*4.4. Signal Processing-Based Methods*

Signal processing techniques can be adopted to design new islanding detection algorithms or to improve the performance of the previous developed algorithms [55,82]. The signal processing islanding detection methods are generally based on (a) Fourier transform; (b) wavelet transform and (c) S-transform.

## 4.4.1. Fourier Transform-Based Methods

The PVS output power is typically affected by variations after grid disconnection, as a consequence, its spectrum varies with continuity in a certain frequency range. Fourier transform (FT) is not proper for the analysis of non-stationary signals. Hence it cannot provide information about fluctuating signals linked to the islanding occurrence [103]. For this reason, the application of this signal processing technique to the analysis of transient phenomena such as islanding is not very common. However, some islanding detection techniques based on the Discrete Fourier transform (DFT) and its modifications have been discussed in literature [104,105]. In [104] a modified VHM islanding detection technique is proposed. Since the equivalent harmonic components measured at the PCC change in case of islanding occurrence, the DFT is employed to assess harmonic components variations. Differently in [105] a kind of FT, named Goertzel algorithm, is employed to develop an active islanding detection method where the Goertzel algorithm extracts the magnitude and phase of some selected components with limited computational burden.

#### 4.4.2. Wavelet Transform-Based Methods

Filters based on the wavelet transform (WT) can track the PVS output power spectrum variations in a certain frequency range. Indeed, WT can process simultaneously signals varying in time and in frequency also in case of non-stationary waveforms. The signal to be processed is decomposed in different levels and the coefficient vectors of each level vary with the signal length. Numerous islanding detection methods based on different mother wavelets were developed [106–111]. As an example, in [108] the multiresolution analysis (MRA) based on the WT is employed to break down the DPGS voltage into different scales. In [109] the WT is adopted just to enhance the performance of the conventional islanding detection methods. In [110] the WT and the back propagation neural network (BPNN) are combined to provide a new islanding detection method based on the normalized logarithmic energy entropy estimation. In [111] the islanding detection technique is based on localization of high-frequency harmonics due to the PVS inverter switching. WT-based algorithms provide generally high performance islanding detection techniques with limited computational burden and implementation complexity. On the contrary these techniques suffer particularly for noise.

#### 4.4.3. S-Transform-Based Methods

S-transform (ST) represents a superior signal processing technique which was born to overcome the noise sensitivity issue of the WT. Various high performance islanding detection techniques based on the ST have been proposed in [112–114]. In [112,113] there are compared the performances of the ST and of the WT. Better results in terms of islanding detection and localization are obtained using the ST instead of the WT. Similar results are achieved in [114] where the islanding detection method is based on the analysis of the negative sequence voltage. For this reason, the method cannot be applied to single-phase PVS avoiding modifications. However, it is demonstrated that the use of the ST results particularly advantageous to detect islanding condition also in presence of noise. In conclusion, higher performances are ensured in the islanding detection since S-transform allows the extraction of the phase of each frequency component related to the time-varying signals involved in the islanding phenomenon. Nevertheless, these techniques require more computational burden than the WT-based methods.

#### *4.5. Hybrid Methods*

In the present standard [25], it is established that any requirements for ride-through shall not be falsely inhibited by any methods or design features utilized to meet the unintentional islanding detection when an actual unintentional island condition does not exist. Conversely, the unintentional islanding detection requirements shall not be inhibited by ride-through during valid unintentional islanding conditions.

Passive methods operating alone cannot provide satisfying results considering their poor islanding detection performance and the need to ensure ride-through capability by the PVS. Better results can be obtained using active methods, but the power quality is often affected.

Taking into account also the recent advancement in computing capability and communication systems, hybrid islanding detection techniques, based on combinations of the four categories previously discussed, represent the most promising techniques [115–125]. Starting from combination or modification of conventional methods, in [115] some islanding detection methods are proposed as integration of well-known passive methods. In [116] a modified active SVS method is presented, and the modulation index is used as injected signal to achieve the voltage magnitude shift and to detect the islanding phenomenon. In [117] a hybrid active method is developed combining a threshold filter (based on a binary tree classifier) with a harmonic amplification factor used as perturbation to detect islanding. In [118] a modified active islanding detection method is obtained varying the amplitude of the PVS current periodically. In this case islanding occurrence is detected through the AFD method when high current variations are registered. In [119] an active technique is obtained combining the AFD with the SMS. In [120] a new active islanding detection method is proposed and based on the droop control theory. The droop control is modified considering a correlation function between the frequency and the reactive power. This function is used to detect the islanding condition. Moving towards more innovative solutions, in [121] a new islanding detection technique is based on the addition of a variable impedance and a hybrid automatic transfer switch. In [122] computational geometry has been applied to derive an islanding detection technique based on a classifier module. As in case of the active methods, the technique discussed in [123] uses harmonic current injection. The islanding condition is detected through cross correlation. In [124] an original islanding detection scheme based on machine learning adoption is proposed. In [125] a communication-based islanding detection method is presented based on a wireless sensors network. The performances are improved adding a combination of selected loads in the system in order to avoid excessive voltage variations.

#### *4.6. Performances Evaluation of the Islanding Detection Methods*

The performances of the considered islanding detection categories are reviewed in Table 1. The main advantages and disadvantages related to the same categories are summarized in Table 2. The hybrid methods are combinations of the islanding detection techniques categorized as communication-based methods, passive methods, active methods and signal processing-based methods. The performances of the hybrid methods depend on the original characteristics of the techniques that they match, hence hybrid methods are not reported in Tables 1 and 2. The hybrid methods are designed to overcome the disadvantages of the islanding detection techniques previously

developed. As a consequence, hybrid methods are progressively updated, and they can be assessed as tradeoff among advantages of the original methods and increased implementation complexity.




## **5. Synchronization and Islanding Detection Coordination**

ZCD methods and ZCD-based PLLs exhibit low dynamic performance and are not suitable for grid voltage monitoring in case of abrupt changes of the grid voltage and power quality disturbances. Arctangent-based PLLs are not particularly widespread due to implementation issues. The PLLs based on Park transform and SOGI OSG, known as SOGI PLLs and the EPLLs represent the most promising synchronization systems for single-phase PVSs due to high filtering capability, also in presence of grid voltage harmonic distortion, accuracy and high dynamic performances also in case of grid voltage abrupt variations. SOGI PLLs and EPLLs are ideal candidates to be employed in the islanding detection and in the reconnection of a PVS to the main grid after an islanding event.

## *5.1. Impact of the Synchronization Systems on the Islanding Detection Methods*

Many islanding detection methods are based on information about the amplitude, the phase and the frequency of the PVS voltage. These methods do not require additional synchronization systems to be included in the PVS control structure. The SOGI PLLs and the EPLLs represent the best synchronization systems for this kind of applications. Other islanding detection techniques require additional synchronization systems in order to monitor some selected harmonics and the PVS current or can require some modification of the synchronization system generally used to track the PVS voltage. There are also some islanding detection techniques which are not based on synchronization systems information. In Table 3 there are reported the main devices used by the different islanding detection methods discussed in Section 4. The islanding detection methods which employ PLLs or EPLLs are pointed out. Hybrid methods are not included in Table 3 since their characteristics depend on the original methods that they combine.

Looking at Table 3, it can be observed that both communication-based techniques and signal processing-based techniques avoid the use of PLLs. Indeed, the communication-based islanding detection techniques are based on communication interface equipment, in particular receivers. The signal processing-based techniques are based on harmonics measurement and localization related to time-varying electrical signals such as voltage, power, entropy, etc. The harmonics decomposition is achieved through the use of the FT, the WT or the ST.


**Table 3.** Main devices of the islanding detection techniques.

The operating principle of most active and passive methods is based on PLLs or EPLLs. Among the passive methods, the OUV, OUF and ROCOF methods are based on PVS voltage amplitude and frequency information. The PVS PLL or EPLL, used to monitor the PVS operation, can be employed to detect the islanding occurrence operating in coordination with the OUV, OUF and ROCOF relays. Some OUV, OUF and ROCOF protections avoid the PLL and are just based on solid-state relays. The choice depends on the PVS power size, the cost, the desired level of performance. Similarly, many active methods act in order to determine an OUV or OUF in the PVS. When the voltage or the frequency exceeds the threshold value, islanding is detected. It occurs for the active and reactive power injections methods, the AFD, the SFS and the SVS methods. Furthermore, for these methods the main devices are solid-state relays or PLLs/EPLLs coordinated with relays.

Among the passive methods the PJ method requires an additional PLL/EPLL to monitor the PVS current phase which has to be compared to the PVS voltage phase. The VHM requires more PLLS/EPLLs to track the selected harmonics variations and to detect the islanding condition. Among the active methods the SMS method is based on an additional PLL or on a modification of the PVS PLL to create the perturbation in the PVS and to detect the islanding occurrence. In the field of the active methods, just the grid impedance variation method does not require information provided by the PLL/EPLL since it is based on the impedance measurement.

## *5.2. Reconnection of a PVS to the Grid after an Islanding Event*

Independently of the adopted islanding detection technique, the reconnection of a PVS after an islanding event needs to be managed by two PLLS or EPLLs circuits. Indeed, an improper reconnection event is not improbable if the PVS breaker *S*<sup>1</sup> connects the system to the grid when the PVS voltage is out of phase compared to the grid voltage. In this occasion overcurrents can be verified or, in the worst case, a second disconnection can occur determined by the PVS protections intervention. Hence the reclosing procedure has to be managed in strict coordination with the PVS synchronization system.

Assuming, for example, to detect the islanding condition using the active and reactive power injections method and to employ SOGI PLLs as synchronization systems, in Figure 12 there are shown the PVS voltage *ePVS* and the grid voltage *e* in case islanding occurs at *t* = 10 s. At this time, the grid utility breaker Sg is opened and during the islanding operation the amplitude and the frequency of the PVS voltage drift from the rated values.

**Figure 12.** Grid and PVS voltages in case of islanding occurrence. (**a**) *e* and *ePVS* waveforms; (**b**) *ePVS* amplitude; (**c**) *ePVS* frequency.

The information about the amplitude and the frequency of the PVS voltage, provided by the SOGI PLL, is employed to assess the islanding phenomenon within 2 s on the basis of the active and reactive power injections method. The grid and the PVS voltage waveforms are not more synchronized and, when the *ePVS* amplitude and frequency deviations exceed the thresholds values, islanding is detected and also the PVS breaker *S*<sup>1</sup> is opened.

Denoting as *ID* the control signal providing information about the islanding condition, it is possible to define *ID* = 1 when islanding is not detected and *ID* = 0 when islanding is detected. Similarly, it is possible to use a control signal to assess synchronization of the PVS with the grid. In this analysis it is indicated with synchronization = 1 the condition when *ePVS* and *e* are in-phase, synchronization = 0 the condition when the two systems are not synchronized.

Assuming that the grid is recovered in few seconds, at *t*<sup>1</sup> = 15 s the grid breaker Sg is closed again (Figure 13). Nevertheless, the reconnection of the PVS cannot be immediate. Since the grid and the PVS are not more synchronized after the islanding occurrence, some reconnection time is required. When the breaker Sg is reclosed, the control signal moves from *ID* = 0 to *ID* = 1. In the considered case study, the grid recovery is detected in less than 0.03 s, but the PVS is reconnected just at *t*<sup>2</sup> = 15.25.

The PVS reconnection is possible only when *ePVS* and *e* are assessed again in-phase. In particular, the synchronization is detected when the phase and the amplitude difference between *ePVS* and *e* is null. Only at this time the synchronization control signal moves from synchronization = 0 to synchronization = 1.

In the described procedure two PLLs/EPLLs are required: one to monitor the PVS voltage and one to monitor the grid voltage. This example is provided to point out the role of the synchronization

**Figure 13.** Grid and PVS voltages during resynchronization process. (**a**) *e* and *ePVS* waveforms; (**b**) ID and synchronization control signals.

#### **6. Conclusions**

An extensive analysis of synchronization and islanding detection methods for single-stage PVSs is presented in this study. Synchronization and islanding detection represent some of the most important control issues for PVSs in the light of the new standards requirements. Abnormal conditions can arise on the utility grid which require a prompt response from the grid-connected PVSs, hence the information provided by the synchronization system are fundamental for the grid voltage monitoring.

Synchronization and islanding detection techniques must operate in coordination. The islanding detection techniques are based also on the information provided by the synchronization techniques. Besides some islanding detection methods use additional PLLs for the harmonics monitoring. In other cases, the normal operation of the PLL is modified in order to detect the islanding phenomenon as it happens in case of the slip-mode frequency shift technique. Finally, it has to be considered that, after a disconnection due to the islanding detection, an improper reconnection event is not improbable if the PVS breaker connects the system to the grid when the PVS voltage is out of phase. In this hypothesis a second disconnection can occur due to the PVS protections action. Hence the reclosing procedure has to be managed with two synchronization systems.

For all these reasons synchronization and islanding detection issues were analyzed together. More than 120 publications were revised and discussed in order to provide a combined review. Both the synchronization and the islanding detection techniques were categorized. The choice of the islanding detection technique depends on numerous criteria. The EPLL and the SOGI PLL represent the preferable synchronization systems to operate in coordination with the islanding detection techniques.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
