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DOE OSTI2025

Grey-Box System Identification of Grid-Forming Inverters

This paper demonstrates the use of grey-box system identification methods for simplifying and understanding the nonlinear power dynamics of grid-forming inverters (GFMs). The power and frequency outputs of complex high-order GFM models are fed into system identification software in order to fit them to a predetermined LTI system and learn system parameters such as (synthetic) inertia and droop constants. The same process is then run for a high-order synchronous generator model, and the outputs are fit to the same set of LTI equations. Simulation of a network of GFM inverters with diverse control architecture is also performed for the same process. The intent is threefold: first, to demonstrate the appropriateness of unified LTI models for describing the power and frequency dynamics of individual resources and connected networks, in order to facilitate analysis of larger heterogeneous networked systems; second, to discover the relationship between internal control parameters of GFMs and their externally observed values; and third, to validate that grey-box data-driven system identification techniques can be a valuable tool to discover the values of important parameters in the absence of explicit vendor models.

analytical models↗

DOE OSTI2022

A Generic Primary-Control Model for Grid-Forming Inverters: Towards Interoperable Operation & Control

This paper outlines an architectural vision centered around the notion of interoperability to integrate grid-forming inverter-based resources in large-scale grids. With the underlying principle of interoperability guiding developments, we focus on modeling the characteristics of droop, virtual synchronous machine, and virtual oscillator controls. Emphasis is placed on these three controllers since they are leading grid-forming control candidates and are likely to be commonplace as primary-control schemes in future systems. We show that these controllers can each be considered as instantiations of a more generic model and that all these controllers exhibit similar droop-like relations between pertinent terminal variables in steady state. This commonality between controllers gives interoperability among them such that automatic synchronization, power sharing, and voltage regulation can be achieved. Simulation results validate the models and demonstrate how the steady-state droop characteristics of these control methods can be aligned with the aid of the developed modeling paradigm.

control↗

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 OSTI2024

Performance Evaluation of a Single-Phase Grid-Forming Inverter Through Hardware Experiments

This study conducts hardware experiments to assess the performance of a commercial single-phase grid-forming (GFM) inverter using a purely hardware-based approach. We adhere to a testing protocol for the GFM inverter and enhance it by exploring the transient performance of GFM inverters across various grid dynamic events. Quantifiable performance metrics are established for each testing scenario to gain insights into the performance of the single-phase GFM inverters. Based on the comprehensive tests, the following observations are summarized: 1) The performance of the single-phase GFM inverter is satisfactory, and it is capable of being the islanding master for residence homes when the main grid is gone. 2) For frequency response, the inverter is able to stay connected but cannot inject the needed active power to support the grid. This may be improved by the manufacturer by using droop control. 3) The GFM inverter exhibits harmful transients in voltage and frequency during islanding operation, which can be enhanced by maintaining the same operating points before and after the breaker is open.

dynamic performance↗

DOE OSTI2021

Open-Source PSCAD Grid-Following and Grid-Forming Inverters and a Benchmark for Zero-Inertia Power System Simulations: Preprint

This paper presents open-source, flexible, and easily-scalable models of grid following and grid forming inverters for the PSCAD software platform. The models are intended for system integration studies, particularly stability analyses of power systems with high penetration of inverter-based generation. To verify the model functionality, they are implemented in a IEEE9-bus system in a zero-inertia operational scenario of 100% inverter-based generation. The models have been made available open source at the PyPSCAD NREL GitHub page.

41 EE - Solar Energy Technologies Office (EE-4S)↗

DOE OSTI2021

Design Power Control Strategies of Grid-Forming Inverters for Microgrid Application: Preprint

This paper compares two control schemes in the application control layer of a non-PLL grid-forming (GFM) inverter to gain the insights and understanding of how the two schemes affect the dynamic responses of the GFM inverters and the transition operation of microgrids. Both schemes can achieve smooth microgrid transition operation and power tracking, however, the first scheme expects to exhibit more transients due to the feedforward of the inverse dynamic model of the output filter. Simulation results show that both control schemes achieve successful transition operation with smooth transients, and the second control scheme exhibits slightly better transients in the system frequency during islanding operation and the first one has slightly superior transients in the system frequency during reconnection operation. The power tracking performance in the grid-connected mode is evaluated, which shows that the first scheme has better active power tracking and the second one has better reactive power tracking. The analysis and results are useful to develop reliable control schemes for non-PLL GFM inverters because more and more inverters will work as non-PLL grid-forming sources in the future grids due to better stability and reliability.

grid-forming inverter↗

DOE OSTI2022

Improved Control Strategy of Grid-Forming Inverters for Fault Ride-Through in a Microgrid System

This paper develops an improved control strategy of grid-forming (GFM) inverters with fault ride-through (FRT) capabilities to guarantee the stable operation of microgrids under fault conditions, especially islanded microgrids and asymmetrical faults. The proposed control strategy includes the dual control of positive-sequence and negative-sequence control as well as the adaptive virtual impedance (VI) control. Unlike existing works, the proposed strategy applies the VI control for only the d component of the positive-sequence control and leaves the q component of the positive-sequence control and the dq component of the negative-sequence control as zero, thus achieving improved stability and balanced three-phase voltages under asymmetrical faults. The adaptive feature of the VI control guarantees the stability of the GFM inverter under severe faults, which could cause the saturation of the inner current loop, and the instability if the VI is not adaptive. Simulation results of various unbalanced faults with high and low fault impedances show that the proposed control strategy improves the stability of the GFM inverter and achieves stable and balanced output voltages in islanded microgrids. And the algorithm also improves the stability of GFM inverters under balanced faults with high and low fault impedances.

adaptive virtual impedance control↗

DOE OSTI2022

Improved Control Strategy of Grid-Forming Inverters for Fault Ride-Through in a Microgrid System

This paper develops an improved control strategy of grid-forming (GFM) inverters with fault ride-through capabilities to guarantee the stable operation of microgrids under fault conditions, especially islanded microgrids and asymmetrical faults. The proposed control strategy includes the dual control of positive-sequence and negative-sequence control as well as the adaptive virtual impedance (VI) control. Unlike existing works, the proposed strategy applies the VI control for only the d component of the positive-sequence control and leaves the q component of the positive-sequence control and the dq component of the negative-sequence control as zero, thus achieving improved stability and balanced three-phase voltages under asymmetrical faults. The adaptive feature of the VI control guarantees the stability of the GFM inverter under severe faults, which could cause the saturation of the inner current loop and instability if the VI is not adaptive. Simulation results of various unbalanced faults with high- and low-fault impedances show that the proposed control strategy improves the stability of the GFM inverter and achieves stable and balanced output voltages in islanded microgrids. And the algorithm also improves the stability of GFM inverters under balanced faults with high- and low-fault impedances.

adaptive virtual impedance control↗

DOE OSTI2025

Virtual Self-Excited Induction Generator-Based Grid-Forming Inverter Control for Robust Voltage Regulation Under Nonideal Loading

This paper presents a generator-inspired control methodology for grid-forming (GFM) inverters that deliberately emulates a self-excited induction generator so that the inverter can hold its voltage and frequency under difficult loading and severe terminal disturbances across wide voltage and frequency ranges. The design integrates a Lyapunov energy function-based inner loop to provide high bandwidth and strong disturbance rejection, and it complements this with a passivity-based argument that furnishes a coherent large-signal stability guarantee beyond small-signal limits. Analytical insights are developed via the Krylov-Bogoliubov-Mitropolsky averaging method, which reveals an intrinsic resistive droop characteristic; these closed-form relations both explain the observed dynamics and yield simple, decentralized tuning rules. The methodology is validated on a controller-hardware-in-the-loop platform and exercised in real time across balanced, unbalanced, and nonlinear loads, as well as during parallel operation. Across these scenarios, the inverter maintains balanced three-phase voltages, limits harmonic content, settles quickly with well-damped transients, and remains resilient when multiple units operate in parallel. The contributions are a self-excited-machine-inspired GFM controller with enhanced dynamic performance and robustness, a single stability rationale grounded in passivity, closed-form expressions that guide tuning, and comprehensive hardware-in-the-loop validations demonstrating effectiveness and superiority under challenging operating conditions.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Performance Evaluation of a Single-Phase Grid-Forming Inverter Through Hardware Experiments: Preprint

Existing state-of-the-art of single-phase grid-forming (GFM) inverter are primarily focused on electromagnetic transient simulation, and there are very few works performing hardware test, and there is no clear understanding how the single-phase GFM inverter should behave from a hardware perspective. Therefore, this paper addresses the gap by performing hardware experiment to evaluate the performance of a single-phase GFM hardware inverter. We enrich the existing GFM testing protocols by investigating transient performance of GFM inverters under different grid dynamic events, and quantifiable performance metrics are made to have a common understanding of expected performance of single-phase GFM inverters. A commercial single-phase GFM inverter is used to verify the test protocols and understand the inverter's performance and functionalities.

dynamic events↗

DOE OSTI2023

Investigating Multi-Microgrid Black Start Methods Using Grid-Forming Inverters

This paper examines state-of-the-art microgrid (MG) black-start technologies with grid-forming (GFM) inverter-based resources (IBRs) and proposes black start and interconnection methods for 100% inverter-based MGs. A multiple-MG approach is proposed and compared to the existing methods in a 4-bus, 12-GFM inverter simulation test setup. This investigation involves intelligent synchronization units that enable the autonomous synchronization of multiple MGs based on their terminal measurements. MGs in this setup are held at different loading levels and comprise averaged models of GFM inverters. The results of the black-start techniques are compared, and conclusions are drawn to better prepare MG planners and distribution system operators for next-generation, multi-MG, GFM inverter-based, black-start procedures.

black start↗

DOE OSTI2024

Microgrid to Microgrid Synchronization with Grid-Forming Inverters: Challenges and Solution

Research on network microgrids has primarily focused on control and optimization. However, application aspects such as microgrid-to-microgrid synchronization have not been fully addressed in existing literature. This paper first addresses the challenges of networking microgrids with grid-forming inverter in droop control. Then, it proposes a pre-synchronization algorithm to improves the synchronization speed and transient stability. To improve the speed, the phase difference between adjacent microgrids is minimized. Transients such as inrush current and oscillations are effectively mitigated by increasing the virtual impedance during interconnection. The proposed strategy allows smooth transitions when reconfiguration of the microgrids is needed. The applicability of this strategy to today’s microgrid systems is demonstrated through a validation in a 480V three-phase network microgrid testbed with commercial-grade inverters, protective devices, and switchgear.

Ferrari Maglia, Max↗

DOE OSTI2023

Oscillatory Power Control and Consensus in Unbalanced Networks Using Grid Forming Inverters

In this paper, a state-space nonlinear control previously designed for balanced operation of grid-forming (GFM) inverters is extended to unbalanced operations. Unbalanced voltages and currents are analyzed, and their time-varying direct, quadrature, and zero components are parameterized in terms of six constant parameters. These parameters provide primary control design choices for not only an inverter’s terminal voltage but also its injections of both real and oscillatory power. It is shown that the proposed GFM control can precisely achieve a desired balanced terminal voltage under unbalanced loads. It is also shown that, by allowing the terminal voltage to be slightly unbalanced, oscillatory power can be adaptively minimized. Lastly, it is illustrated that oscillatory power can also be shared among multiple GFM inverters. Case studies and their simulations demonstrate that the proposed GFM control is effective in meeting the aforementioned objectives.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

A Model Calibration Method for Grid-Forming Inverters Using Iterative Bayesian Optimization

As inverter-based resources (IBRs) are rapidly deployed, especially at the distribution and microgrid levels, the need to include their accurate representations in power systems models increases. With well-calibrated models, IBR-interactions can be examined, preventing any stability and operational issues, especially in islanded systems. This paper proposes a method to calibrate generic inverter models using Bayesian optimization, but with a parameter-grouping approach to improve speed and accuracy. This approach is illustrated for a grid-forming inverter using synthetic data and field measurements from a simple IBRbased microgrid. Tests show that the calibration algorithm has modest computation cost and is robust to noisy measurements..

Biswas, Shuchismita↗

DOE OSTI2025

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.

24 POWER TRANSMISSION AND DISTRIBUTION↗

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↗

DOE OSTI2025

Controller Hardware-in-the-Loop Evaluation of a Microgrid Controller for a Microgrid System with Multiple Grid-Forming Inverters

This paper presents the laboratory evaluation of a commercial Microgrid Management System (MGMS) implemented in the real-world Bronzeville Microgrid which features a futuristic scenario with high renewable energy integration and the use of multiple Grid-Forming (GFM) inverters. The primary objective of the performance evaluation for the MGMS is to assess the MGMS's capability to dispatch GFM units, including a GFM PV unit and two GFM battery units, to maintain the system stability and ensure economic operation, thus guaranteeing the microgrid's resilience during prolonged outages and dynamic events. The laboratory controller hardware-in-the-loop provides realistic testing environment through detailed electromagnetic transient modeling of the microgrid system, hardware MGMS, and standard communication protocols (DNP3). The CHIL evaluation shows how the MGMS effectively manages the GFM inverters, highlighting its performance in maintaining stability, reliability, and survivability in a microgrid environment with a high penetration of renewable energy sources.

controller hardware-in-the-loop↗

DOE OSTI2023

Model Specification of Droop-Controlled, Grid-Forming Inverters (REGFM_A1)

This document describes a positive-sequence model of droop-controlled, grid-forming (GFM) inverter-based resources (IBRs). It can be considered as an initial model for evaluating the impacts of GFM IBRs on the transients and dynamics of transmission systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗