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The focus of this paper is on the design of input shapers for systems with uncertainties in the parameters of the vibratory modes which need to be attenuated. A probabilistic framework is proposed for the design of the robust input shaper, when the uncertain modal parameters are characterized by probability density functions. A convex chance constrained optimization problem is posed to determine the parameters of input shapers (time-delay filter) which can accommodate the users acceptable risk levels for a prescribed residual energy threshold. Robust input shapers are developed for various compact support distributions to illustrate the ability of the proposed formulation to synthesize input shapers which can satisfy a residual energy threshold with a given risk level. This problem formulation can conceivably reduce the conservative nature of worst case controllers which have to ensure that all realizations of the uncertain system have to satisfy a prescribed performance index. The chance constrained input shaper is designed for a spring-mass-dashpot system with three different distributions for the uncertain spring stiffness. Results provide encouragement for the extension of the proposed approach to multi-dimensional and multi-model uncertainties.
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Data-driven decision making in power systems with probabilistic guarantees: Theory and applications of chance-constrained optimization
Uncertainties from deepening penetration of renewable energy resources have posed critical challenges to the secure and reliable operations of future electric grids. Among various approaches for decision making in uncertain environments, this paper focuses on chance-constrained optimization, which provides explicit probabilistic guarantees on the feasibility of optimal solutions. Although quite a few methods have been proposed to solve chance-constrained optimization problems, there is a lack of comprehensive review and comparative analysis of the proposed methods. We first review three categories of existing methods to chance-constrained optimization: (1) scenario approach; (2) sample average approximation; and (3) robust optimization based methods. Data-driven methods, which are not constrained by any particular distributions of the underlying uncertainties, are of particular interest. Key results of the analytical reformulation approach for specific distributions are briefly discussed. We then provide a comprehensive review on the applications of chance-constrained optimization in power systems. Finally, this paper provides a critical comparison of existing methods based on numerical simulations, which are conducted on standard power system test cases.
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- Award ID(s):
- 1636772
- PAR ID:
- 10110826
- Date Published:
- Journal Name:
- Annual reviews in control
- Volume:
- 47
- ISSN:
- 1367-5788
- Page Range / eLocation ID:
- 341-363
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/https://doi.org/10.1016/j.arcontrol.2019.05.005
