Grid-forming Inverters Research Articles

Power System Stability With a High Penetration of Inverter-Based Resources

Inverter-based resources (IBRs) possess dynamics that are significantly different from those of synchronous-generator-based sources and as IBR penetrations grow the dynamics of power systems are changing. This article discusses the characteristics of the new dynamics and examines how they can be accommodated into the long-standing categorizations of power system stability in terms of angle, frequency, and voltage stability. It is argued that inverters are causing the frequency range over which angle, frequency, and voltage dynamics act to extend such that the previously partitioned categories are now coupled and further coupled to new electromagnetic modes. While grid-forming (GFM) inverters share many characteristics with generators, grid-following (GFL) inverters are different. This is explored in terms of similarities and differences in synchronization, inertia, and voltage control. The concept of duality is used to unify the synchronization principles of GFM and GFL inverters and, thus, established the generalized angle dynamics. This enables the analytical study of GFM-GFL interaction, which is particularly important to guide the placement of GFM apparatuses and is even more important if GFM inverters are allowed to fall back to the GFL mode during faults to avoid oversizing to support short-term overload. Both GFL and GFM inverters contribute to voltage strength but with marked differences, which implies new features of voltage stability. Several directions for further research are identified, including: 1) extensions of nonlinear stability analysis to accommodate new inverter behaviors with cross-coupled time frames; 2) establishment of spatial–temporal indices of system strength and stability margin to guide the provision of new stability services; and 3) data-driven approaches to combat increased system complexity and confidentiality of inverter models.

Fusion of Microgrid Control With Model-Free Reinforcement Learning: Review and Vision

Challenges and opportunities coexist in microgrids as a result of emerging large-scale distributed energy resources (DERs) and advanced control techniques. In this paper, a comprehensive review of microgrid control is presented with its fusion of model-free reinforcement learning (MFRL). A high-level research map of microgrid control is developed from six distinct perspectives, followed by bottom-level modularized control blocks illustrating the configurations of grid-following (GFL) and grid-forming (GFM) inverters. Then, mainstream MFRL algorithms are introduced with an explanation of how MFRL can be integrated into the existing control framework. Next, the application guideline of MFRL is summarized with a discussion of three fusing approaches, i.e., model identification and parameter tuning, supplementary signal generation, and controller substitution, with the existing control framework. Finally, the fundamental challenges associated with adopting MFRL in microgrid control and corresponding insights for addressing these concerns are fully discussed.

A Distributed Scheme for Voltage and Frequency Control and Power Sharing in Inverter-Based Microgrids

Grid-forming inverter-based autonomous microgrids present new operational challenges as the stabilizing rotational inertia of synchronous machines is absent. The design of efficient control policies for grid-forming inverters is, however, a nontrivial problem where multiple performance objectives need to be satisfied, including voltage/frequency regulation, current limiting capabilities, and active power sharing and a scalable operation. We propose, in this article, a novel control architecture for frequency and voltage control, which allows current limitation via an inner loop, active power sharing via a distributed secondary control policy, and scalability by satisfying a passivity property. In particular, the frequency controller employs the inverter output current and angle to provide an angle droop-like policy, which improves its stability properties. This also allows us to incorporate a secondary control policy for which we provide an analytical stability result, which takes line conductances into account (in contrast to the lossless line assumptions in the literature). The distinctive feature of the voltage control scheme is that it has a double-loop structure that uses the dc voltage in the feedback control policy to implement a power-balancing strategy to improve performance. The performance of the control policy is illustrated via simulations with detailed nonlinear models in a realistic setting.

Dynamic Interactions between Parallel Grid-Forming Inverters in a Microgrid

The potential instability issues caused by the dynamic interactions between parallel grid-forming inverters are examined. The approach adopted for analysis is s-domain admittance-based eigenvalue and mode shape analysis. This admittance is based on a five-node circuit diagram after the conversion of each electric circuit element and inverter control unit into impedance models. Eigenvalue analysis results show that unstable resonance modes may exist due to the interactions of two parallel inverters. Impacts of transmission line length, the converter control’s virtual impedance unit, and the voltage feed-forward unit are examined via the eigenvalue and mode shape analysis. The results show that the virtual impedance control has a negligible influence on the resonance while the voltage feed-forward unit stabilizes the resonance. Finally, the stability analysis is validated using electromagnetic transient (EMT) simulations.

A Power-Angle-Based Adaptive Overcurrent Protection Scheme for Grid-Forming Inverter Under Large Grid Disturbances

As the capacity of renewable energy generation increases, grid-forming (GFM) inverters are deemed as promising solutions for low inertia power grids. However, power-electronic-based inverters have limited overcurrent capability, so additional overcurrent protection schemes are necessary. More importantly, the stability should not be jeopardized by using additional overcurrent protection schemes. However, GFM inverters with the conventional current reference limiting method tend to be unstable under large grid disturbances such as grid frequency drop. To address this problem, this paper proposes a virtual power angle limiting method. The main idea of this method is to limit the output power by limiting the power angle instead of directly limiting the current reference. Thus, the power synchronization control law is still satisfied when the overcurrent protection is triggered, so that the stability can be maintained. Besides, after redesigning the power angle limiting value, the proposed method is also suitable for grid voltage sag cases. A significant advantage of the proposed method is that the output current can be limited automatically during grid voltage sag or frequency drop events without the need of fault detection or tuning control structures and parameters. Simulation and experimental results have verified the effectiveness of the proposed method.

Small-signal modelling and stability analysis of grid-following and grid-forming inverters dominated power system

In this paper, the explicit state-space model for a multi-inverter system including grid-following inverter-based generators (IBGs) and grid-forming IBGs is developed by the two-level component connection method (CCM), which modularized inverter control blocks at the primary level and IBGs at the secondary level. Based on the comprehensive state-space model representing full order of system dynamics, eigenvalues of the overall system are thoroughly analyzed, identifying potential adverse impacts of not only grid-following inverters, but also grid forming inverters on the system small- signal stability, with the underlying principle of oscillations also understood. Numerical and simulation results validate effectiveness of the proposed methodology on IEEE benchmarking 39-bus system

Transformer Inrush Current Mitigation Techniques for Grid-Forming Inverters Dominated Grids

The use of inverters-based resources (IBRs) is rising rapidly in power networks due to increased renewable energy penetration. This requires revisiting of classical network operation standards. For instance, high transformer energization inrush current has been studied extensively under the classical network paradigm. Whereas this paper investigates transformers' energization techniques in the context of inverters dominated grids, where inverters with limited short-circuit current are expected to utilize their grid-forming capabilities for black-start. Common transformer energization techniques such as controlled switching and soft energization are first analyzed with a new perspective aiming to assess their feasibility when used with grid-forming inverters and existing network assets. Parameters influencing soft energization voltage ramp-up time ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T_{ramp}$</tex-math></inline-formula> ) are investigated, and a new <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$T_{ramp}$</tex-math></inline-formula> estimation framework for transformer energization from IBRs is introduced. Due to the variability of available point-on-wave circuit breakers (CBs) in distribution networks, controlled energization using single-pole and three-pole CBs is investigated for various configurations and their application limits are identified. A comprehensive case study is then presented using a test network with multiple transformers to benchmark the performance and requirements of each technique when the network is energized from an IBR, followed by a set of practical recommendations.

Power hardware-in-the-loop testing for multiple inverters with virtual inertia controls

Virtual inertia (VI) control schemes implemented in inverter-based resources (IBRs) present a promising solution for mitigating the absence of inertial response in power systems after the decommissioning of synchronous generators (SGs). The interaction of multiple grid-following (GFL) and grid-forming (GFM) inverters with the power grid demands a thorough understanding, as different control mechanisms can lead to undesired interference that could severely impact the grid’s stability. Power hardware-in-the-loop (PHIL) simulation is a verification technique that effectively bridges the gap between pure simulation and field demonstration. However, the topic of PHIL testing frameworks for multiple inverters equipped with VI control schemes has not been extensively addressed. To address this gap, this study presents a PHIL test framework that enables the verification of the performance and possible interference of multiple hardware inverters. The proposed framework enables the testing of inverters with different rated capacities and control mechanisms under equivalent capacity and control parameter conditions. This framework allows for the testing of various combinations of two inverters, from different manufacturers, to assess their performance and possible interference. The inverter prototypes from different manufacturers will be combined and tested with the proposed PHIL test framework to examine performance and potential interference for all combinations of the two inverters.

Machine Learning Supervisory Control of Grid-Forming Inverters in Islanded Mode

This research paper presents a novel droop control strategy for sharing the load among three independent converter power systems in a microgrid. The proposed method employs a machine learning algorithm based on regression trees to regulate both the system frequency and terminal voltage at the point of common coupling (PCC). The aim is to ensure seamless transitions between different modes of operation and maintain the load demand while distributing it among the available sources. To validate the performance of the proposed approach, the paper compares it to a traditional proportional integral (PI) controller for controlling the dynamic response of the frequency and voltage at the PCC. The simulation experiments conducted in MATLAB/Simulink show the effectiveness of the regression tree machine learning algorithm over the PI controller, in terms of the step response and harmonic distortion of the system. The results of the study demonstrate that the proposed approach offers an improved stability and efficiency for the system, making it a promising solution for microgrid operations.

Implementation and Applications of Grid-Forming Inverter with SiC for Power Grid Conditioning

Sustainable energy technologies have become promising solutions to global warming and climate change. Operation of the electric power grid has been dominated in the past by synchronous generation, wherein conventional sustainable energy inverters are designed simply to feed maximum real power into the grid. With the increasing penetration of renewable energy, it is undergoing a rapid shift toward the power generation of inverter-based resources (IBRs). As a result, transitioning to a power grid with more IBRs requires introducing advanced inverter technology that can respond to various disturbances in frequency and voltage occurring on the grid. The grid-forming (GFM) inverter equipped with an energy storage system featuring frequency and voltage support functionalities is vital for the stability of the micro power grid system. The GFM inverter also offers PV output smoothing, low voltage ride through, and low frequency ride through. In addition, the GFM inverter functions as a voltage source inverter to supply energy under off-grid state when the main grid is in fault conditions. A SiC-based 30 kVA GFM inverter is presented with a 3-phase 3-level neutral-point-clamped (NPC) topology for high-frequency operation to achieve high efficiency and power density. Designchallenges in gate driver design, PCB layout, and thermal consideration are addressed. The performances of the designated GFMinverter are measured and tested under on-grid and off-grid operations to verify the functionalities of the advanced inverter, as well.

Passivity-Based Stability Analysis and Generic Controller Design for Grid-Forming Inverter

With the remarkable growth of renewable energy resources, the grid-forming (GFM) inverter with the function of grid voltage/frequency support attracts much attention. Due to the inverter-grid interaction, the stability of the GFM inverter is a critical issue. The passivity-based analysis approach, which was widely applied to the conventional grid-following inverter, has been proved to be promising. Yet, its application to the GFM inverter is still insufficient. To this end, this paper conducts a comprehensive passivity-based analysis for the GFM inverter with single-loop voltage control. It finds that the two indices of the passivity-based stability criterion, i.e., the individual stability and the output impedance passivity, bring identical constraints on the voltage controller, and the passivity cannot be ensured with typical voltage controllers. To shrink the unexpected non-passive frequency ranges, a generic grid-current feedforward scheme is explored, and the proper feedforward functions compatible with different voltage controllers are derived. With the proposed scheme, the passivity can be guaranteed up to the Nyquist frequency. Finally, experimental results from a 6-kVA prototype are provided to verify the theoretical analysis.

Accurate Small-Signal Terminal Characteristic Model and SISO Stability Analysis Approach for Parallel Grid-Forming Inverters in Islanded Microgrids

This paper derives a small-signal terminal characteristic model for the grid-forming inverter with droop-control in the synchronous reference ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> -) frame, accurately covering the dynamics of the power controller, the voltage and current control loops and all circuit components, where a new set of terminal characteristics is proposed to characterize the small-signal dynamics of fundamental frequency introduced by the fundamental frequency-active power droop scheme. Based on the terminal characteristics of individual inverters, the stability of parallel grid-forming inverters can be predicted by the generalized Nyquist criterion (GNC). Furthermore, to simplify the stability analysis process and reduce calculation complexity, a single-input single-output (SISO) stability analysis approach is proposed by exploring the interaction among the droop-control of parallel inverters through analyzing mathematical feature of proposed terminal characteristic model of individual inverters as well as the return ratio of the parallel inverters, which uses <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d-d</i> channel element of system return ratio matrix and Nyquist criterion to predict the stability. Finally, simulation and experimental results validate the effectiveness of proposed small-signal model and SISO stability analysis approach.

A Deep Reinforcement Learning-Based Intelligent Grid-Forming Inverter for Inertia Synthesis by Impedance Emulation

In this letter, impedance emulation is exploited for synthesizing inertia in autonomous microgrids. An intelligent grid-forming inverter (GFI) is proposed that facilitates sufficient degrees of freedom for adaptive impedance shaping. The latter adaptively changes the effective bandwidth of the inverter's voltage controller, in response to disturbances for inertia synthesis. Deep reinforcement learning is utilized to tackle the lack of explicit quantitative relation between impedance shaping and inertia. Simulation results prove the effectiveness of the method.

An Islanding Detection Method Using Synchronized Small-AC-Signal Injection for Grid-Forming Inverters in Microgrids

Islanding detection is of great importance for the microgrid in order to change the control objectives and to avoid unsynchronized reclosure. Active islanding detection methods based on impedance measurement have very small non-detection zone (NDZ) in the single-inverter system, but require the coordination of the perturbation current injected by each inverter in the microgrid consisting of multiple inverters. The conventional solution by injecting a harmonic current synchronized with the fundamental output voltage is affected by different winding connections in grid-side transformers of inverters and degrades the voltage quality in stand-alone mode. This paper proposes an islanding detection method based on impedance measurement for the microgrid comprised of grid-forming (GFM) inverters with seamless transfer capabilities. The proposed method achieves synchronized injection of small-AC-signal (SACS) current using the SACS current droop control and the virtual impedance. The synchronized SACS current injection in the proposed method is independent of fundamental components and is not influenced by different winding connections in grid-side transformers of inverters. Moreover, the SACS current limiting control is introduced to mitigate the impact of injected SACS current on the grid current quality. In addition, the control scheme is peer-to-peer and enables plug-and-play functionality. The effectiveness and advantages of the proposed method are validated through simulation and experimental results.

Design and implementation of optimized virtual oscillatory controllers for grid-forming inverters

The percentage of renewable power in conventional power generation is gradually growing due to developments in power electronic converters (PECs). Renewable energy sources (RESs) can be integrated into the main grid through PECs, which are the most prevalent method to accomplish this. Virtual oscillator control (VOC) is a well-known time-domain method to regulate grid-forming inverters. VOC objective is to model the nonlinear dynamics of deadzone oscillator in a system of voltage source inverters to give a steady AC microgrid (MG). VOC is a self-synchronizing control method that just involves the current feedback signal. In contrast, classical droop and virtual synchronous machine (VSM) controllers both require the use of low pass filters to calculate real and reactive powers. The selection of control parameters in deadzone VOC is difficult and time-consuming. The VOC parameters are designed using different optimization techniques such as Particle Swarm Optimization (PSO), Sine Cosine Algorithm (SCA), modified Sine Cosine Algorithm (mSCA), African Vulture Optimization Algorithm (AVOA), and Artificial Jellyfish Search Optimization (AJSO). MATLAB and a real-time digital simulator (Opal RT-OP5142) were used to examine the system’s performance with aforesaid controllers (droop, VSM, conventional VOC, VOC-PSO, VOC-SCA, VOC-mSCA, VOC-AVOA, and VOC-AJSO). In comparison to all control methods, the proposed VOC-AJSO provides faster synchronization. The effectiveness of the suggested VOC-AJSO control approach is proved by the hardware results.

Design of an Optimal Adoptive Fault Ride through Scheme for Overcurrent Protection of Grid-Forming Inverter-Based Resources under Symmetrical Faults

As the integration of inverter-based resources (IBRs) is rapidly increasing in regard to the existing power system, switching from grid-following (GFL) to grid-forming (GFM) inverter control is the solution to maintain grid resilience. However, additional overcurrent protection, especially during fault transition, is required due to limited overcurrent capability and the high magnitude of spikes during fault recovery in IBRs, specifically in the GFM control mode. Furthermore, the power system stability should not be compromised by the employment of additional fault ride through (FRT) schemes. This article presents the design and implementation of an adoptive fault ride through (FRT) scheme for grid-forming inverters under symmetrical fault conditions. The proposed adoptive FRT scheme is comprised of two cascaded power electronic-based circuits, i.e., fault current ride through and a spikes reactor. This adoptive FRT scheme optimizes the fault variables during the fault time and suppresses the fault clearing spikes, without affecting system stability. A three-bus inverter-based grid-forming model is used in MATLAB/Simulink for the implementation of the proposed scheme. Further, a conventionally used FRT scheme, which includes fault current reactors, is simulated in the same test environment for justification of the proposed adoptive scheme. The adoptive FRT scheme is simulated for both time domain and frequency domain to analyze the response of harmonic distortion with the suppression of the fault current. Moreover, the proposed scheme is also simulated under the GFL mode of IBRs to justify the reliability of the scheme. The overall simulation results and performance evaluation indices authenticate the optimal, fault tolerant, harmonic, and spike-free behavior of the proposed scheme at both the AC and DC side of the grid-forming inverters.

A sigmoid-based adaptive inertia control strategy for grid-forming inverter to enhance frequency stability

Introduction: This paper proposes a sigmoid-based adaptive inertia control strategy for grid-forming (GFM) inverter to enhance frequency stability.Methods: Firstly, the frequency response characteristics under different disturbances are analyzed theoretically. Then, to solve the problem that fixed inertia leads to a contradiction between the maximum frequency deviation and the setting time, a non-linear inertia regulator is investigated. This non-linear inertia regulator, which is based on an improved sigmoid function, is applied to achieve real-time inertia by the frequency deviation. Moreover, the full-order small-signal model of the system containing the nonlinear inertia regulator is established and thus the stability of the proposed strategy is analyzed.Result and Discussion: The proposed control strategy is implemented without derivative action, which may suffer from high-frequency noises. Finally, the hardware-inthe-loop (HIL) results verify the remarkable performance of the proposed control strategy.

Frequency Restoration of Grid-Forming Inverters in Pulse Load and Plug-in Events

This article presents a restoration technique using grid-forming inverters in an islanded microgrid during pulse load and plug-in events. In a microgrid powered by droop-controlled inverters, frequency is the variable that is accessible to all inverters for adjusting their power contributions. The problem is that the microgrid frequency deviates from its nominal value after a load change. The presented method enables the inverters to restore the frequency to the nominal value and regulate their bus voltage amplitudes. The frequency and voltage restorations are performed without communication while achieving the desired power-sharing between grid-forming inverters. The restoration is activated after detecting any active or reactive power changes. In this article, the dynamic model of an inverter equipped with enabled restoration paths is developed to verify the stability of the inverter controller under various conditions. The frequency and voltage restorations are examined during pulse load and plug-in events. This study is performed using a laboratory-scale islanded microgrid powered by two 208 V, 60 Hz, 5 kVA inverters.

H∞-Based Control Design for Grid-Forming Inverters With Enhanced Damping and Virtual Inertia

Grid-forming inverters (GFMIs) are identified as an important asset for achieving renewable energy-rich power grids. GFMIs are attracting significant attention due to their superior characteristics over grid-following inverters in both grid-connected (GC) and standalone (SA) scenarios. In this article, a second-order discrete-time controller is proposed to achieve a well-damped step response for power reference commands and improved virtual inertia provision capability. In this article, a control design method based on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{\infty} $ </tex-math></inline-formula> is proposed, which is based on the frequency response of the system, to tune the proposed controller. The proposed control design presents a methodical process to specify the desired performance indices through frequency-domain constraints. The performance of the controller is thoroughly validated analytically and through simulation results. The superior performance of the proposed controller over the virtual synchronous generator controller in terms of tracking performance and virtual inertia provision capability is verified through experimental results.

Autonomous Restoration of Networked Microgrids Using Communication-Free Smart Sensing and Protection Units

This paper presents autonomous restoration of networked microgrids using distributed energy resources (DERs), inverter-based resources (IBRs) in general, and controllable assets of intelligence without communication to achieve a extremely resilient power system restoration. The main innovation of this work lies in use of real-time smart sensing and decision making that enable autonomous recombination of islanded microgrids, which are individually black-started by local grid-forming (GFM) inverter units. The smart circuit breakers (SCBs) designed and demonstrated here play critical roles in the restoration process to achieve autonomy; the autonomous restoration scheme is not pre-engineered and may be subject to encounter overloading, live or downed segments as the boundary of the microgrids dynamically expands without prior knowledge and only with local measurement. We demonstrate autonomous microgrid restoration both in simulation of a modified IEEE 13-bus system, and in a hardware testbed comprising 24 GFM-IBRs and 6-SCBs, depicting several scenarios to evaluate their functionalities and interoperability. This work validates high potential of extremely resilient microgrid using novel approaches for inverter-based bottom-up system restoration in a communication-free paradigm.