Journal
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS
Volume 60, Issue 9, Pages 2533-2546Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCSI.2013.2246233
Keywords
Lyapunov methods; nonlinear systems; power system transient stability; sum of squares; transient energy function
Categories
Funding
- U.S. Department of Energy through the LANL/LDRD Program
- Ministry of Science and Innovation of Spain, MICINN [ENE2009-07685, ENE2012-31326]
- Engineering and Physical Sciences Research Council [EP/J012041/1, EP/I031944/1, EP/J010537/1, EP/H03062X/1]
- EPSRC [EP/J010537/1, EP/H03062X/1, EP/J012041/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/J012041/1, EP/H03062X/1, EP/J010537/1] Funding Source: researchfish
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We present a methodology for the algorithmic construction of Lyapunov functions for the transient stability analysis of classical power system models. The proposed methodology uses recent advances in the theory of positive polynomials, semidefinite programming, and sum of squares decomposition, which have been powerful tools for the analysis of systems with polynomial vector fields. In order to apply these techniques to power grid systems described by trigonometric nonlinearities we use an algebraic reformulation technique to recast the system's dynamics into a set of polynomial differential algebraic equations. We demonstrate the application of these techniques to the transient stability analysis of power systems by estimating the region of attraction of the stable operating point. An algorithm to compute the local stability Lyapunov function is described together with an optimization algorithm designed to improve this estimate.
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