## 4 Limitations of AIDMs When Applied with the Presence of GSCI
### Active Method-Positive Feedback Type
#### 4.2.4 Sandia Voltage Shift and Sandia Frequency Shift  
SVS and SFS are two important AM based on PF strategies [31; 32; 35]. As a difference from SMS and AFD, the used perturbations in these cases are not directly based on current. Derived from Equations (4) and (5), these methods aim to destabilize the voltage or the frequency by modifying the active or reactive power loops. For the following explanation, consider Figure 1a.  
In the SVS case, the variation between the PCC voltage, \(U_{PCC}\), and the rated voltage, \(U_{N}\), is accumulated to the active power reference amplified by a gain factor, \(k_{U}\), as is shown in Figure 6a. \(G_{PU}(s)\) represents the transfer function, including the inverter, between the active power error and \(U_{PCC}\) amplitude. If the grid is connected, the voltage variation is limited and small, offering a null average value (\(\Delta P^{*}\simeq 0\)). Then, it affects only slightly the power reference, \(P^{*}\). If the grid is disconnected, any minor voltage discrepancy boosts (in positive or negative direction) the active power reference, which in the next algorithm iteration, will speed up \(U_{PCC}\) even more.  
The same idea of SVS can be exported to SFS in terms of frequency considering the negative slope of the relation between the reactive power and the frequency (refer to Figure 5b), as can be seen in Figure 6b. In this case, the amplifier factor is \(k_{\omega}\), and \(G_{Q\omega}(s)\) represents the transfer function, including the inverter, between the reactive power error and \(\omega_{PCC}\).  
If the SFS option is simulated under a GSI or a GSCI context, it can be seen how this fact is translated to extremely high positive feedback amplifier gains. The inverter and control parameters used to evaluate this discrepancy are summarized in Table 2. In order to simulate CC-VSI, the voltage loop and the droop control have been removed.  
Figure 7a (CC-VSI) and Figure 7b (VC-VSI) represent the detection time when the inverter delivers 30 kW. The grid to which it is connected is 230 V and 50 Hz. The resonant load is 30 kW and the quality factor \(q=2\) is assumed (\(R_{RL}=1.76\)\(\Omega\); \(L_{RL}=2.8\) mH; \(C_{RL}=3.6\) mF). As previously mentioned, high amplifier gains produce non-convenient disturbances. Figure 7a,b shows the islanding detection times versus the mains' frequency at different \(k_{\omega}\) factors. Figure 7a shows slow detection times as closest to the rated frequency (50 Hz in the example), which is the frequency at the PCC. This is due to the small initial error of the positive feedback loop. Even considering this behavior, the detection times results in being fast enough to achieve the proposed time in the standard. In contrast, in Figure 7b,  
Figure 6: AI-PF methods. (**a**) Sandia voltage shift (SVS). (**b**) Sandia frequency shift (SFS).  
it can be noted that the response for a VC-VSI implies higher amplifying gains to achieve acceptable detection times without guaranteeing the aforementioned threshold times. Analogous results can be obtained using SVS instead of SFS.  
It can be concluded that the SVS and SFS methods reduce the NDZ, generating considerable variations in the voltage or the frequency to increase islanding detection capabilities. Nevertheless, it is essential to remark that the \(k_{\omega}\) and \(k_{U}\) factors gains are significantly higher when applied to VC-VSIs instead of CC-VSIs. The higher the \(k_{\omega}\) and \(k_{U}\) gain factors are, the higher the perturbation under grid-connected operation is required. This fact affects the quality indices of the electric magnitudes. Thus, conflicts with grid regulations can appear, meaning that maybe it is not a valid method for certified installations.