We present a computational scheme, GRIP (geometric random inner products), for testing the quality of random number generators. The GRIP formalism utilizes geometric probability techniques to calculate the average scalar products of random vectors distributed in geometric objects, such as circles and spheres. We show that these average scalar products define a family of geometric constants whic...

In this paper, a robust local controller has been designed to balance the power for distributed energy resources (DERs) in an islanded microgrid. Three different DER types are considered in this study; photovoltaic systems, battery energy storage systems, and synchronous generators. Since DER dynamics are nonlinear and uncertain, which may destabilize the power system or decrease the performanc...

Distributed energy resources (DERs) including distributed generators (DGs) and controllable loads (CLs) are managed in the form of several microgrids (MGs) in active distributions networks (ADNs) to meet the demand locally. On the other hand, some loads of distribution networks (DNs) can be supplied by retailers which participate in wholesale energy markets. Therefore, there are several decisio...

In recent years the use of renewable energy sources (RES) by many power grid companies worldwide has increased significantly. The trend towards RES is mainly due to environmental issues and rising fuel prices associated with conventional electricity generation. This paper introduces a hybrid approach find optimal location size distributed generations (DG) in radial distribution system (RDS). pr...