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Fast detection of islanding is very important for effective operation and control in distributed generation (DG) penetrated distribution networks. The islanding detection techniques such as passive, active, communication, and hybrid have their own merits and demerits. This paper proposed wavelet transform (WT) and wavelet packet transform (WPT) based techniques for detection of islanding and fault disturbances in a microgrid consisting of resources like wind turbine generator, fuel cell (FC), and microturbine. Voltage signal is extracted at the point of common coupling (PCC) and is passed through these detection techniques to obtain the time-frequency multi-resolution analysis. Further, to validate the graphical study, performance indices (PIs) like standard deviation and entropy are calculated for the disturbance detection using suitable selection of threshold. A comparative analysis using WT and WPT is presented in the form of graphical simulation as well as in terms of PIs to analyse their effectiveness and robustness under different operating conditions. It is observed that WPT shows better detection capability in comparison to WT even under 20-dB noisy scenarios. [ABSTRACT FROM AUTHOR]