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Center for Nonlinear Studies |
The analysis and control of oscillatory systems, e.g., neuron oscillators, can significantly be simplified when the N-dimensional dynamics are reduced to scalar phase description models of the pertinent state variables. In this talk, we will exploit phase reduction theory to first reduce the hybrid-states model of a thermostatically controlled load (TCL) to a smooth phase model, characterized by the TCL natural frequency and its phase response curve (PRC). Phase reduction theory is a powerful tool for studying synchronization properties of oscillators that can be inferred from the PRC. Next, we will discuss the use of PRCs in evaluating the capacity and time scales of ancillary services that a population of heterogeneous TCLs can provide to support power distribution grid stability. These properties are usually limited by undesired synchronization of the TCLs caused by coupling induced by the applied control protocol. TCLs such as air conditioners, refrigerators, and water heaters consume a significant portion of electricity produced worldwide. Yet, given their ability to store thermal energy, they are increasingly used in demand response programs to balance supply and demand on the power grid. We then propose a PRC-based controller that can track an area control error signal partitioned in distinct frequency bands. In the second part of our talk, we will showcase the use of phase reduction theory in the design of spatiotemporal spiking patterns in biological neural networks. This theory and its associated control approaches hold promising applications in power systems, neural computing e.g., neuromorphic computing, biology and neuroscience.
Host: Anatoly Ziotnik