4.2.1. OUV and OUF Methods

All grid-connected PVS inverters are required to have OUV and OUF protections. The aim is to avoid power supply by the PVSs when the voltage amplitude and frequency values at the PCC are different from set values [41,90].

Considering an RLC load whose resonant frequency is equal to the grid frequency, no reactive power absorption is verified by the load. In case of grid disconnection, the power absorbed by the load is equal to the active power provided by the PVS. Hence the RMS value of the voltage provided by the PVS at the PCC changes from *EPVS* = *E* before the disconnection to:

$$E\_{PVS} = \delta E \tag{2}$$

where *E* is the rated RMS value of the grid voltage,

$$
\delta = \sqrt{\frac{P\_{PVS}}{P\_L}}\tag{3}
$$

*PPVS* is the active power supplied by the PVS, *PL* is the rated load active power.

In conclusion the voltage value at the PCC increases or decreases depending on the PVS power generation. As a consequence, also the reactive power changes on the basis of the following relationship:

$$Q\_{PVS} = \left(\left(\frac{1}{L\omega\_{PVS}}\right) - \text{Ca}\_{PVS}\right) \mathbf{E}\_{PVS}^2 \tag{4}$$

In (4) *L* and *C* are the inductive and capacitive components of the RLC load, ω*PVS* denotes the voltage frequency at the PCC after the grid disconnection. Hence it results:

$$
\omega\_{PVS} = \frac{-\left(\frac{Q\_{PVS}}{E\_{p\_{VS}}^2 \text{C}}\right) + \sqrt{\left(\frac{Q\_{PVS}}{E\_{p\_{VS}}^2 \text{C}}\right)^2 + \frac{4}{LC}}}{2} \tag{5}
$$

The voltage frequency and amplitude variations allow to detect islanding operation. Unfortunately, in case of power balance between the PVS generation and the load, no active and reactive power

variations are registered and consequently no voltage frequency and amplitude variations can be measured. Similarly, small active and reactive power variations imply small voltage variations in terms of frequency and amplitude. For this reason, the OUV and OUF protection cannot detect islanding. OUV and OUF protections are considered insufficient anti-islanding techniques since the active and reactive power variations due to the islanding phenomenon are commonly limited and, as a consequence, there is high probability to fall into the NDZ.
