**1. Introduction**

Over the last years, the electric energy generated from renewable energy sources (RES) has grown exponentially. In particular, photovoltaic (PV) energy has now become one of the most relevant parts in energy mix in several geographical areas [1]. In such a scenario, as most of the installed PV generators (PVGs) are grid connected, particular attention must be paid to the system reliability [2] in order to meet the requirements of the electric service in terms of efficiency and power quality. Moreover, the continuous increase in capacity of the PV installed plants makes these resources an important agen<sup>t</sup> in active distribution grids, as they are distributed energy resources (DER) also requiring special control strategies [3]. As a consequence, one of the main purposes of the research is to facilitate the integration of variable renewable sources and distributed generation units within the grid [4].

A particular condition arises when a PV DER feeds a critical local load or emergency fixtures in a grid-tied system; it should be capable of operating in parallel with the grid as well as in island (i.e., regardless of the mains). In fact, the island operating mode becomes unavoidable in case of power outage (e.g., for fault conditions or maintenance purposes) in order to ensure continuous energy supply to the local loads. Obviously, in islanded mode, the inherent intermittent nature of PV generation does not allow fulfillment of the load power demand. For this reason, the integration of a Battery Energy Storage System (*BESS*) as a standby backup energy resource can be useful to guarantee continuity of the power supply or at least to compensate for the gap between load demand and PV production. Thus, a proper control action must be implemented to ensure the capability of the overall system to work in di fferent operating modes [5]. The islanding detection (ID) and the consequent disconnection from the grid are significant features that the system must implement. In technical literature, di fferent detection techniques are analyzed [6–11]. The ID methods (IDMs) are mainly divided into two categories: local and remote methods. Local IDMs are then classified as passive and active methods. The former methods are based on the monitoring of change or the rate of change in the power system parameters, while the latter rely on the injection of a small perturbation in the output system parameters to identify islanding condition. Comprehensive review and performance evaluations of the several proposed techniques are reported in [10,11]. One of the most relevant figures of merit (FoM) to compare the various IDMs is the time requested to identify the grid trip (i.e., detection time or speed), which should be lower than the standard requirements. In [10,11], active, passive, and modified passive methods based on signal processing are compared in terms of speed. In particular, among the passive methods, the wavelet transform (WT) technique seems to reach the best speed performance but at the cost of increased computational complexity. Recent research works [12–17] propose enhanced IDMs; [12] reports a feedback-based passive islanding detection technique for one-cycle-controlled (OCC) single-phase inverter used in photovoltaic system. This method, as stated by the authors, is not generic and limited to OCC-based inverters while providing a detection time of about 200 ms (i.e., 10 grid cycles). In [13], an IDM based on parallel inductive impedance (PII) switching at a distributed generation (DG) connection point along with monitoring the rate of change of voltage at the DG output is implemented. However, to identify the islanding, this technique needs a two-step procedure that requires at least 300 ms in the worst case, corresponding to a run-on time of 15 grid cycles. In [14], a methodology to detect islanding in a grid-connected photovoltaic system is proposed. A disturbance is injected into the maximum power point tracking (MPPT) algorithm when the absolute deviation of the point of common coupling (PCC) voltage in any phase exceeds a voltage threshold. This determines a shift of the system operating point from its maximum power point (MPP), thus resulting in a relevant output power reduction, and the detection time results within 300 ms (i.e., 15 grid cycles). In [15], the used method for adjustment and evaluation of a voltage relay is based on the combination of the application region (AR) and the power imbalance application region (PIAR) methods, and it leads to a detection time of hundreds of milliseconds (i.e., 100–400 ms, 5–20 grid cycles). In [16], a combination of rate of change of frequency (ROCOF), rate of change of phase angle di fference (ROCPAD), rate of change of voltage (ROCOV), and over frequency/under frequency (OF/UF) methods is reported. In such a case, the proposed algorithm represents the merge of di fferent passive ID techniques, thus the detection time is always the minimum among the di fferent used algorithms. As a consequence, it seems to work well (e.g., detection time of few milliseconds) but at the cost of a more complex implementation. A variance in the autocorrelation of the modal current envelope (VAMCE) is used as an islanding detection criterion in [17]. This method employs an autocorrelation function (ACF) of a modal current envelope derived by Hilbert transform, and its detection time is of about two or three grid cycles (i.e., 40–60 ms).

This paper proposes a kind of passive method based on the observation of the envelope of the voltage of the point of common coupling. The envelope of the considered quantity is quickly obtained by means of the Hilbert transform and specifically the proposed algorithm outputs the absolute value of the Hilbert transform that can represent a reliable index of fast change in network behavior. In fact, the grid trip phenomenon causes a sudden variation of the PCC voltage, which results in a spike of the monitored quantity. The latter may no longer fall within a predefined safety range, thus allowing islanding detection according to the requirements of the network code. In principle, the monitoring of the envelope does not need to wait for the PCC voltage crest to verify the boundaries' violation, thus leading to a detection time less than a grid cycle (i.e., 10 ms in the best case), thus showing its benefit in terms of speed with respect to the aforementioned techniques. In addition, the proposed method can be used independently of the specific application.

The paper describes a control strategy that is used to implement grid-connected and intentional islanding operations of a PV inverter when the power circuits are in open-delta configuration as a consequence of a local fault. Under ordinary operating conditions, the PV source delivers the energy to the load and, if the load request is not met, the grid provides the residual part while the battery is in idle mode. In islanded mode, the continuous power supply of the load is ensured due to to the integrated *BESS*, thus overcoming the lack of grid supply and obtaining a flat profile of the inverter output power [18].

The starting architecture for the considered energy conversion system is the conventional double-stage configuration of Figure 1. It represents a centralized solution in which PVG is made up of several strings in parallel in order to achieve the desired rated power.

**Figure 1.** Schematic view of double-stage three-phase photovoltaic (PV) inverter with integrated Battery Energy Storage System (*BESS*).

In a previous paper [19], the authors proposed a solution to enhance fault tolerance of the system and its reliability, introducing a particular control strategy aimed at operating even with only two legs (phases) still being fully functional. In fact, in case of failure of one inverter leg, dedicated switches are capable of short-circuiting the *LC* filter (*Lf* − *Cf*) of the failing leg, leading to the new open-delta configuration shown in Figure 2, which allows the PV inverter to operate even in the presence of a fault. With reference to the two-leg configuration of the inverter, the effect of *BESS* integration and the effectiveness of the proposed ID method are discussed.

**Figure 2.** Overall system configuration.

The paper is organized as follows. System modeling is reported in Section 2. Then, Section 3 deals with design and control of the grid-tied PV inverter. In Section 4, the proposed design procedure is validated by carrying out numerical simulations in PLECS environment. Conclusions are summarized in Section 5.
