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The paper presents a new Fast Gauss-Newton algorithm (FGNWA) for the detection of islanding condition in distributed generation systems (DGs) when they are disconnected from the main supply system or there are small load unbalances in the distribution network. During islanding conditions power system parameters like frequency, voltage magnitude, phase change, total harmonic distortion, and various sequence voltage, current, and power components do change and hence by monitoring these changes accurately, an islanding condition can be detected. A forgetting factor weighted error cost function is minimized by the well known Gauss-Newton (GN) algorithm and the resulting Hessian matrix is approximated by ignoring the off-diagonal terms to yield the new FGNW algorithm to estimate, in a recursive and decoupled manner, all the above voltage and current signal parameters accurately for realistic power systems even in the presence of significant noise. A number of test cases considering both islanding and nonislanding, for realistic, hybrid distribution networks has demonstrated the reliability and accuracy of the islanding detection scheme, when a fuzzy expert system (FES) is used in conjunction with the proposed FGNW algorithm.