23 - Distribution systems hosting capacity assessment: Relaxation and linearization

Abstract

High penetration of distributed energy resources (DERs) may cause many technical issues such as overvoltage, overloading, and protection mis-coordination in distribution systems. To cope with these issues, one solution is upgrading the distribution system to which DERs are connected, which could be costly. Another solution is limiting the DERs penetration to the hosting capacity (HC). HC is defined as the maximum DER capacity that can be connected to a given system without violating any technical constraint. Understanding this concept can assist utilities to make percise decisions for interconnection requests and to ensure reliable operation of the system. Traditionally, distribution system operators (DSOs) are reluctant to authorize new DERs’ connections, unless detailed studies are performed. Such studies, however, significantly delay the DER integration and may cause complaints by the DER developers and investors. Hence, a need arises for simplified methodologies that will allow DSOs to assess the network HC in a fast but reliable manner. In this chapter, the HC is formulated as an optimization problem, which can be used in criteria-based HC analysis. We prove that it is not possible to convexify the HC problem by using angle and conic relaxations. Then, we reveal a condition under which the solution of linearized HC model is feasible for the original nonlinear HC problem. Next, we propose a piecewise linear approximation based on the proven condition and separable programming theory. Finally, the performance of the proposed method is compared with some of the most important linear models on the IEEE 33-bus system.