Adaptive Nonlinear Optimization Methodology For Installed Capacity Decisions In Distributed Energy/Cooling Heat And Power Applications.

Evaluation of potential cooling, heating and power (CHP) applications requires an assessment of the operations and economics of a particular system in meeting the electric and thermal demands of a specific end-use facility. Given the electrical and thermal load behavior of a facility, the tariff structure for grid-supplied electricity, the price of primary fuel (e.g., natural gas), the operating strategy and characteristics of the CHP system, and an assumed set of installed CHP system capacities (e.g., installed capacity of prime mover and absorption chiller), one can determine the cost of such a system as compared to reliance solely on traditional, grid-supplied electricity and on-site boilers. It has been shown previously in the literature that net present value cost savings of CHP systems exhibit a concave behavior with respect to installed capacity, and thus, an optimum size exists for a given application. To date, current capacity selection techniques either utilize simple enumeration of candidate choices, heuristic multipliers of the base or peak demand, or apply optimization algorithms on aggregated or averaged demand data. None of these approaches are likely to result in economic optimality. This research utilizes hour-by-hour operation simulation of CHP systems to calculate life-cycle net present value (NPV) savings. Based on maximizing an NPV cost savings objective function, a nonlinear optimization algorithm is used to determine economically optimal CHP system equipment capacities. This research contributes an improved mechanism that will identify economic optimum capacities for CHP system equipment, thereby producing optimal cost benefits and potentially avoiding economic losses

Coronal Heating as Determined by the Solar Flare Frequency Distribution Obtained by Aggregating Case Studies

Flare frequency distributions represent a key approach to addressing one of the largest problems in solar and stellar physics: determining the mechanism that counter-intuitively heats coronae to temperatures that are orders of magnitude hotter than the corresponding photospheres. It is widely accepted that the magnetic field is responsible for the heating, but there are two competing mechanisms that could explain it: nanoflares or Alfv\'en waves. To date, neither can be directly observed. Nanoflares are, by definition, extremely small, but their aggregate energy release could represent a substantial heating mechanism, presuming they are sufficiently abundant. One way to test this presumption is via the flare frequency distribution, which describes how often flares of various energies occur. If the slope of the power law fitting the flare frequency distribution is above a critical threshold, $\alpha=2$ as established in prior literature, then there should be a sufficient abundance of nanoflares to explain coronal heating. We performed $>$600 case studies of solar flares, made possible by an unprecedented number of data analysts via three semesters of an undergraduate physics laboratory course. This allowed us to include two crucial, but nontrivial, analysis methods: pre-flare baseline subtraction and computation of the flare energy, which requires determining flare start and stop times. We aggregated the results of these analyses into a statistical study to determine that $\alpha = 1.63 \pm 0.03$. This is below the critical threshold, suggesting that Alfv\'en waves are an important driver of coronal heating.Comment: 1,002 authors, 14 pages, 4 figures, 3 tables, published by The Astrophysical Journal on 2023-05-09, volume 948, page 7