The sustainable development of an area is highly dependable on reliable electrical energy supply. Microgrids are important in integrating distributed energy resources (DERs) using power electronic converters. However, microgrid control becomes challenging with the increasing number of distributed generators and loads. With the conventional droop control method, power contributions from DER converters cannot be accurately shared due to a mismatch of line impedances. In this paper, an augmented hierarchical control mechanism is proposed to solve the issues mentioned above. This hierarchical control mechanism consists of primary and secondary controllers. The primary stage utilized the droop controller to improve optimal power flow, mainly for the resistive network. The secondary stage is based on an improved methodology to compensate for the voltage and frequency variations during small and large signal disturbances. Moreover, the modelling and analysis for PMSG-based wind energy conversion systems are also presented. The response of the primary controller for the active and reactive power sharing is investigated. The analysis emphasizes the demonstration of optimal power-sharing under normal and abnormal conditions for the considered load. Finally, the suggested robust controller's performance is evaluated in MATLAB environment and simulation results show the proposed scheme's superiority under different operating conditions.

In this work, generalized geometry of second-order tangent groups and affine configuration complexes is proposed. Initially, geometry for higher weights n=4 and weights n=5 is presented through some interesting and suitable homomorphisms, finally, this geometry is extended and generalized for any weight n.

In this article, a generalization of the geometry of Grassmannian chain complex of free abelian groups generated by the projective configuration of points and Cathelineau's infinitesimal complex of polylogarithmic groups is proposed. Firstly, homomorphisms for weight n =2 up to weight n=6 will be introduced to connect sub-complexes of Grassmannian and Cathelineau. Lately, generalization of these morphisms will be shown for weight n=N. The associated diagrams will also be proven to be commutative and bi-complex.