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Topology optimization problems typically consider a single load case or a small, discrete number of load cases; however, practical structures are often subjected to infinitely many load cases that may vary in intensity, location and/or direction (e.g. moving/rotating loads or uncertain fixed loads). The variability of these loads significantly influences the stress distribution in a structure and should be considered during the design. We propose a locally stress-constrained topology optimization formulation that considers loads with continuously varying direction to ensure structural integrity under more realistic loading conditions. The problem is solved using an Augmented Lagrangian method, and the continuous range of load directions is incorporated through a series of analytic expressions that enables the computation of the worst-case maximum stress over all possible load directions. Variable load intensity is also handled by controlling the magnitude of load basis vectors used to derive the worst-case load. Several two- and three-dimensional examples demonstrate that topology-optimized designs are extremely sensitive to loads that vary in direction. The designs generated by this formulation are safer, more reliable, and more suitable for real applications, because they consider realistic loading conditions.
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Analysis of Synchronization in Load Ensembles
While coordinated control of a large population of electric loads can provide important services to the electric grid, situations have been observed where control of load ensembles may lead to undesirable, highly nonlinear behavior such as synchronization, sustained oscillations and bifurcations. In this paper, we investigate the synchronizing tendency of thermostatically controlled loads (TCLs) under control strategies where updates are broadcast periodically for coordinating TCLs. We study the problem using a hybrid dynamical systems framework to model both the continuous and discrete dynamics of load ensembles. Analysis of eigenmodes of the underlying discrete-time system provide insights into synchronizing tendencies and rate of convergence to the synchronized state. Simulations are provided to illustrate the theory.
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- Award ID(s):
- 1810144
- PAR ID:
- 10126141
- Date Published:
- Journal Name:
- 21st Power Systems Computation Conference
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
