## 2 Materials and Methods  
The power system in this study comprises of doubly-fed induction generator (DFIG) wind farm, utility grid, parallel RLC load, grid and wind farm transformers altogether connected to 11 kV, 50 Hz distribution system. Two circuit breakers (CB\({}_{\text{Grid}}\), CB\({}_{\text{DG}}\)) are connected to DG and grid respectively. DFIG contains an induction generator heaving wound rotor and PWM AC/DC/AC converter based on IGBT. AC/DC/AC converter provides variable frequency to the rotor whereas stator windings are directly linked with the power grid. Simulation parameters of the system are given in Table 1. These parameters are adjusted and varied to set desired testing cases. IEEE 1547 generic test system [44] is employed for validation of islanding detection technique performance as shown in Figure 1.  
The control scheme of the DFIG can impact the behavior of different parameters during islanding events and abnormal conditions. The behavior of parameters can become unpredictable if control parameters deviate from default settings. The impact of the control scheme of DFIG on parameters mainly depends on the type of control and islanding detection strategy used. The basic configuration of the DFIG wind turbine scheme is shown in Figure 2a-d. The DFIG control systems have two portions: mechanical control for wind turbine blade pitch angle and electrical control for DFIG. The controlling of DFIG is achieved through the control of voltage frequency converter (AC/DC/AC) that further consists of control of grid side covector (GSC) & control of rotor side covector (RSC) [45; 46]. In our proposed method, a separate relay with synchro-phasor measurement functionality is used at a single DG connection point. However, when multiple DG's will be used then separate relays must be employed for every DG connection point. A multiple  
Figure 2: Control scheme of DFIG (**a**) A basic configuration of a DFIG wind turbine (**b**) Overall vector control scheme of the RSC (**c**) Overall vector control scheme of the GSC (**d**) Wind turbine pitch angle controller. DFIG's network has employed in [6] used four separate relays for each DG connection point. Contrary to this, some inverter base DG has used the islanding detection control schemes added in the inverter control for gaining the cost-efficiency benefits. The inverter-based control schemes can be active or passive. However, the designing of inverter control schemes for islanding detection is complex as compared to passive methods. The proposed method in this study is independent of any type of inverter-based control. In this work, 6 different passive indices are considered for analysis such as voltage, frequency, active power, reactive power, power factor and voltage phase angle. These 6 parameters are inspected on the power system under analysis as presented in Figure 1 via consideration of various islanding and non-islanding situations. Islanding situations include small mismatch (S.M) and large mismatch (L.M) condition whereas non-islanding or abnormal events comprises of load increment (L.I), load decrement (L.D), capacitor energization (C.E), capacitor de-energization (C.D), motor starting (M.S), motor unloading (M.U) and fault switching (F.S) scenarios. All considered situations are accomplished with power mismatch as tabulated in Table 2. The absolute values (magnitudes or phase) are noted for all considered indices after numerous islanding and non-islanding events are shown in Figure 2(a)-f.  
After careful investigation of passive indices (voltage, frequency, active power, reactive power, power factor), it has been noted that the magnitude/phase of passive indices are intermixed for islanding vs. non-islanding scenarios as shown in Figure 2(a)-e. However, the voltage phase angle as shown in Figure 2(f) presents a considerable picture. Voltage phase angle differentiate islanding operations from non-islanding events.