Geometric property of distribution system security region: Size and shape

Abstract

This paper studies the geometric properties of Distribution System Security Region (DSSR) by defining four indexes, including volume, surface area, volume to surface area ratio, and roundness. First, the volume is defined as the size of DSSR, while the surface area is defined as the size of all the security boundaries of DSSR. Then, two algorithms based on Monte-Carlo sampling are proposed for calculating the volume and surface area of DSSR. To investigate the relationship between volume and surface area, a new index named volume to surface area ratio (VSR) is proposed, which represents the reciprocal of the surface area to form a unit volume. Furthermore, the roundness of DSSR is defined by comparing the DSSR VSR with the geometry VSR, which indicates how close the shape of a DSSR is to a circle. Finally, two distribution network cases are used to verify the proposed concepts and methods. The distribution networks with the same total supply capability may have significantly different DSSR, indicating that the new indexes help distinguish planning schemes more effectively. This paper quantifies the size and shape of DSSR, which improves our observation of distribution networks and opens new possibilities for distribution network plan.