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At least 1,621 records · Page 90

Communication: Relationship between solute localization and diffusion in a dynamically constrained polymer system

We investigate the link between dynamic localization, characterized by the Debye–Waller factor, 〈u{sup 2}〉, and solute self-diffusivity, D, in a polymer system using atomistic molecular dynamics simulations and vapor sorption experiments. We find a linear relationship between lnD and 1/〈u{sup 2}〉 over more than four decades of D, encompassing most of the glass formation regime. The observed linearity is consistent with the Langevin dynamics in a periodically varying potential field and may offer a means to rapidly assess diffusion based on the characterization of dynamic localization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Evolution of Astrodynamics for Multibody Environments, Numerical Precision and Dynamical Understanding

The innovative nature of dynamical systems theory and its applications in trajectory design enabled many recent missions by opening up new transfer and capture opportunities to meet mission requirements, reduce fuel costs, and address various launch constraints and contingencies. With a combination of proven numerical methods and an advanced understanding of the dynamics, an ‘experienced’ user can rapidly design multibody and cislunar missions such as Lunar IceCube and Artemis/Themis and relatively quickly conceive trajectory concepts for Sun-Earth mission orbits, such as the Space Weather Follow On-L1 Lissajous orbit—one that can be achieved and maintained.

Dynamical Systems↗

Efficient and Robust Dynamic Simulation of Power Systems With Holomorphic Embedding

Dynamic simulation is vitally important in power system analysis, but traditional approaches based on numerical integration over small time steps are time-consuming. Also, the Newton-Raphson method suffers from difficulty in convergence when solving nonlinear algebraic equations. In this paper, we propose a novel dynamic simulation approach based on holomorphic embedding. By obtaining a high-order approximation of system dynamics, it achieves a much larger time step and thus enhances the computational efficiency significantly. In addition, the new approach avoids non-convergence issues in solving algebraic equations, which improves robustness. The approach includes flexible modeling of synchronous generators and controllers, and we propose a method for modeling generator coordinate transformations. The approach is tested on the IEEE 39-bus, 10-generator system and a Polish 2383-bus, 327-generator system. The results demonstrate promising computational efficiency and satisfactory numerical robustness for the analysis of large-scale power systems.

42 ENGINEERING↗

Certification and prediction of post-disturbance states in dynamic security assessment

Dynamic security assessment usually involves the simulation of system dynamics under large disturbances. The instant large disturbance occurs, the post-disturbance state of the system could deviate significantly from the pre-disturbance one. It is desirable and necessary to develop an efficient method to certify the existence of state and predict the approximate post-disturbance state because: (1) faster warning can be made in online assessment; and (2) the dynamic simulator can be given better initial values to calculate precise solutions, which prevents convergence failure brought on by poor initial values. We propose a novel approach for efficiently certifying and predicting the post-disturbance states in dynamic security assessment. Based on the fixed-point power flow mapping approach applied to salient pole generator models, the criterion for determining the existence and uniqueness of the post-disturbance solution is derived, and the bounds of post-disturbance solution can be rigorously characterized.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Introduction to the Bioproduct Transition Dynamics Model

The U.S. Department of Energy, Bioenergy Technologies Office has a broad understanding of different conversion processes that produce bioproducts (chemicals derived from biomass feedstocks) and the market attributes of those processes. However, bioproducts have in many cases proven to be difficult to scale up to commercial production and bring to market, and there is currently a need for greater understanding around the possible successful scenarios for advancing the bioproducts industry. Insight into the myriad factors that impact the success of individual bioproducts and the growth of the bioproducts industry will enable bioproduct stakeholders to evaluate strategies for development and investment that could achieve the greatest impact. An understanding of these factors will also enable the identification of synergies between the bioproducts and biofuels industries that occur through shared learning and co-production. The Bioproduct Transition Dynamics (BTD) model explores questions such as the following: what are the factors that separate a successful, commercially produced bioproduct like succinic acid from one that never progresses beyond bench-scale lab research? Can these factors be influenced by stakeholders, and to what extent? The BTD model uses system dynamics to capture the impacts of investor decision-making, bioproduct techno-economics, and market factors during the early stages of bioproduct development. Key components of the BTD model include techno-economic benchmarks that inform the investor decision-making process, failures and setbacks in development and the resulting need for additional work, and the impacts of effective or ineffective management during each development stage. These factors and their interactions are tracked through bench-scale laboratory research, piloting, demoing, and the construction and operation of the first commercial-scale plant. Bioproduct development is linked to the biofuels industry through a shared-learning model, enabling the benefit to biofuels from bioproduct technology and feedstock supply chain development to be quantified. A wide variety of bioproducts can be analyzed using the BTD model, including bioproducts that have been developed through economic or policy-driven mechanisms, and those with either niche (low volume) or scalable (high volume) markets. The BTD model also has the potential to apply to technology development processes outside the bioproducts industry; background research performed for this project has shown that the early stages of technology development are similar, and impacted by similar factors, regardless of the exact industry. This presentation will cover the BTD model logic, input data, validation process, and results of a sensitivity analysis based on techno-economic data for succinic acid. The sensitivity analysis was performed to identify factors with the largest impact on the eventual success or failure of a bioproduct. Results indicate that management effectiveness, which affects how efficiently money spent is converted into technological advancements, is the single most important factor in determining whether a bioproduct reaches commercial-scale production. The capacity of the first commercial plant and the type of biomass feedstock used, as well as the presence of government support in the form of cost-sharing, were also identified as significant factors.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Optimal Power Flow Pursuit

Past works that focused on addressing power-quality and reliability concerns related to renewable energy resources (RESs) operating with business-as-usual practices have looked at the design of Volt/VAr and Volt/Watt strategies to regulate real or reactive powers based on local voltage measurements, so that terminal voltages are within acceptable levels. These control strategies have the potential of operating at the same time scale of distribution-system dynamics, and can therefore mitigate disturbances precipitated fast time-varying loads and ambient conditions; however, they do not necessarily guarantee system-level optimality, and stability claims are mainly based on empirical evidences. On a different time scale, centralized and distributed optimal power flow (OPF) algorithms have been proposed to compute optimal steady-state inverter setpoints, so that power losses and voltage deviations are minimized and economic benefits to end-users providing ancillary services are maximized. However, traditional OPF schemes may offer decision making capabilities that do not match the dynamics of distribution systems. Particularly, during the time required to collect data from all the nodes of the network (e.g., loads), solve the OPF, and subsequently dispatch setpoints, the underlying load, ambient, and network conditions may have already changed; in this case, the DER output powers would be consistently regulated around outdated setpoints, leading to suboptimal system operation and violation of relevant electrical limits. The present work focuses on the synthesis of distributed RES-inverter controllers that leverage the opportunities for fast feedback offered by power-electronics interfaced RESs. The overarching objective is to bridge the temporal gap between long-term system optimization and real-time control, to enable seamless RES integration in large scale with stability and efficiency guarantees, while congruently pursuing system-level optimization objectives. The design of the control framework is based on suitable linear approximations of the AC power-flow equations as well as Lagrangian regularization methods. The proposed controllers enable an update of the power outputs at a time scale that is compatible with the underlying dynamics of loads and ambient conditions, and continuously drive the system operation towards OPF-based solutions.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Robust Combined Heat and Hybrid Power (CHHP) for High Electrical Efficiency Cogeneration

Georgia Tech (Prime Recipient), the University of Texas at El Paso (UTEP) and the National Energy Technology Laboratory (NETL) investigated a hybrid fuel cell/ gas turbine system concept as a combined heat and hybrid power (CHHP) system for both robust and high power-to-process heat ratio cogeneration. The novelty of the proposed system entailed the distinct, elevated electrical efficiencies it maintains while simultaneously supporting a broad span of heating needs (e.g., supply temperatures) demanded across variable heat loads. The scope included: 1) leveraging a pioneering national lab facility configured for dynamic system operability development of hybrid fuel cell/gas turbine cycles; 2) enabling technology development to adjust and modulate the quality and quantity of thermal supply to bottoming heat loads via novel extreme temperature gas bypass valves. Hybrid fuel cell/gas turbine systems have primarily been reduced-to-practice in a constrained (e.g., initial proof-of-concept) manner and have still demonstrated considerable electrical efficiencies. However, these pre-pilot systems have focused upon electrical efficiencies and electrical power generation as the exclusive energy demand. Such hybrid systems had not been extensively researched or developed for flexible and variable operation consisting of both power and heat demands; however, these variable combined power and heat demands are characteristic of many types of manufacturers such as animal/poultry processing, bakeries and milk/flour/pastry manufacturing, textile mills, and electrochemical processing. Commercially, developing the system into a working combined heat and power system benefits these types of manufacturers by allowing them to meet their power and heat demands at a lower cost, higher efficiency, and/or through onsite generation. Therefore, the technical scope of this project was largely to study and facilitate these hybrid systems as combined heat and hybrid power (CHHP) systems that include dynamic operability for variable heat and power loads and/or grid dynamics for various types of manufacturers. Simulation results were used to predict the performance of the CHHP system and conceptually develop it to achieve desired dynamic operability. Experimentally, the primary goal was to design, manufacture, and experiment upon a high-temperature bypass valve. Experimental data included air mass flow rates through the valve orifice when the valve was changed to variable extent between fully closed and fully open. The experimental data was then used to create a semi-empirical computational model of the bypass valve. Concluded simulation goals for the research included developing computational heat exchanger models for the hybrid system inclusive of the bottoming heat exchanger and the recuperative heat exchanger, and then combining the computational recuperator model with the computational valve model. Afterwards, the computational models were then integrated to predict the dynamic operation of hybrid fuel cell/gas turbine cycles throughout a design space and reporting such. The scope stated in the preceding paragraph was packaged into five specific goals: 1) enabling the simulation of dynamic combined heat and power through the creation of computational, modular heat exchanger models; 2) simulation and exploration of the CHHP system’s performance by integrating the heat exchanger models with the national lab’s pre-existing hybrid system (computational) simulation, but without the recuperator bypass valve concept in order to initially determine how the (baseline) system behaves and can be controlled in order to meet variable heat and power demands; 3) development and initial deployment of the high-temperature recuperator bypass valve technology in order to confirm and characterize the approach; 4) usage of the experimental data for the valve to create a semi-empirical computational model for the bypass valve which could then be combined with the heat exchanger computational models; 5) repeat of the second task of simulating and exploring the system’s performance, but this time including the bypass valve to resolve its efficacy. Tasks were successfully completed, and the general notion of flexibly operating, high electrical efficiency CHHP was further corroborated. Supportive details are provided in the report.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

A Trajectory-Driven Algorithm for Differentiating SRB Measures on Unstable Manifolds

Sinai-Ruelle-Bowen (SRB) measures are limiting stationary distributions describing the statistical behavior of chaotic dynamical systems. Directional derivatives of SRB measure densities conditioned on unstable manifolds are critical in the sensitivity analysis of hyperbolic chaos. These derivatives, known as the SRB density gradients, are by-products of the regularization of Lebesgue integrals appearing in the original linear response expression. In this paper, we propose a novel trajectory- driven algorithm for computing the SRB density gradient defined for systems with high-dimensional unstable manifolds. We apply the concept of measure preservation together with the chain rule on smooth manifolds. Due to the recursive one-step nature of our derivations, the proposed procedure is memory-efficient and can be naturally integrated with existing Monte Carlo schemes widely used in computational chaotic dynamics. Here, we numerically show the exponential convergence of our scheme, analyze the computational cost, and present its use in the context of Monte Carlo integration.

97 MATHEMATICS AND COMPUTING↗

Tau leaping of stiff stochastic chemical systems via local central limit approximation

Stiffness manifests in stochastic dynamic systems in a more complex manner than in deterministic systems; it is not only important for a time-stepping method to remain stable but it is also important for the method to capture the asymptotic variances accurately. In the context of stochastic chemical systems, time stepping methods are known as tau leaping. Well known existing tau leaping methods have shortcomings in this regard. The implicit tau method is far more stable than the trapezoidal tau method but underestimates the asymptotic variance. On the other hand, the trapezoidal tau method which estimates the asymptotic variance exactly for linear systems suffers from the fact that the transients of the method do not decay fast enough in the context of very stiff systems. We propose a tau leaping method that possesses the same stability properties as the implicit method while it also captures the asymptotic variance with reasonable accuracy at least for the test system S{sub 1}↔S{sub 2}. The proposed method uses a central limit approximation (CLA) locally over the tau leaping interval and is referred to as the LCLA-τ. The CLA predicts the mean and covariance as solutions of certain differential equations (ODEs) and for efficiency we solve these using a single time step of a suitable low order method. We perform a mean/covariance stability analysis of various possible low order schemes to determine the best scheme. Numerical experiments presented show that LCLA-τ performs favorably for stiff systems and that the LCLA-τ is also able to capture bimodal distributions unlike the CLA itself. The proposed LCLA-τ method uses a split implicit step to compute the mean update. We also prove that any tau leaping method employing a split implicit step converges in the fluid limit to the implicit Euler method as applied to the fluid limit differential equation.

97 MATHEMATICS AND COMPUTING↗

A highly specific test for periodicity

We present a method that allows to distinguish between nearly periodic and strictly periodic time series. To this purpose, we employ a conservative criterion for periodicity, namely, that the time series can be interpolated by a periodic function whose local extrema are also present in the time series. Our method is intended for the analysis of time series generated by deterministic time-continuous dynamical systems, where it can help telling periodic dynamics from chaotic or transient ones. We empirically investigate our method's performance and compare it to an approach based on marker events (or Poincaré sections). We demonstrate that our method is capable of detecting small deviations from periodicity and outperforms the marker-event-based approach in typical situations. Our method requires no adjustment of parameters to the individual time series, yields the period length with a precision that exceeds the sampling rate, and its runtime grows asymptotically linear with the length of the time series.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A Convex Data-Driven Approach for Nonlinear Control Synthesis

We consider a class of nonlinear control synthesis problems where the underlying mathematical models are not explicitly known. We propose a data-driven approach to stabilize the systems when only sample trajectories of the dynamics are accessible. Our method is built on the density-function-based stability certificate that is the dual to the Lyapunov function for dynamic systems. Unlike Lyapunov-based methods, density functions lead to a convex formulation for a joint search of the control strategy and the stability certificate. This type of convex problem can be solved efficiently using the machinery of the sum of squares (SOS). For the data-driven part, we exploit the fact that the duality results in the stability theory can be understood through the lens of Perron–Frobenius and Koopman operators. This allows us to use data-driven methods to approximate these operators and combine them with the SOS techniques to establish a convex formulation of control synthesis. The efficacy of the proposed approach is demonstrated through several examples.

97 MATHEMATICS AND COMPUTING↗

Energy Analysis of Combi Heat Pump System Configurations for Space Conditioning and Domestic Hot Water Heating in Residential Buildings

Combi heat pump systems, also referred to multifunctional variable refrigerant flow heat recovery (MF-VRFHR) systems, are specifically designed for residential applications to manage both space conditioning and domestic hot water (DHW). They have attracted attention due to their potential for energy conservation through heat recovery. The incorporation of a hot water tank introduces various system configurations, each characterized by distinct pros and cons related to energy efficiency, system stability, and maintenance. Despite this, a critical gap exists as the specific energy performance remains unquantified under diverse operational modes (e.g., heating mode and heat recovery mode). This paper aims to bridge this gap by conducting a comprehensive comparative analysis of two prevalent system configurations while considering feasible proposed control logics. Configuration 1 integrates a separate hot water tank and a refrigerant-to-water heat exchanger (HEX), also known as a Hydro Kit while Configuration 2 incorporates a refrigerant-wrapped hot water tank. To facilitate this analysis, we developed high-fidelity system models for both configurations in Modelica, capturing system dynamics and detailed control sequences effectively. These system models were built upon the TIL library for HVAC equipment components and the Buildings library for residential building thermal load calculations. The validation of the simulation testbed utilized data from experiments conducted in the PNNL lab home for Configuration 1. To establish the simulation testbed for Configuration 2, we extended the modeling setup derived from Configuration 1. This extension specifically involved substituting the separate hot water tank and Hydro Kit with a refrigerant-wrapped hot water tank of similar sizing sourced from an actual product. The simulation analysis of heating-only and heat recovery modes reveals that Configuration 2 not only saves energy and maintains warmer tank temperatures but also demonstrates faster water heating capabilities. This is attributed to decreased energy loss and improved heat transfer. The study encompasses a wide range of scenarios, considering diverse thermal loads and water usage patterns across heating and heat recovery modes. Overall, the comprehensive results indicate that Configuration 2 achieves energy savings ranging from 3.5% to 12.2% compared to Configuration 1, depending on factors such as water usage patterns, thermal loads, and operational modes.

Configuration, Comparison, Multi-functional, Resid↗

Control of linear uncertain systems utilizing mismatched state observers

The control of linear continuous dynamical systems is investigated as a problem of limited state feedback control. The equations which describe the structure of an observer are developed constrained to time-invarient systems. The optimal control problem is formulated, accounting for the uncertainty in the design parameters. Expressions for bounds on closed loop stability are also developed. The results indicate that very little uncertainty may be tolerated before divergence occurs in the recursive computation algorithms, and the derived stability bound yields extremely conservative estimates of regions of allowable parameter variations.

Goldstein, B.↗