Book contents
- Frontmatter
- Dedication
- Contents
- Preface and Acknowledgments
- Notation
- 1 Introduction
- 2 Preliminaries
- 3 Static Systems: Probabilistic Input Uncertainty
- 4 Static Systems: Probabilistic Structural Uncertainty
- 5 Discrete-Time Systems: Probabilistic Input Uncertainty
- 6 Continuous-Time Systems: Probabilistic Input Uncertainty
- 7 Static Systems: Set-Theoretic Input Uncertainty
- 8 Discrete-Time Systems: Set-Theoretic Input Uncertainty
- 9 Continuous-Time Systems: Set-Theoretic Input Uncertainty
- Appendix A Mathematical Background
- Appendix B Power Flow Modeling
- References
- Index
7 - Static Systems: Set-Theoretic Input Uncertainty
Published online by Cambridge University Press: 17 January 2022
- Frontmatter
- Dedication
- Contents
- Preface and Acknowledgments
- Notation
- 1 Introduction
- 2 Preliminaries
- 3 Static Systems: Probabilistic Input Uncertainty
- 4 Static Systems: Probabilistic Structural Uncertainty
- 5 Discrete-Time Systems: Probabilistic Input Uncertainty
- 6 Continuous-Time Systems: Probabilistic Input Uncertainty
- 7 Static Systems: Set-Theoretic Input Uncertainty
- 8 Discrete-Time Systems: Set-Theoretic Input Uncertainty
- 9 Continuous-Time Systems: Set-Theoretic Input Uncertainty
- Appendix A Mathematical Background
- Appendix B Power Flow Modeling
- References
- Index
Summary
This chapter covers the analysis of static systems under set-theoretic input uncertainty. In the first part of the chapter, we assume that the input belongs to an ellipsoid and analyze both linear and nonlinear systems. For the linear case, we provide techniques to exactly characterize the set containing all possible values that the state can take. For the nonlinear case, we again resort to linearization to approximately characterize the set containing all possible values that the state can take. The second part of the chapter considers linear and nonlinear systems when the input is known to belong to a zonotope. For the linear case, we are able to compute the exact set containing all possible values the state can take, whereas for the nonlinear case, we settle for an approximation thereof obtained via linearization. The techniques developed are utilized to analyze the power flow problem under uncertain active power injections.
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- Large-Scale System Analysis Under UncertaintyWith Electric Power Applications, pp. 202 - 236Publisher: Cambridge University PressPrint publication year: 2022