4.2.4. Voltage Harmonic Monitoring Method

The voltage harmonic monitoring (VHM) method is based on the voltage harmonic distortion estimation to detect the occurrence of the islanding phenomenon [49]. In grid-connected operation the voltage at the PCC is set by the grid, but, in case of grid disconnection, the PVS inverter determines the voltage at the PCC. Nevertheless, the voltage harmonic distortion varies with the grid impedance and it depends on the loads connected to the PCC. As a consequence, the accuracy of the method can be hazarded if the islanding detection thresholds are not properly set. Better performance can be achieved monitoring some selected harmonics variations rather than the overall voltage harmonic distortion. In this hypothesis the harmonics variations can be detected by means of PLLs tuned in order to track the selected harmonic components.

#### *4.3. Active Methods*

The active islanding detection methods are developed with the goal to achieve better performance than the passive methods. The active methods introduce a perturbation in the PVS through the injection of an active signal [50,93]. The active signal injection is designed considering starting from ideal operating conditions of the PVS. The main active methods can be classified in: Grid impedance variation methods, active and reactive power injections methods, active frequency drift (AFD), Sandia frequency shift (SFS), Sandia voltage shift (SVS), slip-mode frequency shift (SMS).

#### 4.3.1. Grid Impedance Variation Methods

Islanding phenomenon assessment can be based on grid impedance variations monitoring [78,94,95]. A small harmonic current component is drained into the PVS. The grid impedance is evaluated at the frequency of the injected harmonic component. Additional equipment can be employed to measure the grid impedance. Otherwise the grid impedance measurement can be embedded in the PVS inverter control system.

Stability and power quality issues must be tackled when this technique is applied to numerous PVS connected in parallel due to the combination of the injected perturbations and possible inter-harmonics.

#### 4.3.2. Active and Reactive Power Injections Methods

The rationale of the active power injections method is to use controlled active power injections causing active power variations Δ*PPVS* in the PVS. Consequently, voltage variations can be observed exceeding the threshold voltage value of the islanding protections [50]. Assuming a resistive load *R,* whose power *PL* is constant, it is possible to express the power provided by the PVS as function of the voltage at the PCC. In case of islanding condition, it results:

$$P\_{PVS} = P\_L = \frac{{E\_{PVS}}^2}{R} \tag{6}$$

Hence it can be obtained:

$$\frac{\partial P\_{PVS}}{\partial E\_{PVS}} = 2 \cdot \frac{E\_{PVS}}{R} = 2 \cdot \frac{\sqrt{R \cdot P\_{PVS}}}{R} = 2 \cdot \sqrt{\frac{P\_{PVS}}{R}} \tag{7}$$

The voltage variation can be evaluated as:

$$
\Delta E\_{PVS} = \frac{\Delta P\_{PVS}}{2} \cdot \sqrt{\frac{R}{P\_{PVS}}} \tag{8}
$$

The method is effective but is requires some tuning procedure in order to avoid overcurrents due to the active power injections. The disadvantage is that the islanding technique has to be coordinated with the MPPT operation. Hence the main challenge is to determine when the active power injection can be applied without jeopardizing the other control functions.

Similarly, reactive power injections can be used to cause reactive power variations Δ*QPVS* in the system [96]. As a consequence, frequency variations are obtained exceeding the frequency threshold value and islanding condition can be detected.
