Propagating Uncertainty in Power-System DAE Models with Semidefinite Programming

Hyungjin Choi, Peter J. Seiler, Sairaj V. Dhople

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


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
Issue number4
StatePublished - Jul 2017

Bibliographical note

Funding Information:
This work was supported in part by the National Science Foundation under the CAREER Award 1453921. Paper no. TPWRS-00673-2016.

Publisher Copyright:
© 1969-2012 IEEE.


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


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