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Unified Model of Current-Limiting Grid-Forming Inverters for Large-Signal Analysis
Grid-forming (GFM) inverters can hardly withstand any overloading. As such, GFM inverters need a current limiter in their control system to avoid hardware damage during overloading or grid disturbances. When the current limiter is engaged for inverter protection, however, it dynamically changes the inverter output impedance, which can significantly affect the system behavior against large disturbances. For example, when the current limiter curtails the output power, the primary controller of the GFM inverter-which generates the voltage and angle reference-is prone to losing synchronization with the grid. This can cause large-signal instability in the network. This paper presents a unified GFM current-limiter model to gain a deeper understanding of the impact of the GFM inverter current limiting on large-signal instability and other system behaviors. The unified model captures several well-known current limiters for GFM inverters, and it reveals their large-signal equivalence characterized by the limiter angle. We use the unified model to present in-depth insights into the driving forces that cause large-signal instability in GFM inverter-driven grids. Further, this paper illustrates that the unified model can be used as a tool for assessing the system-level impacts of various GFM current-limiter designs during grid disturbances. Using numerical, analytical, electromagnetic transient models, and a hardware setup, the validity of the unified model is evaluated.
A Survey of Open-Source Tools for Transmission and Distribution Systems Research
This work presents a review of open-source electric power transmission and distribution systems analysis tools suitable for use by industry professionals and academic researchers. Due to the high complexity of the electric grid, there exist numerous tools and extensive research pertaining to nearly every aspect of the design, operation, and control of transmission and distribution networks. In addition to the commercial tools, a wide range of free, open-source tools, models, and data usable by the scientific community for related research have been developed by different organizations, including both international and US universities and national laboratories. However, due to the absence of a catalog of available tools, models and data, researchers often lack a knowledge of existing capabilities and may develop duplicative software and tools. Increasing awareness of these available resources seeks to accelerate their broader use, leading to more efficient and standardized grid analysis. This review paper (which is part of a larger survey effort that studied over 400 tools in the transmission, distribution, buildings, and electric vehicles space) outlines selected open-source resources that have been developed in power transmission and distribution systems research. It is anticipated that this work can serve as a guide for industry and academic researchers alike, ensuring that research efforts are well-channeled.
Challenges and Opportunities for Electric Utility Modeling and Asset Valuation Frameworks: Case Study on Valuing New Pumped Storage Hydropower
Asset valuation by electric utilities is becoming increasingly difficult in the rapidly changing electric sector. Rapid deployment of variable generation and inverter-based storage systems along with uncertain demand growth, climate, policies, and other factors create a challenging environment for understanding the value proposition of a new potential asset. This report describes an effort between the Tennessee Valley Authority (TVA) and three U.S. Department of Energy laboratories to perform a detailed review of utility modeling and analysis practices for asset valuation and identify challenges and opportunities for advancing its methods into the future. It focuses on a case study of new potential pumped storage hydropower (PSH) because of growing interest in new PSH capacity to provide energy balancing, firm capacity, and a range of ancillary services. Staff from the DOE labs conducted systematic interviews about current practices in capacity expansion modeling, production-cost modeling, hydrological modeling, and transmission stability modeling while also discussing how scenario analysis is conducted and how models and data are integrated. The effort resulted in a set of model, integration, and scenario recommendations that could be valuable to TVA, other utilities, system operators, and other stakeholders conducting integrated grid analysis. Individual model recommendations suggest exploring computational tradeoffs with detail and resolution across spatiotemporal structure, supply- and demand-side details, transmission overlays, market interactions, and ancillary services. Automated processes to pass data between models and conduct larger scenario suites could also enhance valuation practices by enabling a more consistent study of asset value across a broader range of uncertain future grid conditions where PSH could be particularly valuable. TVA and other industry stakeholders can learn from and adapt applied research-grade methods developed by DOE laboratories and other research institutions to improve decision making and accelerate progress towards a reliable, economic, sustainable energy system.
Leading Energy Analysis: Data-Driven Insights That Power Our Energy Future
Energy analysts at the National Renewable Energy Laboratory (NREL) use a broad set of expertise and cutting-edge tools to capture the complexities of our interconnected energy system. Decision-makers rely on these insights to drive cost savings, enhance grid reliability, support long-term innovation, and bolster America's energy workforce and global competitiveness. This fact sheet highlights some of NREL's high-impact analyses, data, and tools, largely focusing on power grid analysis.
Future grid mix impacts on whole-building life cycle assessment
Building construction and operation are a significant contribution to global greenhouse gas emissions, so understanding and mitigating emissions is crucial for reliable and realistic emissions accounting. Whole-building Life Cycle Assessment (WBLCA) is an emissions accounting method that considers lifetime environmental impacts of a building during its construction, operation, and eventual end-of-life. When performing WBLCAs, emission calculations from the building's operation over the entire building lifespan are typically based on today's energy grid mixes. This method does not consider changes or advancements in the clean energy proportion within the grid mix and can over or under-inflate results, skewing the ratio of embodied vs. operational environmental impacts. While a variety of prediction tools estimate what future grid emissions might be, predictions can vary widely. To predict the clean energy ratio within future grid mixes and the potential impact these changes might have on WBLCA, annual data from several existing U.S. grid models was averaged and probabilistic modeling was used to extend the usable projections of shorter forecasts. Results show that clean energy sources will likely continue to increase over time, although the rate of growth varies by model. On average, by 2085, the clean energy penetration of the grid is projected to reach ~81% and renewable energy is projected to reach ~71%, although no widespread consensus is reached. To understand how the future grid mix impacts lifetime building emissions within a WBLCA context, the team analyzed two 2021 IECC-compliant all-electric residential buildings: one built from traditional materials and construction processes and the other built with carbon sequestering materials and modular assembly, with a portion of energy generated on site. The results indicate that a moderate estimate of future electricity grid mixes shows a reduction of yearly operational emissions for traditional residential buildings of 55% between 2025 and 2085, and a corresponding reduction of 48% of total emissions over a 60 year building lifespan. This study offers a nuanced approach to account for the variability of future grid mix models and provides an average trend-line based on a robust collection of scenarios.
Planning for Seattle at the Convergence of Resilience and Energy
Grid reliability metrics obscure important temporal, spatial, and categorical considerations for increasing energy resilience. Systemwide or feeder-level outage metrics do not identify which kinds of services are affected by outages, where, and for how long. These outage metrics indicate the impacts of outages but cannot measure the consequences to customers that could result from those outages. The consequences of power outages for surrounding community members are caused by disruptions to electricity-dependent critical services, rather than to electricity itself. Power outages can decrease a community's access to healthcare, fuel, safe indoor temperatures, and provisions like food and water. This project developed critical service access, a new consequence-focused resilience metric that quantifies the relative access to critical services provided to households by distribution infrastructure during normal conditions and major disruptions. We use a spatially granular grid analysis that facilitates targeted resilience interventions; dividing feeders into isolatable sections and combining those sections with the critical service access metric allows us to identify where energy improvements like solar-plus-storage microgrids could create the most benefits for community members by protecting access to food, fuel, health, shelter, and public safety services. We identify locations in a South Seattle study area that could be high priorities for resilience investment and summarize their potential neighborhood-scale resilience benefits. This analysis was complemented by direct feedback from study area residents collect through a survey and focus groups. Results can help utilities understand how and where long power outages can create real consequences for customers, set strategic targets based on that understanding, and measure the potential benefits of energy resilience upgrades for more informed decisions.
A State-Space Model for Stability Boundary Analysis of Grid-Following Voltage Source Converters Considering Grid Conditions
With the growing significance of renewable energy resources and energy storage systems, the number of grid-connected inverters has been rising at an increasingly rapid pace. Generally, these inverters are directly integrated with the distribution network by synchronizing with the grid voltage at the point of common coupling. However, the low grid strength and varying R/X ratios, as the common characteristics of most distribution networks or weak grids, can lead to dynamic interactions that comprise stability and limit the power transfer capacity of grid-connected inverters. To ensure stable operation of the inverters, researchers must determine the stability boundary, described as the maximum power transfer capacity of grid-connected inverters under the premise of maintaining system small-signal stability. For this purpose, we propose to formulate a state-space model of the system in the synchronously rotating dq-frame of reference and perform eigenvalue analysis to determine the stability boundary. With a detailed model of the control structure and parameters of the grid-connected inverters, the stability boundary is identified as a surface with respect to different grid strengths and R/X ratios. Case study results of proposed eigenvalue analysis are compared with those of admittance model-based stability analysis as well as time-domain simulation using a switching model in Matlab/Simulink, validating the effectiveness and accuracy of the proposed eigenvalue analysis for stability boundary identification.
Analysis of Grid-Forming Inverter Controls for Grid-Connected and Islanded Microgrid Integration
Autonomous grid-forming (GFM) inverter testbeds with scalable platforms have attracted interest recently. In this study, a self-synchronized universal droop controller (SUDC) was adopted, tested, and scaled in a small network and a test feeder using a real-time simulation tool to operate microgrids without synchronous generators. We presented a novel GFM inverter control adoption to better understand the dynamic behavior of the inverters and their scalability, which can impact the distribution system (DS). This paper provides a steady-state and transient analysis of the GFM power inverter controller via simulation to better understand voltage and frequency stabilization and ensure that the critical electric loads are not affected during a prolonged power outage. The controllers of the GFM inverter are simulated in HYPERSIM to examine voltage and frequency fluctuations. This analysis includes assessing the black start capability for photovoltaic microgrids, both grid-connected and islanded, during transient fault conditions. The high photovoltaic PV penetration levels open exciting opportunities and challenges for the DS. The GFM inverter control demonstrated appropriate response times for synchronization, connection, and disconnection to the grid. The DS has become more resilient and independent of fossil fuels by increasing the penetration of inverter-based distributed energy resources (DERs).
Large-signal Stability Analysis of Grid-forming Inverters with Equivalent-circuit Models
Here, this paper proposes an energy function-based direct method for large-signal stability assessment of grid-forming (GFM) inverters leveraging an equivalent-circuit representation of all involved control- and physical-layer dynamics. Three different primary controls, a standard inner-current outer-voltage cascaded-control architecture, output LCL filter, and reference-current saturation limiting are featured in the modeling and analysis framework. A composite energy function for the GFM inverter is obtained by summing up individual energy contributions gleaned from the circuit representation. The approach can readily be generalized to different primary controls, output-filter arrangements, and current limiters since it is based on a circuit-theoretic foundation. Numerical simulations validate the efficacy of the approach in estimating the critical clearing time following a large-signal disturbance.
A discontinuous piecewise polynomial generalized moving least squares scheme for robust finite element analysis on arbitrary grids
A variational approach is developed with a meshless discretization to enable accurate and robust numerical simulation of partial differential equations for meshes that are of poor quality. Traditional finite element methods use the mesh to both discretize the geometric domain and to define the finite element shape functions. The latter creates a dependence between the quality of the mesh and the properties of the finite element basis that may adversely affect the accuracy of the discretized problem. Here, we propose a new approach for defining finite element shape functions that breaks this dependence and separates mesh quality from the discretization quality, which we call discontinuous piecewise polynomial generalized moving least squares (DPP-GMLS). At the core of the approach is a meshless definition of the shape functions, which limits the purpose of the mesh to representing the geometric domain and integrating the basis functions without having any role in their approximation quality. The resulting non-conforming space can be utilized within a standard discontinuous Galerkin framework, providing a rigorous foundation for solving partial differential equations on low-quality meshes. We present a collection of numerical experiments demonstrating our approach in a wide range of settings: strongly coercive elliptic problems, linear elasticity in the compressible regime, and the stationary Stokes problem. We demonstrate convergence for all problems and stability for element pairs for problems which usually require inf-sup compatibility for conforming methods, also referring to a minor modification possible through the symmetric interior penalty Galerkin framework for stabilizing element pairs that would otherwise be traditionally unstable. Mesh robustness is particularly critical for elasticity, and we provide an example that our approach provides a greater than 5 x improvement in accuracy and allows for taking an 8 x larger stable timestep for a highly deformed mesh, compared to the continuous Galerkin finite element method.
GPU-based transient analysis of modern grids deploying a hybrid DDM algorithm
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Reliability Analysis of Power Grids Considering Component Failures of Variable Energy Resources
This paper proposes an improved model for the reliability assessment of power systems considering component failures of variable energy resources (VER). The inherent intermittency of VER such as solar photovoltaic (PV) and wind farms, along with their susceptibility to component failures, present significant challenges to reliable system operation. These issues, combined with power grid operation and network constraints, complicate the reliable operation of VER-integrated power systems. Here, to address these concerns, this paper introduces a reliability assessment framework that considers VER input variability, its impact on component availability, and their resulting impact on overall system reliability. Stochastic models based on discrete Markov processes are developed to incorporate variable irradiance, wind speeds, and their effects on PV and wind component failure rates. A next-event and state transition-based approach is then developed to integrate the stochastic models into a mixed-timing sequential Monte Carlo simulation framework for composite reliability assessment. Case studies on the RTS-GMLC system demonstrate the effectiveness of the proposed model in evaluating the reliability of VER-integrated systems.
STM/S Grid LDOS Data and Analysis Code for Deciphering Majorana Zero Modes in Topological Superconductor
This dataset provides raw millikelvin scanning tunneling microscopy/spectroscopy (STM/S) grid spectroscopy data and Python analysis scripts supporting the manuscript “Deciphering Majorana Zero Modes in Topological Superconductor FeTe0.55Se0.45 with Machine-Learning-Assisted Spectral Deconvolution.” The dataset includes a raw grid spectroscopy file acquired on FeTe0.55Se0.45 at 40 mK under magnetic field, together with Python/Jupytext analysis scripts used for STM/S data processing, visualization, spectral deconvolution, Lorentzian peak fitting, feature extraction, machine-learning-assisted clustering, and figure generation. These files support the analysis of vortex-core local density of states and the identification of zero-bias-peak-related spectral components from complex in-gap states. The dataset is intended to provide a citable archival record of the data and analysis code associated with the published manuscript and to support transparency and reproducibility of the reported STM/S and machine-learning workflow.
Geomagnetically Induced Current Field Test on Large Grid-Connected Power Transformers: Analysis, Model Development, and Simulations
Geomagnetic-induced current (GIC) flow in power grids can cause undesirable effects such as transformer overheating, harmonics, higher reactive power demand, etc. Many simulation models have been developed to study these effects, but real-world verification on modern transformer designs is rare. Here, this paper presents the first long-duration GIC field test in the U.S. performed on high-voltage, grid-connected transformers featuring winding clamps and tie rods instead of conventional tie bars. Field measurements were taken to evaluate GIC effects. These measurements also aided in developing and validating thermal and electromagnetic transient (EMT) models of the transformers. During the test, significant current and voltage distortions were observed along with considerable transformer reactive power losses. Analysis of the field measurements showed that the transformers’ hottest spot was at the inner windings, and their k-factors were close to factory test and software default values. Thermal simulations indicated that the transformers would not violate their thermal limits even for a GIC waveform that peaks at about 200 A/phase. EMT simulations revealed that increased transformer loading may reduce GIC-induced reactive power demand and harmonics in certain scenarios. The study also highlighted potential inaccuracies in using the k-factor method to calculate transformer reactive power losses.
xCDAT: A Python Package for Simple and Robust Analysis of Climate Data
xCDAT (Xarray Climate Data Analysis Tools) is an open-source Python package that extends Xarray (Hoyer & Hamman, 2017) for climate data analysis on structured grids. xCDAT streamlines analysis of climate data by exposing common climate analysis operations through a set of straightforward APIs. Some of xCDAT’s key features include spatial averaging, temporal averaging, and regridding. These features are inspired by the Community Data Analysis Tools (CDAT) library (Dean N. Williams et al., 2009) (D. N. Williams, 2014) (Doutriaux et al., 2019) and leverage powerful packages in the Xarray ecosystem including xESMF (Zhuang et al., 2023), xgcm (Abernathey et al., 2022), and CF xarray (Cherian et al., 2023). To ensure general compatibility across various climate models, xCDAT operates on datasets that are compliant with the Climate and Forecast (CF) metadata conventions (Hassell et al., 2017).
Feedback and Oscillations: Constructing Feedback Systems for Root Cause Analysis of Oscillations in Power Grids
Dynamic phenomena linked to inverter-based resources (IBRs) have gained global attention. Several IBR-induced dynamics have caused bulk power system-connected wind or solar power plants to trip, and some have even led to widespread outages. In addition, many oscillations have been observed involving IBR power plants. In 2023, the IEEE Power & Energy Society (PES) IBR Subsynchronous Oscillations (SSO) task force published a journal article, “Real-World Subsynchronous Oscillation Events in Power Grids With High Penetrations of Inverter-Based Resources,” in which 19 IBR oscillation events were examined for their causation. Earlier in 2020, another PES task force article, “Definition and Classification of Power System Stability-Revisited & Extended,” authored by prominent academics, introduced converter-driven stability as a new category of stability. The international power grid industry community also took action by publishing the CIGRE Green Book, Power System Dynamic Modelling and Analysis in Evolving Networks (led by Babak Badrzadeh and Zia Emin) in 2024. In August 2024, the Energy Systems Integration Group (ESIG) released a practical guide led by Nick Miller, “Diagnosis and Mitigation of Observed Oscillations in IBR-Dominant Power System: A Practical Guide.” The goal of the guide is to assist practicing engineers in making initial judgments and conducting detailed analyses about oscillations. Finally, when addressing the classification of stability and oscillations, the guide emphasizes a causality-based taxonomy for grouping, such as voltage control-induced oscillations, synchronization-induced oscillations, and frequency or active power control-induced oscillations.