This paper designs a multi-variable hybrid islanding-detection method (HIDM) using signal-processing techniques. The signals of current captured on a test system where the renewable energy (RE) penetration level is between 50% and 100% are processed by the application of the Stockwell transform (ST) to compute the Stockwell islanding-detection factor (SIDF) and the co-variance islanding-detection factor (CIDF). The signals of current are processed by the application of the Hilbert transform (HT), and the Hilbert islanding-detection factor (HIDF) is computed. The signals of current are also processed by the application of the Alienation Coefficient (ALC), and the Alienation Islanding Detection Factor (AIDF) is computed. A hybrid islanding-detection indicator (HIDI) is derived by multiplying the SIDF, CIDF, AIDF, and an islanding weight factor (IWF) element by element. Two thresholds, designated as the hybrid islanding-detection indicator threshold (HIDIT) and the hybrid islanding-detection indicator fault threshold (HIDIFT), are selected to detect events of islanding and also to discriminate such events from fault events and operational events. The HIDM is effectively tested using an IEEE-13 bus power network, where solar generation plants (SGPs) and wind generation plants (WGPs) are integrated. The HIDM effectively identified and discriminated against events such as islanding, faults, and operational. The HIDM is also effective at identifying islanding events on a real-time distribution feeder. The HIDM is also effective at detecting islanding events in the scenario of a 20dB signal-to-noise ratio (SNR). It is established that the HIDM has a small non-detection zone (NDZ). The effectiveness of the HIDM is better relative to the islanding-detection method (IDM) supported by the discrete wavelet transform (DWT), an IDM using a hybridization of the slantlet transform, and the Ridgelet probabilistic neural network (RPNN). An IDM using wavelet transform multi-resolution (WT-MRA)-based image data and an IDM based on the use of a deep neural network (DNN) were used. The study was performed using the MATLAB software (2017a) and validated in real-time using the data collected from a practical distribution power system network.