Extreme phase sensitivity in systems with fractal isochrons

Sensitivity to initial conditions is usually associated with chaotic dynamics and strange attractors. However, even systems with (quasi)periodic dynamics can exhibit it. In this context we report on the fractal properties of the isochrons of some continuous-time asymptotically periodic systems. We define a global measure of phase sensitivity that we call the phase sensitivity coefficient and show that it is an invariant of the system related to the capacity dimension of the isochrons. Similar results are also obtained with discrete-time systems. As an illustration of the framework, we compute the phase sensitivity coefficient for popular models of bursting neurons, suggesting that some elliptic bursting neurons are characterized by isochrons of high fractal dimensions and exhibit a very sensitive (unreliable) phase response.Comment: 32 page

Applied Koopman Operator Theory for Power Systems Technology

Koopman operator is a composition operator defined for a dynamical system described by nonlinear differential or difference equation. Although the original system is nonlinear and evolves on a finite-dimensional state space, the Koopman operator itself is linear but infinite-dimensional (evolves on a function space). This linear operator captures the full information of the dynamics described by the original nonlinear system. In particular, spectral properties of the Koopman operator play a crucial role in analyzing the original system. In the first part of this paper, we review the so-called Koopman operator theory for nonlinear dynamical systems, with emphasis on modal decomposition and computation that are direct to wide applications. Then, in the second part, we present a series of applications of the Koopman operator theory to power systems technology. The applications are established as data-centric methods, namely, how to use massive quantities of data obtained numerically and experimentally, through spectral analysis of the Koopman operator: coherency identification of swings in coupled synchronous generators, precursor diagnostic of instabilities in the coupled swing dynamics, and stability assessment of power systems without any use of mathematical models. Future problems of this research direction are identified in the last concluding part of this paper.Comment: 31 pages, 11 figure

Improving HVAC Performance Through Spatiotemporal Analysis of Building Thermal Behavior

HVAC systems often make up half of the annual energy consumption of a commercial office building. Because of this, optimizing thermal factors which influence building energy efficiency is a prioritized task in the development of high performance buildings. The optimization is often achieved through a combination of effective envelope planning during building design, selection of efficient HVAC equipment during construction, and the specification of control loops and operational sequences during building commissioning. Unfortunately, these three tasks are often performed by separate practitioners with little communication between each other. Building performance decreases as a result of the original design intent being incorrectly implemented. Ideally, a building operator would like to know whether their building is comfortable, functioning normally, and running efficiently, but due to the time required in performing this assessment, often these questions may remain unanswered until a major problem arises. In building operation, an increased level of instrumentation can facilitate additional sophistication in building analysis and control, but techniques are required aggregate data into actionable information. In this work, an energy audit of a low EUI LEED silver building is performed by decomposing building data into spatiotemporal modes. These modes quickly identify spatial structures in building data and help identify influences of heat loads from the environment and internal sources such as equipment usage and occupancy. This technique has previously been used to analyze the thermal behavior of building models, but has seen only limited implementation using actual building data. Using this technique, examples of energy waste are identified including faulty equipment operation, unnecessary equipment usage, and HVAC operating conditions requiring high energy to maintain either due to improper initial commissioning or post occupancy retrofits. Through addressing the issues discovered, building energy usage is reduced by 16.5%, occupant comfort is improved. Both improvements are achieved solely through changes in building operation