Normal form analysis of complex system models: A structure-preserving approach

Irma Martínez, A. R. Messina, Vijay Vittal

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


A modeling framework based on normal form theory and singular perturbation techniques is proposed for analyzing the nonlinear behavior of power system models described by nonlinear differential-algebraic equations (DAEs). The method exploits the time scale separation of power system dynamic processes, to avoid reduction of the original DAE model and may therefore be used to assess control effects and network characteristics on system behavior. This approach allows the full potential of the normal form formulation to be reached, and is applicable to a wide variety of nonlinear phenomena described by DAEs. Using a control theory framework, a constructive approach is outlined for transforming a system of DAEs to a state space approximation that is suitable for normal form analysis. By casting the problem in the context of singular perturbation theory, a structure-preserving nonlinear mathematical model of the power system is then established for the study of nonlinear behavior. Criteria for this representation are derived and implementation issues are discussed. The developed procedures are tested on a four-machine, twoarea test system. The accuracy of the model is quantified by comparing normal form simulations with those from a commercial stability software.

Original languageEnglish (US)
Pages (from-to)1908-1915
Number of pages8
JournalIEEE Transactions on Power Systems
Issue number4
StatePublished - Nov 2007


  • Differential algebraic equations
  • Dynamic programming
  • Nonlinear power system behavior
  • Nonlinear programming
  • Normal form theory
  • Perturbation techniques
  • Singular perturbation analysis

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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