## 1 Introduction  
The islanding operation of distributed generation (DG) refers to a phenomenon in which electricity is continuously generated from the DG despite a power outage in the power grid [1]. This islanding operation causes many problems, such as a potential electric shock at the Point of Common Coupling (PCC) that was considered to be inactive, a high inrush current due to reconnection after power recovery, damage to the circuit breaker, an increase in harmonics, and flickering [2, 3, 4, 5]. Therefore, many domestic and foreign standards require the function of the anti-islanding method (AIM) to stop the generation of DGs when the grid is disconnected, with the goal of securing safety [6, 7]. As a part of the energy transition, renewable-energy-based DGs, such as Photovoltaic (PV) and wind power, are occupying more and more parts of the power grid worldwide [8, 9, 10]. For this reason, there is a dropout of large-scale DG sources due to a partial transient state of the power grid, which adversely affects the stability and power quality of the power grid, involving issues such as false tripping of feeders, blinding of protection, and unintentional islanding occurring [11, 12, 13, 14]. In order to respond to this issue, recent power regulations require a function to maintain the connection to the power grid as much as possible, control active power or reactive power, or both in response to variations in voltage and frequency in the power system [15, 16, 17]. This is called the grid support function of DG resources, and the enactment is being promoted as a grid regulation of each country around the world [18, 19, 20, 21]. However,the grid support function creates a very difficult condition for detecting the islanding phenomenon with the conventional technology. Accordingly, many studies are being conducted to create a new islanding detection technique in response to these challenging problems [22; 23; 24]. The conventional AIM is divided into a passive method and an active method [1]. The passive method simply monitors the main parameters, such as voltage/frequency/phase of the inverter's output stage, and when it exceeds the set value, it is determined as islanding operation [25; 26; 27]. In the passive method, when the generated power and the load power of the DG are balanced, the fluctuation amount of the main parameter is not large, and there is a problem that the islanding cannot be detected. On the other hand, the active method forcibly changes parameters, such as current/frequency/phase/active power/reactive power, and causes a large change in the parameter after islanding operation occurs, so that it is designed to exceed the set value [28; 29; 30]. As shown in Figure 1, active methods based on the frequency variation include active frequency drift (AFD), active frequency drift with positive feedback (AFDPF), slip mode frequency shift (SMS), and reactive power variation (RPV) methods. The AFD method in particular uses the chopping fraction, cf, as a frequency perturbation parameter, which is defined as the ratio of zero time (\(t_{z}\)) to half of the period of voltage waveform (\(T_{1}/2\)). Its concept is based on varying the frequency of the inverter output current. If the frequency of the inverter voltage is out of the frequency relay set value after islanding occurs, it is determined to be an islanding operation, and the inverter stops. This technique inherently raises the harmonic component of the current, thereby lowering the power quality. It also has a limitation in that the performance varies depending on the value of the resonance index of the RLC local load. Another representative active method is a technique of periodically changing reactive power causing frequency fluctuations due to fluctuations in reactive power when islanding occurs. This method inherently lowers the value of the displacement power factor, which has a problem of lowering the power quality, and also has a limitation in that the performance varies according to the value of the resonance index of the RLC local load.