A Geometric Analysis of Power System Loadability Regions

Yang Weng, Ram Rajagopal, Baosen Zhang

Research output: Contribution to journalArticle

Abstract

Understanding the feasible power flow region is of central importance to power system analysis. In this paper, we propose a geometric view of the power system loadability problem. By using rectangular coordinates for complex voltages, we provide an integrated geometric understanding of active and reactive power flow equations on loadability boundaries. Based on such an understanding, we develop a linear programming framework to 1) verify if an operating point is on the loadability boundary, 2) compute the margin of an operating point to the loadability boundary, and 3) calculate a loadability boundary point of any direction. The proposed method is computationally more efficient than existing methods since it does not require solving nonlinear optimization problems or calculating the eigenvalues of the power flow Jacobian. Standard IEEE test cases demonstrate the capability of the new method compared to the current state-of-the-art methods. Understanding the feasible power flow region is of central importance to power system analysis. This paper proposes a geometric view of the power system loadability problem. By using rectangular coordinates for complex voltages, this paper provides an integrated geometric understanding of active and reactive power flow equations on loadability boundaries. Based on such an understanding, this paper develops a linear programming framework to 1) verify if an operating point is on the loadability boundary, 2) compute the margin of an operating point to the loadability boundary, and 3) calculate a loadability boundary point of any direction. The proposed method is computationally more efficient than existing methods since it does not require solving nonlinear optimization problems or calculating the eigenvalues of the power flow Jacobian. Standard IEEE test cases demonstrate the capability of the new method compared to the current state-of-the-art methods.

Original languageEnglish (US)
Article number8790784
Pages (from-to)3580-3592
Number of pages13
JournalIEEE Transactions on Smart Grid
Volume11
Issue number4
DOIs
StatePublished - Jul 2020
Externally publishedYes

Keywords

  • Power flow
  • geometric understanding
  • loadability boundary
  • maximum power output
  • renewable integration%

ASJC Scopus subject areas

  • Computer Science(all)

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