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Robust Optimal Control of Inverter-Based Resources Under Grid-Forming Operation

In this paper, we propose and solve a robust control problem for inverter-based resources under grid-forming operation to regulate the voltage and frequency. One major challenge is to mitigate the effect of unmeasurable load current disturbance, grid and load parametric uncertainties. Moreover, strong coupling between the state variables on both the AC and DC sides, as well as between the modulating control input and the frequency impose additional challenges. To address these challenges, first, a robust control problem is solved at the high level via transformation into an equivalent, but more tractable, optimal control problem. Then, in the middle layer a voltage control law is designed on the one side, and a frequency control law on the other side. Finally, an inverter filter current controller is designed to complete the controller design. Theoretical results are derived to provide stability guarantees for the resulting closed-loop system. Specifically, we show that the inverter current injection error is dissipative, the frequency error is semi-globally asymptotically stable, and the inverter terminal voltage error is globally asymptotically stable, all with provided sufficient conditions. Here, numerical simulation experiments are used to validate the theoretical claims. Furthermore, the developed controller is compared with existing work in literature to show the efficacy of the proposed approach.

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A Large-Scale Hardware Experiment Demonstration of Operating High Inverter-Based Resource Power Systems With Grid-Forming Inverters

This paper presents experimental hardware results from a microgrid system as the penetration level of grid-forming (GFM) inverters increases. The experiment aims to showcase the advantages of GFM inverters in enhancing system stability and to investigate the operational challenges in systems relying entirely on inverter-based resources (IBRs). Five test scenarios are devised to progressively increase GFM inverter penetration levels: 0% (S1), 19% (S2), 37% (S3), 68% (S4), and 100% (S5). To ensure consistency, identical loading conditions and dynamic events are applied across all scenarios. The conducted tests include load step changes, output variation of grid-following (GFL) inverters during islanded mode, transition operations (such as synchronization to the grid and islanding), and rateof- change-of-frequency (ROCOF) and voltage jump tests during grid-connected mode. Key findings from the tests are summarized as follows: (1) Scenario S1 proved most challenging for load steps, and GFL variations because of insufficient GFM capacity, leaving the diesel generator unable to handle transient ridethrough; (2) Scenario S5 was the most difficult for transition operations, because the lack of a diesel generator to maintain stiff bus voltage resulted in unexpected reactive power flows during synchronization, causing the point of common coupling (PCC) breaker to trip; (3) Scenarios S4 and S5 were particularly challenging for ROCOF tests because of minimal system inertia, leading to large transients that triggered breaker trips; and (4) Scenario S4 exhibited the strongest voltage recovery capability because of the presence of the diesel generator and a higher number of GFM inverters, both of which possess the highest capacity for reactive power injection.

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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.

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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.

black start

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

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

Coordinated Frequency Regulation in Grid-Forming Storage Network via Safety-Consensus

Inverter-based storages are poised to play a prominent role in future power grid with massive renewable generation. Grid-forming inverters (GFMs) are emerging as a dominant technology with synchronous generators (SG)-like characteristics through primary control loops. Advanced secondary-layer control schemes, e.g., consensus algorithms, allow GFM-interfaced storage units to participate in frequency regulations and restore nominal frequency following grid disturbances. However, it is imperative to ensure critical frequency safety limits are not violated while the grid transitions from pre- to post-disturbance operating point. This paper presents a novel safety-enforced consensus method, having three distinct objectives: safe transient frequency evolution, minimizing frequency deviation, and coordinated power sharing. The proposed technique is illustrated using a GFM-interfaced grid-wide storage network on the IEEE 68-bus system under multiple grid transient scenarios.

consensus control

Oscillation Risks of Grid-Following and Grid-Forming Inverter-Based Resources in Series-Compensated Networks

Here, this paper investigates the dynamic behavior of a grid-connected inverter-based resource (IBR) when connected radially to a series compensated line. Potential interactions between the series compensation and the IBR have been identified for both types: grid-following (GFL) or grid-forming (GFM). The study begins with electromagnetic transient (EMT) simulations to demonstrate stability issues. Subsequently, nonlinear analytical models are formulated in the dq frame, validated against the EMT simulation, and leveraged to assess eigenvalues and participation factors. Influencing factors of the dominant oscillation modes have been identified. The analysis results show that series compensation may make a mode associated with the synchronization unit unstable. Furthermore, customized feedback systems are built for the synchronizing loop. Series compensation can increase the sensitivity of the voltage phase angle towards the synchronizing angle, and introduce phase lag in the real power response towards the synchronizing angle. These factors may cause interactions with the phase-locked loop in GFL-IBR systems and with power-based synchronization in GFM-IBR systems, potentially leading to instability.

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UNIFI's Grid-Forming (GFM) Inverter Reference Design: A Tutorial on Modeling, Control, and Experimental Implementation of GFM Inverters

The UNIFI Consortium's tutorial on grid-forming (GFM) inverters provides a comprehensive guide to the modeling, control, and experimental implementation of GFM inverters. As the integration of renewable energy accelerates, the transition from traditional grid following (GFL) to GFM inverters is crucial to ensure stable and sustainable power systems. This document outlines a reference design for three-phase and single-phase GFM inverters developed at the University of Texas at Austin. The tutorial also provides step-by-step guidance for accessing and using UNIFI’s GitHub repository, enabling users to design, build, and test GFM inverters efficiently. By fostering collaboration and equipping users with accessible resources, this initiative aims to drive widespread adoption of GFM technology across academia, utilities, and industries.

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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.

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Advanced grid-forming (GFM) inverter controls, modeling and system impact study for inverter dominated grids

Our main goals in this project are to understand: 1) the stability of the power system with very high penetration of PV or other inverter-based resources (IBR), 2) the interactions among IBRs and traditional generators, and 3) the impact of the GFM inverters on bulk power system. To achieve these goals, we took a holistic research and development approach. First, an impedance-based large system modeling and stability analysis tool was developed to aid the large IBR system small-signal stability analysis. Second, consensus-based control and transient overload ride through were developed to control and coordinate multiple GFM inverters in a large system to maintain transient stability during big grid events. Third, high fidelity electromagnetic transient (EMT) IBR models were developed and integrated into a large reduced WECC model to study the system impact from IBRs. Lastly, extensive validation tests of the GFM control which was developed in this project and implemented in two 1MW commercial solar inverters were performed using different validation platforms, e.g., control hardware-in-the-loop (CHIL) platform, power hardware- in-the-loop (PHIL) platform, and a real PV plant.

14 SOLAR ENERGY

Grid Forming Control Tuning for a Hybrid Inverter-Based Resource Power Plant

A hybrid inverter-based resource (IBR) power plant consists of grid-following (GFL) and grid-forming inverter-based resources (GFM-IBR) connected in parallel. Here, this research focuses on how to design and tune GFM's control parameters to ensure stable operation of the hybrid power plant for weak and strong grid conditions. We consider two design cases: one where the GFL-IBR does not provide frequency support, and one where it does. It is found that the GFM's power-frequency synchronizing system can lose stability when the power-frequency droop constant is large and/or the grid is strong. Additionally, if the GFL has its frequency support enabled, oscillation stability worsens. To explain the mechanism of the interactions, we construct a feedback system for the synchronizing loop, which consists of the GFM's power-frequency droop control that generates the GFM's synchronizing angle, the GFL's phase-locked loop that measures the voltage phase angle, the GFL's frequency-power control that generates its power order, and the rest of the system. The feedback system is effective in illustrating the potential stability risks. Successful design ensures that the hybrid power plant can operate smoothly and ride through grid disturbances.

feedback systems

Equivalent-Circuit Models of Grid-Forming IBRs for Electromagnetic-Transient Simulations

We derive equivalent-circuit models of control- and physical-layer subsystems of grid-forming (GFM) inverter-based resources (IBRs) for electromagnetic-transient (EMT) simulations. Three different primary controllers are considered: Droop, Virtual Synchronous Machine (VSM), and dispatchable Virtual Oscillator Control (dVOC). In addition, the models include cascaded voltage- and current-control loops, and LCL output filters. Simulations for a single-inverter setup and for a network of five inverters in a modified IEEE 14-bus topology are presented. The equivalent-circuit models simulated with analog electronic circuit-simulator software (in our case, LTspice) offer the same accuracy, and with no explicit tuning of the solver, lower computational burden compared to block-diagram-based implementations in commercial off-the-shelf EMT software (in our case, MATLAB-Simulink).

electromagnetic transient simulation

Field Verification of Grid-Forming Inverter-Based Power Plant Performance for Transmission System Reliability

This report describes some examples of the operation of two grid-forming (GFM) inverter-based photovoltaic-battery hybrid power plants connected to the electric system of the island of Kauai in Hawaii. Both plants are photovoltaic power plants with battery energy storage and are connected to the networked transmission system operated by Kauai Island Utility Cooperative (KIUC), along with several other power plants including an oil-fired plant, diesel generators, small hydroelectric plants, a biofuel plant, and several other photovoltaic plants.

14 SOLAR ENERGY

Standard Library Plant Controller Model Specification for a Grid-Forming Hybrid Control Inverter-Based Resource (REPCGFM_C1)

This document describes a standard library plant controller model to interface with the grid-forming hybrid control inverter-based resource (IBR) model. The initial version of model specification was jointly developed by Pacific Northwest National Laboratory (PNNL), Tesla Energy, and EPRI, and it was revised multiple times later to incorporate suggestions from WECC MVS members. Tesla Energy provided main control algorithms to support the development of this model specification. This standard library model is developed to help the utility industry better understand the GFM technology. The model could be used to represent equipment for long-term planning studies where vendor-specific models are not available. As equipment matures and improves, standard library models will be updated to capture the new functionalities of GFMs. It is not intended that these models will always remain representative of all future GFM technologies.

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Control and Real-Time Simulation of Microgrids with EV Fast-Charging and Grid-Forming Resources

Fast charging stations (FCSs) for electric vehicles (EVs) can behave as constant power loads, which is problematic for the operation of grid-forming (GFM) inverter-based resources (IBRs). To tackle this problem, this paper proposes a control suite that makes FCSs responsive to ac voltage and frequency disturbances. To test the performance of the FCS controls, the paper also sets forth theory to compensate for time-delays appearing in the real-time simulation of microgrid models divided into several central processing units (CPUs). Furthermore, these contributions are showcased via multi-CPU real-time simulations of a faulted microgrid having EV FCSs and GFM IBRs powered by photovoltaic solar arrays as well as power hardware-in-the-loop experiments. These contributions are significant to address NERC recommendations and IEEE standards.

14 SOLAR ENERGY

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

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.

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