## 1 Introduction
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Standard** & **Voltage Threshold** & **Time** & **Frequency Threshold** & **Time** \\  & **(\%)** & **(s)** & **(Hz)** & **(s)** \\ \hline \multirow{4}{*}{VDE \({}^{a}\) 4105} & \(U<80\) & 0.20 & \(f<47.5\) & 0.20 \\  & \(80\leq U\leq 115\) & 5.00 & \(47.5\leq f\leq 51.5\) & 5.00 \\  & \(U>115\) & 0.20 & \(f>51.5\) & 0.2 \\  & & & \(f<59.3\) & 0.16 \\  & \(U<50\) & 0.16 & \(59.3\leq f^{1}<60.5\) & 2.00 \\  & \(50\leq U<88\) & 2.00 & \(f^{1}>60.5\) & 0.16 \\ IEEE \({}^{b}\) 1547 & \(88\leq U\leq 110\) & 2.00 & \(f^{2}<57.0\) & 0.16 \\  & \(110<U<120\) & 1.00 & \(57.0\leq f^{2}<59.8\) & 0.16–300 3 \\  & \(U>120\) & 0.16 & \(59.8\leq f^{2}\leq 60.5\) & 2.00 \\  & \(U<50\) & 0.10 & \(f^{2}>60.5\) & 0.16 \\ IEC \({}^{c}\) 61727 & \(50\leq U<85\) & 2.00 & \(f<49.0\) & 0.20 \\  & \(85\leq U\leq 110\) & 2.00 & \(49.0\leq f\leq 51.0\) & 2.00 \\  & \(110<U<135\) & 2.00 & \(f>51.0\) & 0.20 \\  & \(U>135\) & 0.05 & & \\ \hline \hline \end{tabular}  
* DER size \(\leq 30\) kW; \({}^{2}\) DER size \(>30\) kW; \({}^{3}\) adjustable. \({}^{a}\) Verband der Elektrotechnik, Elektronik und Informationstechnik. \({}^{b}\) Institute of Electrical and Electronics Engineers. \({}^{c}\) International Electrotechnical Comission.  
\end{table} 
Table 1: Summary of islanding threshold detection times. management, and business are finding their way, such as microgrids [13; 14], smart-grids [15], energy hubs [16], power routers [17], or virtual power plants [18]. In the mentioned new framework, GSIs will start to coexist in the grid with other devices such as GCIs and GSCIs. Hence, VC-VSIs will be required, and their implications for AI detection need to be analyzed and incorporated. The present paper aims to face the challenge of using AIMM with VC-VSI, mainly focusing on GSCI, because of their future expected participation in DER integration. To the best knowledge of the authors, this has resulted in it being difficult to find works dealing with the interactions between AIMM and VC-VSIs. In fact, recent literature shows the same trend as in the past [19; 20; 21; 22; 23; 24]. These authors devoted efforts to enhance previously-existing AIMM, analyzing the effect under different grid faults or considering the criticality of the loads, but regularly assuming the inverter as a CC-VSI. The only exceptions found are not always focused on power electronics. Some authors as in [25; 26] mentioned AIMM for diesel generators, but this AIMM is based on remote strategies, in which the AI detector is not part of the generator itself. The present authors have published some preliminary papers in line with the challenge of AIMM for VC-VSI in [27; 28]. This paper addresses two main contributions. Firstly, we explore the lack of effectiveness of islanding detection methods based on voltage and frequency displacements applied to VC-VSI, paying special attention to GSCI. In this sense, the conventional definition of resonant load present in the literature should be reconsidered. In this work, it is redefined from a zero power flow point of view, extending its applicability to any kind of inverter (whether it be VC or CC). Secondly, and according to the first part of the paper, IM strategies are chosen to overcome island detection in any inverter type, but their limitations are analyzed. One of the main contributions of the present article resides in the use of a new concept called DFBW (detection frequency bandwidth), which facilitates judging the performance of islanding detection depending on the local load type and the strength of the mains. For this purpose, an AIMM for VC-VSI based on the IM variation concept is applied. This method considers selecting appropriately a perturbation frequency according to the DFBW. The used AI method is based on [29], but it has been modified to lessen the computational burden, being another of the key contributions.