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This paper describes a geometric approach to parameter identifiability analysis in models of power systems dynamics. When a model of a power system is to be compared with measurements taken at discrete times, it can be interpreted as a mapping from parameter space into a data or prediction space. Generically, model mappings can be interpreted as manifolds with dimensionality equal to the number of structurally identifiable parameters. Empirically it is observed that model mappings often correspond to bounded manifolds. We propose a new definition of practical identifiability based the topological definition of a manifold with boundary. In many ways, our proposed definition extends the properties of structural identifiability. We construct numerical approximations to geodesics on the model manifold and use the results, combined with insights derived from the mathematical form of the equations, to identify combinations of practically identifiable and unidentifiable parameters. We give several examples of application to dynamic power systems models.
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This content will become publicly available on December 23, 2025
Parameter Identifiability and Reduction for Smooth and Nonsmooth Differential-Algebraic Equation Systems
We extend the sensitivity rank condition (SERC), which tests for identifiability of smooth input-output systems, to a broader class of systems. Particularly, we build on our recently developed lexicographic SERC (L-SERC) theory and methods to achieve an identifiability test for differential-algebraic equation (DAE) systems for the first time, including nonsmooth systems. Additionally, we develop a method to determine the identifiable and non-identifiable parameter sets. We show how this new theory can be used to establish a (non-local) parameter reduction procedure and we show how parameter estimation problems can be solved. We apply the new methods to problems in wind turbine power systems and glucose-insulin kinetics.
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- PAR ID:
- 10582562
- Publisher / Repository:
- Institute of Electrical and Electronics Engineers Inc.
- Date Published:
- Journal Name:
- IEEE Control Systems Letters
- Volume:
- 8
- ISSN:
- 2475-1456
- Page Range / eLocation ID:
- 3159 to 3164
- Subject(s) / Keyword(s):
- Differential algebraic systems nonlinear systems identification hybrid systems.
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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