Dynamic Equivalent Based on Balanced Realizations for Interconnection of Photovoltaic Distributed System

This paper presents a hybrid methodology to analyze electromagnetic transients in a photovoltaic distributed system. The methodology consists in split the system into two parts: The external zone, where the system is reduced by a dynamic equivalent obtained by the application of Balance Realization (BR) theory and the internal zone, where the system is modeled in detail and solved by a time domain technique. The methodology, that uses a predictor-corrector method to join both zones, does not need a transmission line to interconnect the systems but an element with reactive behavior to deal with the time coupling. In the first zone, the use of BR permits to obtain a new and reduced state-space description of the system that keeps the domain dynamics of the full system. The size of this system can be reduced as much as desired. Nevertheless, the resulting size is proportional to the accuracy. The BR decreases significantly the computational cost to simulate distributed networks. No restrictions are done in the internal zone where all the dynamics elements including the control if desired, can be simulated. The internal zone commonly contains non-linear or power electronic elements.