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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Critical Clearing Time for Droop-Controlled Grid-Forming Inverters With Circular Current Limiting and Virtual Impedance Current Limiting

The critical clearing time is a crucial parameter for assessing the large-signal stability of grid-forming (GFM) inverters. Variations in current limiters can significantly impact an inverter's transient behavior during large disturbances. Here, this letter introduces a method based on the power-angle relationship to evaluate the fault recovery of a droop-controlled GFM inverter under a three-phase bolted fault scenario, considering both the circular current limiter and the virtual impedance method. High-fidelity simulations validate the accuracy of the proposed formulas in estimating the critical clearing time of the GFM inverter.

42 ENGINEERING↗
DOE OSTI2026

Small-Signal Analysis of Current-Limiting Grid-Forming Inverters

Grid-forming (GFM) inverters are equipped with a current limiter to protect the device during grid disturbances. Because the intervention of the current limiter can compromise the transient stability of the GFM inverter, various types of current limiter designs and additional frequency-stabilization control methods have been proposed in recent literature to aid in transient GFM inverter stability; however, the small-signal stability implications of adding these additional control blocks during, in particular, off-nominal conditions are not fully understood. To address this challenge, this paper presents a generic small-signal model of a GFM inverter that incorporates various types of current limiters and frequency stability-enhancing controls. With the proposed model, we analyze the root causes of inverter instability, which reveals two critical design trade-offs. First, due to current-limiter engagement caused by a disturbance, the GFM inverter dynamics are altered, which can lead to voltage oscillations. Second, additional frequency-stabilization controls can improve the small-signal stability of the GFM inverter, but at the cost of reduced power and voltage support to the grid. Comprehensive hardware experiments validate the theoretical concept and analysis. The findings in this work underscore the importance of incorporating both transient-response and small-signal dynamics requirements into the design procedure of GFM current limiters and frequency-stabilization controls.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

A Two-Stage Current Limiting Control Strategy for Direct-Droop-Controlled Grid-Forming Inverters

This paper presents a two-stage current limiting control strategy with fault ride-through capability for the direct-droop-controlled grid-forming (GFM) inverters. The proposed approach comprises Stage 1 and Stage 2 current limiting controls. During faults, Stage 1 current limiting control instantly clamps the inverter output current magnitude to its maximum transient limit by blocking the switching pulses to the insulated-gate bipolar transistors (IGBTs) with the help of a hysteresis loop control, and Stage 2 current limiting control limits the inverter output current magnitude to its steady-state limit by regulating the amplitude and frequency of the modulating waveform utilizing the active and reactive current limiting control loops. By implementing the current limiting actions in two stages, this approach can effectively limit the over-current within a few cycles after the fault occurrence and ensure synchronism to the grid after long-term fault events. The efficacy of the proposed control approach is validated through electromagnetic transient (EMT) simulation results conducted on a single GFM inverter-based test system and the IEEE 39-bus test system with multiple GFM inverters in the PSCAD platform.

Mohiuddin, Sheik Mohammad↗
DOE OSTI2025

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.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Conductivity-Driven Origin of the Limiting Current in Concentrated Electrolytes

Next-generation electrolyte materials are hindered by their ability to support high currents essential for fast-charge and high-power battery applications. The maximum current supported by an electrolyte, the limiting current, is dictated by the formation of concentration gradients across the electrolyte under an electric field. Most of the literature attributes the onset of the limiting current in concentrated electrolytes to the salt concentration at the positive electrode approaching the solubility limit. Here, in this study, we leverage operando X-ray transmission imaging to measure spatiotemporal salt concentration profiles of a polymer electrolyte in a lithium–indium symmetric cell at a current exceeding the limiting current. The measurement of concentration profiles enables mapping the spatiotemporal electric potential, which comprises an ohmic contribution, governed by conductivity, and an overpotential related to maintaining concentration gradients. We find that a precipitous drop in conductivity at the positive electrode drives the divergence of electric potential, rather than a thermodynamic solubility limit.

Abdo, Emily E. [University of California, Berkeley↗
DOE OSTI2025

Small-Signal Stability of Grid-Forming Inverters Using Current-Limiting and Frequency Stabilization

This paper presents a small-signal stability analysis of grid-forming (GFM) inverters under current-limiting conditions. It examines how adjustments in virtual impedance angles, implemented through advanced current-limiting and frequency stabilization techniques, influence small-signal stability. This paper studies a GFM inverter control integrating a fictitious power technique stabilizing primary control by adding a virtual power term and a hybrid current limiter integrating virtual impedance in the anti-wind-up feedback with current reference saturation limiting. A small-signal model is developed to assess the impact of virtual impedance angles on GFM inverter dynamics during grid disturbances, such as voltage drops. The findings indicate that although increasing the virtual impedance angle (to make it more inductive) enhances large-signal stability and voltage support during faults, it can induce oscillations and lead to instability if the angle exceeds certain thresholds. Based on the small-signal models, this paper provides design considerations for the current-limiter impedances to ensure reliable GFM inverter behavior under grid disturbances while maintaining small-signal stability.

current limiting↗
DOE OSTI2025

The Implications of Collisions on the Spatial Profile of Electric Potential and the Space-Charge-Limited Current

The space-charge-limited current (SCLC) in a vacuum diode is given by the Child-Langmuir law (CLL), whose electric potential ϕ(x) ∝ (x/D) 4/3 , where x is the spatial coordinate across the gap and D is the gap separation distance. For a collisional diode, SCLC is given by the Mott-Gurney law (MGL) and ϕ(x) ∝ (x/D) 3/2 . Here, we apply a capacitance argument for SCLC and use the transit time from a recent exact solution for collisional SCLC to show that ϕ(x) ∝ (x/D)ξ for a general collisional gap, where 4/3 ≤ ξ ≤ 3/2 . Furthermore, ξ is strictly a function of νT, where ν is the collision frequency and T is the electron transit time. Using this definition of ξ, we estimate the spatial dependence of the electron velocity and use the gap capacitance to derive an analytic equation for collisional SCLC that agrees within ~4.5% of the exact solution that requires solving parametrically through T. This analytic equation for general ξ asymptotically recovers the CLL as ν → 0 and the MGL as ν → ∞. As a result, matching these limits shows that ξ ≈ 1.40 and V ∝ D 2 ν 2 at the transition from a vacuum to a collisional diode for any device condition.

Anodes↗
DOE OSTI2026

Universal Relationship between Limiting Current and Electrochemical Transport Properties in Malonate-Based Polymer Electrolytes

There is considerable interest in developing high-performance electrolytes for rechargeable lithium batteries. For practical applications, the electrolyte must support large dc currents. However, the parameters most often reported in the literature, conductivity, κ, and current fraction, ρ + , reflect ion transport in the limit of infinitesimal currents. In this limit, the efficacy of an electrolyte is given by the product κρ + . The limiting current density, i lim , is the maximum current density that can be applied across an electrolyte; the cell voltage diverges if the applied current density exceeds ilim. This parameter reflects ion transport in the limit of large dc currents and is therefore of practical interest. It would therefore be convenient if i lim could be predicted from measurements of κρ + . In order to explore this possibility, we studied six malonate-based polymers and PEO at a fixed salt concentration (r = 0.08) and temperature (90°C) using symmetric cells with planar electrodes. Unfortunately, there is no correlation between ilim and κρ + . When the applied current density, i, is less than ilim, the cell voltage approaches a stable plateau, ϕ plateau . Here, we found a linear dependence between i and thickness-normalized plateau potential, ϕ plateau L –1 , irrespective of the magnitude of the applied current. In all seven polymer electrolytes, we found a linear correlation between ilim and the slopes of these lines, σ. In other words, measurements of σ can be used to predict the limiting current.

Jana, Rounak [Lawrence Berkeley National Laborator↗
DOE OSTI2025

A Methodology for the Analysis of Water Oxidation Electrocatalysts in the Absence of Limiting Current that Avoids the Pitfalls of Existing Methods

Water oxidation is an important reaction studied as a way to generate electrons from water, to promote water splitting and the formation of green hydrogen. When using electrodes to drive homogeneous water oxidation catalysis, cyclic voltammograms are analyzed to provide catalytic rate constants. There are two main methods, foot-of-the-wave analysis (FOWA) and limiting current analysis. FOWA relies on approximations inherent to analyzing water oxidation catalysis, such as determining the formal potential of the catalytic intermediate, E 0 cat . Limiting current methods are the optimal way to analyze catalyst performance but rely on observable limiting current, which is virtually never seen in water oxidation. To avoid those issues, a method is proposed for analyzing nonideal cyclic voltammetry waveshapes in water oxidation: by analyzing rate data across a large range of potentials, an optimal potential, E 0 cat , can be obtained, where catalytic current, i cat , is nearly independent of scan rate and has a linear dependency on buffer concentration. Here, the method is applied to four homogeneous water oxidation catalysts with prior extensive electrochemical elucidation, all of which lack an ideal, purely kinetic waveshape in cyclic voltammetry. Application of the method avoids the biases of the other methods cited for the kinetic analyses of water oxidation catalysts.

14 SOLAR ENERGY↗
DOE OSTI2025

Transient Stability-Enhancing Method for Grid-Forming Inverters Under Current Limiting

The primary controller of a grid-forming (GFM) inverter governs the internal reference voltage and angle, which enables the inverter to naturally synchronize and share power with the connected grid; however, during disturbances on the grid caused by, e.g., line faults, overloading, or frequency and phase shifts, a GFM inverter can be pushed into a current-limited operation to protect the device against thermal damage. This can lead to a windup of the internal reference frequency generated by the primary controller and cause a total loss of synchronism with the grid. Here, to make the primary controller of GFM inverters more robust against transient instability, this paper proposes a method that manipulates the reference signals governed by the primary controller by introducing the concept of fictitious power. The fictitious power counteracts the integrator windup in the primary controller, which enables the current-limited inverter to conceive a stable operating point. This method is benchmarked against five state-of-the-art GFM inverter stabilization methods to evaluate its stability-enhancing performance. Full-order electromagnetic-transient simulations and experimental results of a hardware inverter test setup validate the benefits of the method to improve the transient stability of GFM inverters in the face of grid disturbances.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Calculating the space-charge-limited current density for nonplanar geometries by simulating the charge-free electric field

Calculating the space-charge-limited-current density (SCLCD) for a complicated diode geometry often requires computationally expensive particle-in-cell (PIC) codes. Here, this paper addresses this issue by using the charge-free electric field $E_0$ calculated using COMSOL Multiphysics to determine local and global SCLCD. The SCLCD obtained by using the surface average of $|E_0|^2$ on the cathode recovers theoretical results for one-dimensional (1D) planar, cylindrical, and tip-to-tip geometries in appropriate limits. We next compared tip-to-tip calculations with the SCLCD obtained using the PIC code Empire. The SCLCD calculated using COMSOL agreed well with Empire for flatter 1D tip-to-tip geometries and diverged with increasing sharpness. Physically, Empire predicts lower SCLCD than COMSOL because the electrons spread due to concentrated space-charge at the tip, whereas theory assumes that the electrons follow the charge-free electric field lines. We further assess the behavior of the SCLCD for tips protruding from the centers of flat, circular plates of various areas. Larger plate areas with constant tip size recover the 1D planar SCLCD globally and 1D tip-to-tip SCLCD locally, while reducing the difference between Empire and COMSOL calculations since larger plates capture more of the emitted electrons, reducing SCLCD suppression due to beam spreading. These results show that charge-free electric field simulations can be used to determine the SCLCD without needing to simulate particle dynamics in PIC.

Wright, Jack K. [Purdue Univ., West Lafayette, IN ↗
DOE OSTI2025

Simulations of the fault current limiting operation of a long-length REBCO CORC ® superconducting cable cooled by helium gas

Conductor-on-round-core (CORC®) cables composed of rare-earth-barium-copper-oxide high-temperature superconducting (HTS) tapes are of great interest for power transmission applications due to their many advantages such as high power density, light weight, and low loss. Closed circulation loops of cryogenic helium gas can be used to cool HTS cables down to low temperatures to significantly improve their current-carrying capacity. Coupled circuit-electromagnetic-thermal finite element simulations implemented in the COMSOL Multiphysics package were developed, validated, and then used for simulating the fault current limiting (FCL) performance and the cooling processes of an 8-layer CORC® cable cooled with a flow of cryogenic helium gas. In the simulations, the temperature dependence of the electrical and thermal properties of all component materials is implemented for improved accuracy. To overcome computational challenges caused by the considerable difference in geometrical scales (i.e. few-µm-thick HTS layers versus 10 m-long HTS cable), the model is divided into two separate simulations. The first simulation is performed on the transverse cross-section of the cable to calculate the electric field, heating power and temperature rise in each component of a CORC® cable during FCL operation. The heating power calculated in the first simulation is transferred to the second model to simulate the cooling of a 10 m-long cable after the fault is cleared. The effect of the helium gas flow rate on the cooling process is also investigated to develop strategic approaches for optimizing cooling systems for HTS cables with FCL capability. The simulations indicated that a 40 ms fault with a voltage drop of 20 V m −1 along the cable can result in a temperature increase from 60 K to about 165 K inside the cable, and it takes about 500 s to cool the cable back to nearly 60 K with a flow of cold helium gas at a rate of 5 g s −1 .

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

A Guide to Current Limiting and Stability with Grid-Forming Inverters

The electric power grid is changing. For many decades, the synchronous generator - an electromechanical device invented in 1887 - has been the workhorse and backbone of power grids across the globe. Our entire infrastructure is built around it. But times change, and so does the power grid. Since the early 21st century, we have seen a gradual shift in modern power grids away from synchronous generators to ones dominated by power electronic inverter-based resources (IBRs). Sources such as photovoltaics, wind turbines, battery storage, fuel cells, and other technologies like high-voltage DC transmission interconnections all rely on an inverter to connect and interface with the grid. They are increasingly being installed on the grid to augment, or even replace, traditional energy sources. This change is a fundamental shift that brings tremendous technical challenges and questions: Can a power grid remain stable with many more inverter-based resources? How do we avoid more blackouts on the grid? How do we keep the grid secure and resilient during disturbances? After all, power electronic inverters are nothing like the big, rotating, iron-and-copper machines that the grid heavily relies on. Many of these questions can be answered by using grid-forming (GFM) inverters, yet many research challenges remain. This document explores GFM inverters and how they can help stabilize the future grid, especially during disturbances and contingencies. It summarizes a two-year research and development fellowship program at NREL. We point interested readers to more detailed works developed during the project along the way. Let's dive in

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Influence of Control and Limiter Schemes on Sequence-Domain Fault Models of Grid-Forming Inverter-Interfaced Distributed Generators

Unlike synchronous generators, the fault response of grid-forming (GFM) inverter-interfaced distributed generators (IIDGs) is notably governed by the selection of control and current limiting strategies rather than inherent physical traits. While recent research has focused on the sequence domain fault model of GFM IIDGs, a research gap exists in elucidating the influence of control and current limiting schemes on this model's characteristics. This article aims to fill this void by examining how different control and current limiting schemes influence the positive and negative sequence impedances in the phasor-domain fault model of GFM IIDGs. This investigation encompasses droop-based, virtual synchronous machine-based, and virtual oscillator-based reference generation controls alongside rotating and stationary reference-frame-based voltage controls. Furthermore, saturation-based, latching-based, circular and virtual impedance-based current limiting schemes are analyzed. To achieve this goal, a thorough numerical simulation study is conducted. Findings indicate that outer reference generation controls exhibit minimal impact. Conversely, the choice of voltage control and various current limiting schemes emerge as the predominant factors shaping the sequence models of GFM IIDGs. These analyses and results are instrumental in devising reliable protection strategies within inverter-based grids, as a comprehensive understanding of electrical elements in the sequence domain is imperative for effective protective measures.

current limiters↗
DOE OSTI2025

Time-reversed Young’s experiment: Deterministic, diffractionless second-order interference effect

The classic Young’s double-slit experiment exhibits first-order interference, producing alternating bright and dark fringes shaped by the diffraction effect of the slits. In contrast, here we demonstrate that its time-reversed configuration generates an ideal, deterministic second-order ‘ghost’ interference pattern free from diffraction and first-order effects with the use of only a position-fixed detector. The pattern’s size is governed by the dimensions of the ‘effectively extended light source’ formed by point emitter(s). Beyond highlighting the nonreciprocal physics between the two configurations, this system unlocks a range of novel phenomena inaccessible in traditional double-slit experiments. These include fully programmable, digitized interference fringe formations and the ability to align the pattern plane with the source plane on the same side of the setup. Remarkably, our proposed experiment achieves these outcomes without relying on nonclassical correlations or quantum entanglement. Here, by restoring time-reversal symmetry and eliminating diffraction, our theoretical analysis reveals that this approach offers exciting potential for advancing optical imaging and sensing technologies with improved transverse and longitudinal phase-shift sensitivity and resolution limit beyond current limitations.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2026

Theoretical assessment of the transition between electron emission mechanisms in a collisional crossed-field gap

Understanding the transition to the limiting current under vacuum and collisional conditions for thermal-field emission in a crossed-field gap is critical for characterizing the operating regime for numerous applications, such as high-power microwaves and Hall thrusters. By deriving the exact solution for the current density as a function of cathode temperature (and, by extension, initial velocity), cathode electric field, applied voltage, collision frequency, and magnetic field, we determine the transition from the canonical current source (thermal-field emission) to the vacuum and collisional limiting currents under different operating conditions. Here, we further show that the exact solution recovers the asymptotic solutions for the canonical and limiting currents for vacuum and collisional crossed-field gaps under appropriate limits. The exact solution demonstrates that the critical current decreases with both increasing magnetic field strength and increasing collisionality. Nexus phase space plots constructed by matching the individual asymptotic solutions provide the conditions for the transitions between mechanisms, elucidating when a single mechanistic equation would suffice and when theories combining multiple mechanisms are necessary.

Breen, Lorin I. [Purdue Univ., West Lafayette, IN ↗
DOE OSTI2025

Counter-Current Flow Limitation Studies in Complex Geometries Utilizing Interface Capturing Simulations Coupled with PID Flow Rate Controller

In nuclear thermal-hydraulic studies, counter-current flow limitation (CCFL) typically refers to steam rising at a fast rate such that it prevents coolant from draining down within a confined channel. CCFL is a crucial issue in nuclear reactor safety analysis. This study investigates CCFL in debris bed channels using high-resolution interface-capturing simulations. A novel proportional-integral-derivative flow rate controller is developed to efficiently achieve the CCFL conditions. Verification studies confirm that CCFL occurs under the same conditions with or without the controller, demonstrating that PID control ensures accurate prediction. Three debris bed channel geometries were examined: a cylindrical channel, a channel with small obstacles, and a channel with large obstacles. Results show that obstacles significantly impact flow behavior, interfacial shear, wall shear, and pressure gradients required for CCFL. Furthermore, the comparison with experimental data confirmed that simulations incorporating geometric complexities align more closely with experimental CCFL conditions. A pressure gradient correlation was also developed for CCFL prediction.

Counter-current flow limitation↗
DOE OSTI2024

Equivalent-Circuit Models for Grid-Forming Inverters under Unbalanced Steady-State Operating Conditions: Preprint

Positive- and negative-sequence equivalent-circuit models are put forth to capture the operation of grid-forming (GFM) inverters in unbalanced steady-state operating conditions acknowledging the impact of current limiting. The particular control architecture examined adopts droop control (for primary control), nested inner-current and outer-voltage control (in the stationary reference frame), and it is adaptable to two different types of current limiting (current-reference saturation and virtual-impedance limiting). We anticipate the proposed models to be of interest in modeling, analysis, and simulation of GFM inverters in unbalanced settings that may arise, e.g., in the face of faults. Validation of the equivalent-circuit models is pursued via comparison with full-order electromagnetic-transient (EMT) simulations for representative balanced and unbalanced faults.

equivalent-circuit models↗