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This paper presents an intelligent non-model-based differential relay for protecting microgrid systems in the case of islanding scenarios. For this purpose, by using discrete Fourier transform, different types of electrical signals including voltage and current phasors are processed during fault events by which the most observable signals are estimated to identify system abnormal conditions. In order to identify proper protection signals, an intelligent decision tree (IDT) technique is implemented from which the most effective signals for designing differential protection relay are provided. The proposed IDT-based differential scheme is trained comprehensively in off-line environment using different fault scenarios, both operational and topological. Then, it is implemented in online working mode where, by applying candidate protection signals as input to the proposed intelligent relay, the proper differential protection is derived. The proposed protection relay is an online and non-model-based scheme which can be implemented within a wide range of topologies including mesh and radial topologies in terms of the system operating conditions. The proposed strategy is implemented on a modified IEC case with different fault scenarios. Through considering two grid-connected and islanded system operating modes, the performance of the proposed intelligent differential relay is evaluated. Simulation test results indicate the considerable ability of the proposed technique for proper estimation of decision signals in different fault scenarios within real-time environment.

In this article, homotopy perturbation method is applied to solve nonlinear parabolichyperbolic partial differential equations. Examples of one-dimensional and two-dimensional are presented to show the ability of the method for such equations.

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