4.3.3. Active Frequency Drift

The active frequency drift (AFD) is based on a perturbation of the PVS inverter current. In particular, the PVS inverter current reference is modified adding a disturbance current [29]. Denoting as *T* the period of the grid voltage, it occurs that the PVS inverter current is null for a time portion indicated with *tc* in each half cycle as shown in Figure 10.

**Figure 10.** Half wave of the PVS inverter current with and without active frequency drift (AFD).

During grid-connected operation the PVS inverter voltage is not affected by the perturbation. Differently in islanding operation the PVS inverter voltage "drifts" up or down as a consequence of the continuous inverter current variation. The frequency change has to be detected by the UOF protections. Successively the PVS is promptly disconnected.

The AFD method is characterized by a chopping factor *c* which measures the amount of the perturbation:

$$c = \frac{2t\_c}{T} \tag{9}$$

The method ensures correct islanding detection and simple implementation, but the main disadvantage is the power quality detriment due to the current variation. Hence the method is not appropriate in case of numerous PVSs connected in parallel.

#### 4.3.4. Sandia Frequency Shift

The Sandia frequency shift (SFS) methods derives from the AFD technique. SFS perturbs the PVS adding a dead-time to the PVS inverter reference current. Hence the inverter current exhibits a phase "shift" [29,97–99].

For this method, the chopping factor *cS* is defined as:

$$c\_S = c\_{So} + k\_{SFS}(f\_{PVS} - f) \tag{10}$$

where *kSFS* is a proportional gain, *cSo* is the chopping factor in absence of frequency error, *f* is the grid frequency and *fPVS* is the output frequency of the PVS inverter.

When the PVS is connected to the grid, the frequency error is null since the grid sets the frequency at the PCC. On the contrary, during islanding operation, the frequency error is not negligible. As a consequence, the PVS inverter current grows in order to overcome the phase shift, the chopping frequency increases, and the frequency varies beyond the OUF threshold values. Hence islanding is detected.

The SFS NDZ is smaller than the AFD NDZ. The improved islanding detection performances are achieved to the detriment of the power quality performances. In addition, in case of high PVSs penetration, unexpected transient disturbances can be registered.

#### 4.3.5. Sandia Voltage Shift

The Sandia voltage shift (SVS) method operates with positive feedback of the PCC voltage amplitude [29,100]. During grid-connected operation of the PVS no significant variations are observed. In case of disconnection of the grid, voltage variations are monitored at the PCC. As a consequence, also the PVS inverter voltage varies and later the PVS is tripped since the voltage variations exceed the OUV protections threshold values. The NDZ of the SVS method is very small. However, the power quality is worsened and also the efficiency is reduced since the power processed by the inverter varies.

#### 4.3.6. Slip-Mode Frequency Shift

The slip-mode frequency shift (SMS) detects islanding phenomenon using positive feedback to lead the PVS towards instability in case of grid disconnection [80,101,102]. In case of grid disconnection, the PVS frequency changes naturally. The PVS PLL action can be modified in order to increase the frequency rate of change rather than to annul it. The phase is forced to be a function of the voltage frequency at the PCC. The PLL acts to increase the frequency until the PVS inverter voltage phase grows faster than the phase of the RLC load (unstable region). The PVS is tripped when the inverter voltage frequency exceeds the threshold value. The method can fail when the load phase slope is higher than the slope achieved by the SMS technique. In this case instability could not be recognized.

In Figure 11 there is shown how the action of the PVS PLL is modified on the basis of the SMS rationale. The PVS phase angle changes from θˆ *PVS* to θ*SMS*.

**Figure 11.** PVS PLL operation in case of SMS islanding-detection technique.
