A hybrid dynamic equivalent using ANN-based boundary matching technique

Feng Ma, Vijay Vittal

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


In this paper, a hybrid dynamic equivalent consisting of both a coherency-based conventional equivalent and an artificial neural network (ANN)-based equivalent is developed and analyzed. The ANN-based equivalent complements the coherency-based equivalent at all the boundary buses of the retained area. It is designed to compensate for the discrepancy between the full system model and the reduced equivalent developed using any commercial software package, such as the dynamic reduction program (DYNRED), by providing appropriate power injections at all the boundary buses. These injections are provided by the ANN-based equivalent which is trained using the outputs from a trajectory sensitivity simulation of the system response to a candidate set of disturbances. The proposed approach is tested on a system representing a portion of the WECC system. The case study shows that the hybrid dynamic equivalent method can enhance the accuracy of the coherency-based dynamic equivalent without significantly increasing the computational effort.

Original languageEnglish (US)
Article number6152193
Pages (from-to)1494-1502
Number of pages9
JournalIEEE Transactions on Power Systems
Issue number3
StatePublished - 2012


  • Artificial neural network (ANN)
  • dynamic equivalents
  • dynamic reduction program (DYNRED)
  • trajectory sensitivity

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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