This paper presents a methodology that aims at identifying virtual inertia (VI) gain limitations from virtual synchronous generators (VSGs) while maintaining the frequency stability considering the delay associated with the frequency measurement process. The phase-locked loop (PLL) is typically used for frequency estimation that is used to calculate the rate of change of frequency (RoCoF) and it drives the VI loop. The PLL is generally accompanied by a low-pass filter that aims to suppress the impact of harmonics. This filter introduces a delay that when used with the VI control loop causes stability issues for high values of VI gain. A comparison of various PLL approaches suggests that certain variants tend to permit higher value of cut-off frequencies which can be utilized to increase the VI gain limit from VSG. This study presents a method by which the upper limit on VI gain can be quantified and related to the cut-off frequency of the PLL low pass filter that is indirectly representing the delay. It is performed using small signal frequency stability analysis on the frequency domain model of the grid with virtual inertia emulating VSG. The effective maximum VI gain from VSG is explored while satisfying the frequency measurement accuracy specification considering harmonics. The results show that the requirements of reaching a stable operation with sufficient stability margins can still be met with a faster PLL-based system and the potential increases in VI support from VSG can be quantified using the proposed method. The study has been first performed on a single machine single inverter bus (SMSIB) system and is generalized to the multi-machine and multi-inverter system.

The integration of large amounts of generation into distribution networks faces some limitations. By deploying reactive power-based voltage control concepts (e.g., volt/var control with distributed generators), the voltage rise caused by generators can be partly mitigated. As a result, the network hosting capacity can be accordingly increased, and costly network reinforcement might be avoided or postponed. This works however only for voltage-constrained feeders (opposed to current-constrained feeders). Due to the low level of monitoring in low voltage networks, it is important to be able to classify feeders according to the expected constraint in order to avoid the overloading risk. The main purpose of this paper is to investigate to which extent it is possible to predict the hosting capacity constraint (voltage or current) of low voltage feeders on the basis of a large network data set. Two machine-learning techniques have been implemented and compared: clustering (unsupervised) and classification (supervised). The results show that the general performance of the classification or clustering algorithms might be considered as rather poor at a first glance, reflecting the diversity of real low voltage feeders. However, a detailed analysis shows that the benefit of the classification is significant.