Propagating Uncertainty in Power-System DAE Models With Semidefinite Programming

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...

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Vydáno v:IEEE transactions on power systems Ročník 32; číslo 4; s. 3146 - 3156
Hlavní autoři: Hyungjin Choi, Seiler, Peter J., Dhople, Sairaj V.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 01.07.2017
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algebra
Approximation
Buses (vehicles)
Computational modeling
Derivation
Differential equations
Dynamical systems
Mathematical analysis
Mathematical model
Mathematical models
Power system dynamics
Propagation
Quadratically constrained quadratic programming
Semidefinite programming
Sensitivity
Trajectories
Trajectory
trajectory sensitivity analysis
Uncertainty
uncertainty propagation
Vehicle dynamics
ISSN:0885-8950, 1558-0679
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Shrnutí: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.
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ISSN:0885-8950
1558-0679
DOI:10.1109/TPWRS.2016.2615600