whole set of uncertain parameters has been reduced to a finite number of test points, four points for the characteristic polynomial with independent coefficients. As a result the robust stability margin can be determined using a reasonable amount of computation. It is impossible to apply the results of the test to a practical system as the coefficients of the characteristic polynomial for a physical system are usually functions of uncertain parameters. However, many physical systems may be represented by a second-order mass-spring-damper system with a special multilinear form in its characteristic polynomial. This paper investigates second-order mass-spring-damper systems and the reduction of the number of test points. It is shown that such a system with arbritrary compensators always has a multilinear characteristic polynomial. It is also shown that a line in the two-dimensional parameter space forms the boundary after the mapping of a multilinear characteristic polynomial and this interior extreme line forms a conic curve in the complex plane. The boundary of uncertain domain for a multilinear polynomial with two uncertainty parameters can be determined analytically using this curve, and the four sides image of a square of the uncertain parameter. Therefore, the stability margin may be determined by checking the intersections of the boundary with the zero point. A similar procedure can be used for second-order systems with more than two uncertainty parameters when parameter optimization is used in determining the boundary.
The integration of large-scale uncertain and uncontrollable wind and solar power generation has brought new challenges to the operations of modern power systems. In a power system with abundant water resources, hydroelectric generation with high operational flexibility is a powerful tool to promote a higher penetration of wind and solar power generation. In this paper, we study the day-ahead scheduling of a thermal-hydro-wind-solar power system. The uncertainties of renewable energy generation, including uncertain natural water inflow and wind/solar power output, are taken into consideration. We explore how the operational flexibility of hydroelectric generation and the coordination of thermal-hydro power can be utilized to hedge against uncertain wind/solar power under a multistage robust optimization (MRO) framework. To address the computational issue, mixed decision rules are employed to reformulate the original MRO model with a multi-level structure into a bi-level one. Column-and-constraint generation (C &CG) algorithm is extended into the MRO case to solve the bi-level model. The proposed optimization approach is tested in three real-world cases. Furthermore, the computational results demonstrate the capability of hydroelectric generation to promote the accommodation of uncertain wind and solar power.
Global sensitivity analysis (GSA) of the voltage to uncertain power injection variations plays an important role for appropriate Volt-VAR optimization. This paper proposes a data-driven GSA method for large-scale distribution systems with a large number of uncertain sources. Specifically, the deep Gaussian process is used to identify the mapping relationship between uncertain power injections and voltages. This allows us to resort to the analysis of variance framework to calculate the Sobol indices for GSA. Unlike the existing polynomial chaos expansion and Gaussian process-based approaches, our proposed method has much better scalability. Test results on the EPRI 1747-node K1 circuit with a different number and different probability distributions of uncertain sources demonstrate that the proposed method can achieve accurate GSA under various conditions.
This work proposes a physics-informed sparse Gaussian process (SGP) for probabilistic stability assessment of large-scale power systems in the presence of uncertain dynamic PVs and loads. The differential and algebraic equations considering uncertainties from dynamic PVs and loads are reformulated to a nonlinear mapping relationship that allows the application of SGP. Thanks to the nonparametric characteristic of Gaussian process, the proposed framework does not require distributions of uncertain inputs and this distinguishes it from existing approaches. As the original Gaussian process is not scalable to large-scale systems with high dimensional uncertain inputs, this paper develops the SGP with a stochastic variational inference technique. It leads to approximately two orders of complex reduction. A data pre-processing step is also introduced to tackle the coexistence of stable and unstable cases by sample clustering and constructing separate SGPs. The probabilistic transient stability index is analyzed to assess system stability under different uncertain dynamics loads and PVs. Comparisons are performed with the sampling-based, the polynomial chaos expansion-based, and traditional Gaussian process-based methods on the modified IEEE 118-bus and Texas 2000-bus systems under various scenarios, including different levels of uncertainties and the existence of nonlinear correlations among dynamic PVs. The impacts of data quality and quantity issues are also investigated. It is shown that the proposed SGP achieves significantly improved computational efficiency while maintaining high accuracy with a limited number of data.
WIYN/Hydra spectra (R ∼ 13,500, signal-to-noise pixel{sup −1} = 50–1000) of a 400 Å region around Li 6708 Å are used to determine radial and rotational velocities for 287 photometrically selected candidate members of the open cluster M48. The sample ranges from turnoff A stars to late-K dwarfs and eight giants. We combine our V {sub RAD} measurements and power spectrum analysis with parallax and proper motion data from Gaia DR2 to evaluate membership and multiplicity. We classify 152 stars as single cluster members, 11 as binary members, 16 as members of uncertain multiplicity, 56 as single nonmembers, 28 as single “likely” nonmembers, two as single “likely” members, one as a binary “likely” member, five as binary nonmembers, 10 as “likely” members of uncertain multiplicity, three as nonmembers of uncertain multiplicity, and three as “likely” nonmembers of uncertain multiplicity. From a subsample of 95 single members, we derive V {sub RAD} = 8.512 ± 0.087 km s{sup −1} (σ {sub μ}, and σ = 0.848 km s{sup −1}). Using 16 isolated Fe I lines for a subsample of 99 single members (that have σ{sub T{sub e{sub f{sub f}}}}<75 K (from 10 colors from UBVRI), v sin i < 25 km s{sup −1}, and well-behaved Fe I lines), [Fe/H]{sub M48} = −0.063 ± 0.007 dex (σ {sub μ}). [Fe/H] is independent of T {sub eff} over an unprecedentedly large range of 2500 K. The minimum cluster binary fraction is 11%–21%. M48 exhibits a clear but modest broadening of the main-sequence turnoff, and there is no correlation between color and v sin i.
Invited Talk at AGU Fall Meeting 2023 Modeling how human institutions and infrastructure interact with the water cycle is essential to better understand the vulnerability, and resilience of water resources systems from the local to the global scale. This is especially true when investigating multi-sector, multi-actor responses to the effects of long-term changes and short-term shocks. It is also well recognized that uncertainty present throughout the modeling cycle (e.g., in data, functional relations, and model coupling approaches) limits our ability to trace the interactive dynamics of human-water systems, as well as to quantify their implications for management and planning. Systems with large numbers of diverse stakeholders further compound this challenge, as uncertain drivers and complex dynamics might have very disparate effects on water users. The work presented is conducted through the Integrated Multisector Multiscale Modeling (IM3) Science Focus Area, which explores how human and natural systems co-evolve in response to change. Through this multi-year effort, we have developed exploratory modeling methods to better characterize how the uncertain human and natural drivers of water scarcity yield consequential vulnerabilities in institutionally complex, multi-sectoral systems. This talk will specifically present on a series of uncertainty characterization experiments performed in the Upper Colorado River Basin, a sub-basin of the Colorado with thousands of water users. These complementary and systematic experiments are aimed at understanding: How are various uncertain stressors (e.g., climate change, demand growth) affecting the diverse water users of this basin in terms of water shortage? What are the key drivers of this shortage for each user? Methods and results from this work are used to address additional questions on the ability of adaptation to modulate the effects of these uncertain drivers, and on their compounding effects across spatial scales and through sectoral interactions.
Viewgraphs and a paper on parametric uncertainty modeling for application to robust control are included. Advanced robust control system analysis and design is based on the availability of an uncertainty description which separates the uncertain system elements from the nominal system. Although this modeling structure is relatively straightforward to obtain for multiple unstructured uncertainties modeled throughout the system, it is difficult to formulate for many problems involving real parameter variations. Furthermore, it is difficult to ensure that the uncertainty model is formulated such that the dimension of the resulting model is minimal. A procedure for obtaining an uncertainty model for real uncertain parameter problems in which the uncertain parameters can be represented in a multilinear form is presented. Furthermore, the procedure is formulated such that the resulting uncertainty model is minimal (or near minimal) relative to a given state space realization of the system. The approach is demonstrated for a multivariable third-order example problem having four uncertain parameters.
Earth observing (EO) mission portfolios provide data on many geophysical parameters that collectively inform our understanding of the Earth system. To observe large-scale climate trends, it is important to collect data on many parameters over time. However, gaps may occur between missions due to formulation complexity, development delays, and uncertain events in operations. These gaps may impact the ability to provide sustained measurements. Developing a balanced EO mission portfolio is key to supporting study of the Earth system. Yet, decision-making at the portfolio level is a complex task because missions often address multiple parameters. Currently, the likelihood of data gaps is often assessed for an individual parameter, but decisions and events can impact data collection for many parameters. This poster introduces a modeling approach that supports management of the many parameter impacts of decisions and uncertain events. The approach provides a foundation for analyzing changeability in EO mission portfolios. Changeability analysis provides insight into a portfolio’s sensitivity to changes caused by decisions or uncertain events. The model is developed to analyze two aspects of changeability, robustness and flexibility, in EO mission portfolios. In context of these portfolios, the authors define robustness as a portfolio’s ability to provide sustained measurements despite future uncertainties, and they define flexibility as the availability of decision alternatives that contribute to parameter coverage at little detriment to the rest of the portfolio. The proposed model characterizes a portfolio’s sensitivity to change by capturing mission-parameter interconnectivity and redundancy in parameter coverage. The model can be analyzed to identify events that can create substantial gaps, thereby revealing focus areas for mitigation efforts. The model can also be analyzed to identify gap mitigation decisions that may improve parameter coverage with little detriment to the rest of the portfolio, thereby revealing favorable pathways for portfolio improvement. Developing a process for identifying these threats and opportunities will be the focus of future work. A parallel poster proposes a standard for visualizing and communicating portfolio-level impacts of decisions and uncertain events.
A strategy that calculates an explicit state feedback policy to regulate constrained uncertain discrete‐time uncertain linear systems is presented. We consider uncertain processes, affected by box‐bounded multiplicative uncertainty as well as bounded additive uncertainty with linear state and inputs constraints. The proposed method includes (i) the calculation of a terminal set constraint and (ii) the robust reformulation of state constraints in the prediction horizon. These features allow the derivation of the desired policy by solving a single multiparametric quadratic programming problem that guarantees feasible operation in the presence of uncertainty. Additionally, we employ variable and constraint elimination approaches to enhance the computational performance of the strategy. We demonstrate the steps and benefits of these developments with a numerical example and a chemical engineering case study.
Simulating subsurface contaminant transport at the kilometer-scale often entails modeling reactive flow and transport within and through complex geologic structures. These structures are typically meshed by hand and as a result geologic structure is usually represented by one or a few deterministically generated geological models for uncertainty studies of flow and transport in the subsurface. Uncertainty in geologic structure can have a significant impact on contaminant transport. In this study, the impact of geologic structure on contaminant tracer transport in a shale formation is investigated for a simplified generic deep geologic repository for permanent disposal of spent nuclear fuel. An open-source modeling framework is used to perform a sensitivity analysis study on transport of two tracers from a generic spent nuclear fuel repository with uncertain location of the interfaces between the stratum of the geologic structure. The automated workflow uses sampled realizations of the geological structural model in addition to uncertain flow parameters in a nested sensitivity analysis. Concentration of the tracers at observation points within, in line with, and downstream of the repository are used as the quantities of interest for determining model sensitivity to input parameters and geological realization. Finally, the results of the study indicate that the location of strata interfaces in the geological structure has a first-order impact on tracer transport in the example shale formation, and that this impact may be greater than that of the uncertain flow parameters.