Grid-forming inverters are sensitive to large grid disturbances that may engender overcurrent due to their voltage source behavior. To overcome this critical issue and ensure the safety of the system, current limitation techniques have to be implemented. In this context, the variable virtual impedance (VI) appears as a suitable solution for this problem. The design of the variable virtual impedance basically rests on static considerations, while, its impact on the system stability and dynamics considering both small-signal and large-signal aspects can be significant. This paper proposes small-signal and nonlinear power models to assess the impact of the virtual impedance parameters on the grid current dynamics and on the angle stability. Thanks to the developed theoretical approaches in this paper, the virtual impedance ratio X/R, which is the unique degree of freedom has shown a contradictory effect on the small and large signal stability. To overcome this constraint, a Variable Transient Virtual Resistance (VRTVR) has been proposed as an additional degree of freedom to the variable virtual impedance. It acts as a transient damper to ensure the maximum angle stability margin allowed by the variable virtual impedance. The effectiveness of the proposed control has been proven through time-domain simulations.

The inner cascaded structure-based grid-forming control is a typical solution used to impose an AC voltage magnitude across the output filters of the power inverters. Yet, because of the limited inverter’s bandwidth resulting from the low-switching frequencies in transmission systems, the interaction (i.e., coupling) between control loops is highly likely making the understanding of the system behavior complex and its simplification unaffordable and may also lead to instabilities. The novelty of this paper consists in proposing a simple open-loop direct voltage control to reduce the number of the inner control regulators, and thereby guaranteeing a decoupling between the inner and outer control layers as well as increasing the system stability margin. This statement is well supported with a small-signal analysis and progressive order model reduction of the system. The overall concept is validated in a 10-bus grid case while comparing the EMT and Phasor-based simulations. The practical feasibility of the control itself is experimentally proved with different test cases.

Under grid distortions, Modular Multilevel Converters (MMC) must adopt proper control strategies to fulfill the power system requirements and ensure a stable operation. An inappropriate control under such conditions may lead to energy unbalances between the MMC legs, inaccurate current injection, and failure in the synchronization process. In this context, sequence extraction methods play a critical role in enhancing the performance of the control, firstly, by aiding the Phase-Locked Loop (PLL) to maintain the synchronization with the AC grid by following the positive sequence fundamental component of the voltage, secondly, by allowing an accurate active and reactive currents injection via the decoupled Voltage Oriented Control (dVOC), thirdly, by properly managing the internal energy of the MMC through the circulating current control. In prior researches, some sequence extraction methods have been used for MMC STATCOM. However, the sequence extraction was not the core of the performed studies and their impact on the system behavior has not been highlighted or tested in several grid conditions. This work fills this gap by first assessing the performance of a Single Delta Bridge Cell MMC (SDBC-MMC) STATCOM with four well-known sequence extraction methods (i.e., Decoupled Double Synchronous Reference Frame (DDSRF), Dual Second Order Generalized Integrator (DSOGI), Improved DSOGI, and Fortescue matrix-based (FMB) filter) under normal and abnormal grid conditions, then, finding the most suitable one in terms of stability, dynamics, and functionalities.