Propagating Uncertainty in Power-System DAE Models with Semidefinite Programming

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

This paper outlines a convex-optimization-based method to estimate maximum and minimum bounds on states of differential algebraic equations (DAEs) that describe the electromechanical dynamics of power systems while acknowledging parametric and input uncertainty in the model. The method is based on a second-order Taylor-series approximation of the DAE-model state trajectories as a function of the uncertainties. A key contribution in this regard is the derivation of a DAE model that governs the second-order trajectory sensitivities of states to uncertainties in the model. Bounds on the states are then obtained by solving semidefinite programs, where the objective is to maximize/minimize the Taylor-series approximations subject to constraints that describe the uncertainty space. While the computed bounds are approximate (since they are derived from a Taylor-series approximation of the state trajectories) the method nevertheless is an efficient system-theoretic approach to uncertainty propagation for power-system DAE models. Numerical case studies are presented for a DAE model of the IEEE 39-bus New England system to demonstrate scalability and validate the approach.

Original languageEnglish (US)
Article number7585069
Pages (from-to)3146-3156
Number of pages11
JournalIEEE Transactions on Power Systems
Volume32
Issue number4
DOIs
StatePublished - Jul 1 2017

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Differential equations
Taylor series
Trajectories
Convex optimization
Uncertainty
Scalability

Keywords

  • Quadratically constrained quadratic programming
  • semidefinite programming
  • trajectory sensitivity analysis
  • uncertainty propagation

Cite this

Propagating Uncertainty in Power-System DAE Models with Semidefinite Programming. / Choi, Hyungjin; Seiler, Peter J.; Dhople, Sairaj V.

In: IEEE Transactions on Power Systems, Vol. 32, No. 4, 7585069, 01.07.2017, p. 3146-3156.

Research output: Contribution to journalArticle

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