## 1 Introduction  
In recent years, the penetration of dispersed generations (DGs) such as photovoltaic and wind energy in electricity systems has significantly increased. Some of the distributed generations are natively DC. The developments of DC loads and storage technologies have also considerably increased [1]. The DC grid has much more advantages such as higher system efficiency, easier integration and lower losses due to reduced conversion devices than the AC grid [2; 3; 4; 5]. Therefore, the DC grid has been rapidly increasing in the power system. One of the major challenges with DC grid-connected DG is the detection of the unintentional islanding phenomenon. According to the IEEE 929-2000 standard [6], islanding problem occurs when the distributed network isolated from the main utility and the loads are supplied by DGs only. Based on this standard, the islanding phenomenon must be detected within 2 s to prevent damage to electrical devices and ensure the safety of maintenances. Nowadays, islanding detection has received considerable attention through recent studies. In [7], a novel islanding detection method based on two additional compensators and positive feedback of active and reactive power control loops. The method does not have a non-detection zone, no affect on power quality and normal operation of synchronous DG. Because of it need additional compensators, it may cause the method to complicate and costly. A novel islanding detection method for micro-grid was proposed in [8]. The method can detect islanding phenomenon in hardest condition (low active and reactive power mismatches) by using a differential morphological filter (a dilation-erosion differential filter (DED)) of the RMS signal (DEDFOR) at the point of common coupling. The method has a small non-detection zone (NDZ), fast detection time, and high accuracy. However, the method is used for double-fed induction generators (DFIGs) system. A new passive islanding detection includes in Smart Islanding Detector (SmartID) was proposed in [9]. It combines with classical voltage and frequency relays to make a better anti-islanding protection system. The method is used to backup in case of the classical method fail. However, the combination of SmartID and classical relays also complicated. In [10], a new islanding detection strategy for low-voltage inverter-interfaced microgrids was presented. This strategy was based on adaptive neuro-fuzzy inference system (ANFIS). The ANFIS method monitors seven inputs measured at the point of common coupling (PCC) such as root-mean square of voltage and current (RMSU and RMSI), total harmonic distortion of voltage and current (THDU and THDI), frequency, and active and reactive powers based on practical measurement in a real microgrid. The ANFIS method detects islanding condition by using its pattern recognition capability and nonlinear mapping of relation between input signals. A novel hybrid islanding detection method for grid-connected microgrids in the case of multiple inverter-based distributed generators was proposed in [11]. This method was based on the slope of linear reactive power disturbance (RPD) and four passive criteria, namely, voltage variation, voltage unbalance, rate of change of frequency and correlation factor between the RPD and frequency variation. Islanding is detected when the frequency exceeds its thresholds. However, the cancellation issue in the case of multiple inverter-based distributed generators was ignored in this study. In [12], a new method used the transient response of voltage waveform to detect the islanding condition. This method was based on two new criteria, namely, the peak of the transient index value (TIV) and the positive sequence superimposed phase angle at the point of common coupling. In [13], a method based on Kalman filter (KF) was proposed to extract and filter the harmonic components of the measured voltage signal at distributed generation terminals.