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Modeling and Analysis of Stirling Power Convertors

Modeling and Analysis of Stirling Power Convertors Luis A. Rodriguez1 Steven M. Geng, Terry V. Reid, Scott D. Wilson NASA Glenn Research Center, Cleveland, OH, 44135, USA NASA Glenn’s Thermal Energy Conversion Branch is supporting the development of the next generation free-piston Stirling power convertors. American Superconductor (AMSC) and Sunpower Inc. are the two firms under contract to develop the Flexure Isotope Stirling Convertor (FISC) and the Sunpower Robust Stirling Convertor (SRSC), respectively. To comprehend and forecast convertor performance, Sage, ANSYS® Maxwell, and ANSYS® Fluent were used to model the Stirling thermodynamic cycle, alternator electromagnetics, and piston and displacer dynamics. I. Introduction Stirling convertors are being developed by NASA as a potential steady source of electrical power for NASA’s future scientific space missions. Currently, NASA Glenn Research Center has two corporations under contract, American Superconductor (AMSC) and Sunpower Inc., for the development of the next generation of free-piston Stirling convertors for dynamic radioisotope power systems. AMSC is developing the Flexure Isotope Stirling Convertor (FISC), which uses flexures to prevent side motion and rubbing of the piston. Similarly, Sunpower Inc, is developing the Sunpower Robust Stirling Convertor (SRSC). The SRSC uses gas bearings to prevent radial contact of the moving piston. As convertor development continues, it is increasingly important to understand and predict the interactions of components in the system, how they respond to one another, and how they perform as a response to changes in operating conditions. A suitable and enlightening way to demonstrate and foresee these interactions is with the use of accurate modeling software. Sage, ANSYS® Maxwell, and ANSYS® Fluent are the current modeling tools used by NASA to analytically determine convertor performance. Sage is a one-dimensional object-oriented commercial software package used for modeling and optimizing Stirling convertors for Dynamic Radioisotope Power Systems (DRPS) and it is one of the most accurate Stirling convertor codes in use by NASA. This code is the successor to GLIMPS (Globally-Implicit Stirling Cycle Simulation) and GLOP (GLIMPS Optimization) software created by Gedeon Associates [1]. Model input parameters are typically material/gas type, component physical dimensions, temperatures, frequency, charge pressure, and number of time/space nodes. Sage is used to model both the FISC’s and SRSC’s Stirling cycle thermodynamics and piston/displacer dynamics. Performance maps were created and analyzed for both power systems to better understand the relationship between the following conditions: cold-end temperature, hot-end temperature, piston/displacer amplitudes, pressure drop, and thermal input power. The synergy between these conditions will help determine parameter sensitivity. ANSYS® Maxwell was used to create a three-dimensional (3-D) axisymmetric model for both FISC and SRSC alternators. The significant physical components included in each model are the magnets, magnet carrier, outer/inner laminations, and the coil. Inputs to the model are piston amplitude, piston frequency, alternator load, coil resistance, tuning capacitance, and specific material properties. The alternator models calculate terminal voltage, current, piston/current phase, voltage/current phase, coil inductance, terminal power and efficiency. The RI2 losses, core (hysteresis and eddy) losses, and magnet/can eddy losses are also a part of the final results. ANSYS® Fluent is used to build 3-D computational fluid dynamic (CFD) models to examine the Stirling cycle thermodynamics for both the FISC and SRSC systems. Three-dimensional Computer Aided Design (CAD) models were used to create the physical components of each convertor. Steady-state simulations were conducted for hardware testing, prediction of environmental losses during testing, and generation of radiation look-up tables. The model inputs to the aforementioned analysis are the material properties and boundary thermal conditions. The steady-state model calculates temperature and heat flow distributions. Transient 3-D calculations were also part of the CFD analysis. In this study a physically reduced version of the FISC is used to obtain a prediction of available engine power. For the gas bearing SRSC, the transient effort is used to obtain a prediction of bearing pad performance and its sensitivity to micro-channel geometric variation. The model inputs to the transient simulations are the piston amplitude, displacer amplitude, frequency, displacer/piston phase angle, dynamic deforming CFD grid, temperature boundary conditions, and user defined files describing motion profile of piston/displacer. The results of the model are temperature distributions, heat distributions, and PV power produced at pre-determined conditions.

Luis A Rodriguez↗
DOE OSTI2025

Synchro-Waveform-Based Event Identification Using Multi-Task Time-Frequency Transform Networks

Influenced by the transient dynamics and reduced inertia characteristics of high-penetration renewable energy systems, power system events frequently exhibit distinct characteristics such as high-frequency components including wide-band oscillations and hyper-harmonics. This makes standard systems face challenges including significant latency and reduced accuracy due to limited data resolution. However, current methods face significant limitations, including insufficient pattern capture ability, low noise immunity, limited feature learning, and restricted localization capabilities, thereby hindering real-time performance. To tackle this issue, this paper proposed a novel synchro-waveform-based event identification approach via a Multi-task Time-frequency Transform Network (MTTNet). Initially, a Time-frequency Transform Block (TTB) is developed to extract both local and global information. The TTB leverages both Fourier and S-transforms to derive comprehensive time-frequency information from synchro-waveforms. Subsequently, a multi-task learning strategy is employed to identify the type and distinguish localization of events. Integrating the TTB and multi-task learning, the MTTNet is designed for synchro-waveform-based event identification, incorporating an adaptive weighting strategy and simplified computation for the S-transform. Two different datasets, comprising simulated and actual synchro-waveforms, are collected from the IEEE 123 bus system and a real-world high-penetration renewable energy system using a universal grid analyzer. Extensive experiments on various conditions are carried out. In conclusion, results demonstrated that the MTTNet consistently surpasses both basic and advanced baselines, with maximum improvements of 13.24% and 9.86%, respectively, while reducing the calculation burden by 15-19 times to achieve real-time event identification.

Event identification↗
DOE OSTI2024

A Trade-Off Study Between the Primary and Transient Responses of Grid-Forming Inverters

The control parameters of the grid-forming (GFM) inverter-based resources (IBRs) directly impact power system dynamics. The primary control requires the GFM inverter to balance generation and load. It is also preferred that a GFM inverter maintain the terminal frequency after a power system fault. In this paper, we investigate the trade-off between the primary control objective and the transient response. To quantify the transient performance of the GFM inverter, we introduce a new real-time transient stability index (TSI). This index plays a crucial role in our investigation, as it allows us to compare the performance trade-offs of different sets of GFM control parameters.

Lin, Xuheng↗
DOE OSTI2024

Structural Impact of Grid-Forming Inverters on Power System Coherency

This paper addresses the following fundamental research question: how does the integration of grid-forming inverters (GFMs) replacing conventional synchronous generators (SGs) impact the slow coherent eigen-structure and the low frequency oscillatory behavior of future power systems? Due to time-scale separated dynamics, generator states inside a coherent area synchronize over a fast time-scale due to stronger coupling, while the areas themselves synchronize over a slower time scale. Our mathematical analysis shows that due to the large-scale integration of GFMs, the weighted Laplacian structure of the frequency dynamics is preserved, however, the entries of the Laplacian may be significantly modified based on the location and penetration levels of the GFMs. This can impact and potentially significantly alter the coherency structure of the system. We have validated our findings with numerical results using the IEEE 68-bus test system.

Mukherjee, Sayak [BATTELLE (PACIFIC NW LAB)]↗
DOE OSTI2025

Stochastic Adaptive Droop Control in Frequency Regulation of Power Systems With Intermittent Generators

Modern power systems (MPSs), including microgrids (MGs), are increasingly incorporating multiple renewable energy sources (RESs) such as wind and solar power, as well as battery storage and controllable loads. While environmentally beneficial, these sources pose challenges for control and management due to their intermittent and stochastic nature, especially in maintaining frequency stability with multiple interconnected generators of varying capacities. Traditional droop control methods are effective in systems with generators that are dispatchable and have fixed generation capacities, but they fall short when applied to systems with RESs, where generation capacities are dynamic and affected by unpredictable environmental conditions. To address these challenges, this paper introduces a novel stochastic adaptive droop control (SADC) method for load frequency control (LFC). The proposed method adapts droop coefficients in real time, based on the measured stochastic data of power generation capacities, enabling more effective frequency regulation in systems with variable and intermittent power generation. Unlike traditional adaptive control methods, which assume constant or slowly-varying system parameters, this approach accounts for stochastic processes by modeling them as Markov chains, enabling robust performance under highly dynamic and unpredictable conditions. The key contributions of this work include the development of real-time droop coefficient adaptation algorithms, derivation of their stability and convergence properties, and the demonstration of the advantages of the method through simulations. Case studies highlight the improved performance of frequency regulation, particularly in addressing the impact of stochastic weather conditions and the benefits of reducing dependence on battery reserves in dealing with intermittency of RESs. Finally, this paper provides a comprehensive analysis of the theoretical foundations of the method, as well as practical implementation insights for future power systems with high penetration of RESs.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

A Brief Survey on High Performance Computing Systems Power Management

This paper provides a survey of software-based power management techniques in High Performance Computing (HPC) systems. Seven existing power management and monitoring tools and frameworks are discussed. These are: Variorum, dynamic energy-performance optimizer (DEPO), Powersched, Bull Dynamic Power Optimizer (BDPO), Energy Aware Runtime (EAR), Global Extensible Open Power Manager (GEOPM), and PoLiMEr. Each of these tools is evaluated based on hardware abstraction, optimization methods, usability, and experimental validation. This survey highlights the diversity of approaches in managing energy efficiency, from vendor-neutral APIs to algorithm-driven power capping, and dynamic frequency adjustments. Given that energy requirements for large computational systems is increasing quickly, the importance of integrating these tools into existing HPC environments and the need for further research in this rapidly evolving field is also discussed.

97 - MATHEMATICS AND COMPUTING↗
NASA NTRS1980

MOD-2 wind turbine farm stability study

The dynamics of single and multiple 2.5 ME, Boeing MOD-2 wind turbine generators (WTGs) connected to utility power systems were investigated. The analysis was based on digital simulation. Both time response and frequency response methods were used. The dynamics of this type of WTG are characterized by two torsional modes, a low frequency 'shaft' mode below 1 Hz and an 'electrical' mode at 3-5 Hz. High turbine inertia and low torsional stiffness between turbine and generator are inherent features. Turbine control is based on electrical power, not turbine speed as in conventional utility turbine generators. Multi-machine dynamics differ very little from single machine dynamics.

Hinrichsen, E. N.↗
DOE OSTI2025

Open-Source Ambient-Signal-Based Inertia Monitoring Tool for Power systems [SWR-25-59]

This script, developed by NREL, implements an inertia estimation algorithm using a sliding window approach. The inertia (H) is estimated based on frequency deviations and active power deviations, utilizing the swing equation from power system dynamics. An example application is provided using the WECC 240-bus system.

Peng, Jiangkai [National Renewable Energy Laborato↗
DOE OSTI2024

2023 Reftek Colt Seismometer Exploratory Evaluation

Sandia National Laboratories has tested and evaluated three Colt broadband seismometers designed and manufactured by Reftek. The purpose of this seismometer evaluation is to measure performance characteristics in areas such as power consumption, sensitivity, frequency response, full scale, self-noise, dynamic range, calibration system response, and passband. The Colt model of sensors are being evaluated to explore the potential for a future seismometer Type Approval process in the International Monitoring System (IMS) of the Comprehensive Nuclear-Test-Ban Treaty (CTBT).

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

2023 T120 Horizon and Slim Posthole Seismometer Exploratory Evaluation

Sandia National Laboratories has tested and evaluated a suite of four T120 broadband seismometers designed and manufactured by Nanometrics. Specifically, two T120 Horizon V2 sensors, one T120 Horizon V1 sensor and one T120 Slim Posthole (PH) sensor were evaluated. The purpose of this seismometer evaluation is to measure performance characteristics in areas such as power consumption, sensitivity, frequency response, full scale, self-noise, dynamic range, calibration system response, and passband. The T120 model of sensors are being evaluated to explore the potential for a future seismometer Type Approval process in the International Monitoring System (IMS) of the Comprehensive Nuclear-Test-Ban Treaty (CTBT).

47 OTHER INSTRUMENTATION↗
DOE OSTI2026

Quantifying System Strength From Grid-Forming Resources Using Frequency Scan Approach: Preprint

Current industry practices for quantifying the system strength contribution from grid-forming (GFM) resources to ensure stability of power systems dominated by inverter-based resources (IBRs) are primarily based on iterative electromagnetic transient (EMT) time-domain simulation studies. While feasible, these approaches are resource-intensive, lack scalability and intuition, and might not evaluate the system strength contribution over the entire frequency range of interest. This paper introduces a novel, frequency-domain approach to quantify system strength support provided by a GFM resource using frequency scans. The proposed method uses transfer functions from the grid voltage magnitude (V) and phase (?), respectively, to the reactive (Q) and active power (P) output of a GFM resource for quantifying its contribution to system strength. These transfer functions provide a direct measure of the ability of a GFM resource to behave as a stiff voltage source behind a reactance over a specified frequency range, enabling robust quantification of its system strength contribution. The key innovation of this work is the development of a frequency domain system strength metric called the dynamic short-circuit ratio (dSCR) that is suitable for IBR-dominated power systems and is directly related with the familiar short circuit ratio (SCR) metric. The new metric, dSCR, enables the assessment of system strength contributions from both synchronous machines and converter-based GFM resources using a unified benchmark, which is not possible with the traditional SCR metric. The paper also demonstrates how impedance scans could identify if an unstable condition observed during weak grid conditions is a result of the lack active or reactive power support or both. By leveraging the proposed frequency-domain dSCR metric for quantifying system strength contribution from GFM IBRs, the paper demonstrates targeted mitigation strategies for weak grid instabilities without resorting to repeated, time-consuming time-domain simulations. The result is a scalable and efficient approach to remediate stability challenges in power systems with high shares of IBRs and accelerating the integration of GFM technologies for system strength support in power systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1989

Performance testing of a high frequency link converter for Space Station power distribution system

The testing of a brassboard version of a 20-kHz high-frequency ac voltage link prototype converter dynamics for Space Station application is presented. The converter is based on a three-phase six-pulse bridge concept. The testing includes details of the operation of the converter when it is driving an induction machine source/load. By adapting a field orientation controller (FOC) to the converter, four-quadrant operation of the induction machine from the converter has been achieved. Circuit modifications carried out to improve the performance of the converter are described. The performance of two 400-Hz induction machines powered by the converter with simple V/f regulation mode is reported. The testing and performance results for the converter utilizing the FOC, which provides the capability for rapid torque changes, speed reversal, and four-quadrant operation, are reported.

Sul, S. K.↗
NASA NTRS1988

High dynamic range infrared radiometry and imaging

The use is described of cryogenically cooled, extrinsic silicon infrared detectors in an unconventional mode of operation which offers an unusually large dynamic range. The system performs intensity-to-frequency conversion at the focal plane via simple circuits with very low power consumption. The incident IR intensity controls the repetition rate of short duration output pulses over a pulse rate dynamic range of about 10(6). Theory indicates the possibility of monotonic and approx. linear response over the full dynamic range. A comparison between the theoretical and the experimental results shows that the model provides a reasonably good description of experimental data. Some measurements of survivability with a very intense IR source were made on these devices and found to be very encouraging. Evidence continues to indicate that some variations in interpulse time intervals are deterministic rather than probabilistic.

Coon, Darryl D.↗
NASA NTRS1988

A study of helicopter stability and control including blade dynamics

A linearized model of rotorcraft dynamics has been developed through the use of symbolic automatic equation generating techniques. The dynamic model has been formulated in a unique way such that it can be used to analyze a variety of rotor/body coupling problems including a rotor mounted on a flexible shaft with a number of modes as well as free-flight stability and control characteristics. Direct comparison of the time response to longitudinal, lateral and directional control inputs at various trim conditions shows that the linear model yields good to very good correlation with flight test. In particular it is shown that a dynamic inflow model is essential to obtain good time response correlation, especially for the hover trim condition. It also is shown that the main rotor wake interaction with the tail rotor and fixed tail surfaces is a significant contributor to the response at translational flight trim conditions. A relatively simple model for the downwash and sidewash at the tail surfaces based on flat vortex wake theory is shown to produce good agreement. Then, the influence of rotor flap and lag dynamics on automatic control systems feedback gain limitations is investigated with the model. It is shown that the blade dynamics, especially lagging dynamics, can severly limit the useable values of the feedback gain for simple feedback control and that multivariable optimal control theory is a powerful tool to design high gain augmentation control system. The frequency-shaped optimal control design can offer much better flight dynamic characteristics and a stable margin for the feedback system without need to model the lagging dynamics.

Zhao, Xin↗
DOE OSTI2024

Dynamic Shaping of Grid Response of Multi-Machine Multi-Inverter Systems Through Grid-Forming IBRs

We consider the problem of controlling the frequency response of weakly-coupled multi-machine multi-inverter low-inertia power systems via grid-forming inverter-based resources (IBRs). In contrast to existing methods, our approach relies on dividing the larger system into multiple strongly-coupled subsystems, without ignoring either the underlying network or approximating the subsystem response as an aggregate harmonic mean model. Rather, through a structured clustering and recursive dynamic shaping approach, the frequency response of the overall system to load perturbations is shaped appropriately. We demonstrate the proposed approach for a three-node triangular configuration and a small-scale radial network. Furthermore, previous synchronization analysis for heterogeneous systems requires the machines to satisfy certain proportionality property. In our approach, the effective transfer functions for each cluster can be tuned by the IBRs to satisfy such property, enabling us to apply the shaping control to systems with a wider range of heterogeneous machines.

frequency-shaping control↗
DOE OSTI2025

Distributed Control and Optimization of Virtual Inertia in Power Systems

The integration of renewable energy sources into power grids through inverter-based resources (IBRs) reduces system inertia, leading to faster frequency dynamics and potential grid instability. This paper proposes a distributed, consensus-based approach for the real-time control and optimization of inertia sources during system disturbances, enhancing both system stability and economic performance. Furthermore, we integrate this approach with the traditional inertia placement problem, demonstrating its suitability for existing frameworks. We validate its effectiveness in a 4-bus test system and a two-area 8-bus test system, showcasing its potential for scalable, dynamic inertia management in low-inertia grids.

Yadav, Ajay [ORNL] (ORCID:000000016111881X)↗
NASA NTRS1977

Coupled dynamics analysis of wind energy systems

A qualitative description of all key elements of a complete wind energy system computer analysis code is presented. The analysis system addresses the coupled dynamics characteristics of wind energy systems, including the interactions of the rotor, tower, nacelle, power train, control system, and electrical network. The coupled dynamics are analyzed in both the frequency and time domain to provide the basic motions and loads data required for design, performance verification and operations analysis activities. Elements of the coupled analysis code were used to design and analyze candidate rotor articulation concepts. Fundamental results and conclusions derived from these studies are presented.

Hoffman, J. A.↗
DOE OSTI2024

Dynamic Shaping of Grid Response of Multi-Machine Multi-Inverter Systems Through Grid-Forming IBRs: Preprint

We consider the problem of controlling the frequency response of weakly-coupled multi-machine multi-inverter low-inertia power systems via grid-forming inverter-based resources (IBRs). In contrast to existing methods, our approach relies on dividing the larger system into multiple strongly-coupled subsystems, without ignoring either the underlying network or approximating the subsystem response as an aggregate harmonic mean model. Rather, through a structured clustering and recursive dynamic shaping approach, the frequency response of the overall system to load perturbations is shaped appropriately. We demonstrate the proposed approach for a three-node triangular configuration and a small-scale radial network. Furthermore, for small-scale radial microgrids, we demonstrate the ability of IBRs to tune the effective transfer functions of synchronous machines. This enables us to relax the uniform turbine time-constant assumptions and widen the scope of existing synchronization results for proportionally heterogeneous machines.

frequency-shaping control↗