Atmospheric flows are often decomposed into balanced (low frequency) and unbalanced (high frequency) components. For a dry atmosphere, it is known that a single mode, the potential vorticity (PV), is enough to describe the balanced flow and determine its evolution. For a moist atmosphere with phase changes, on the other hand, balanced–unbalanced decompositions involve additional complexity. In this paper, we illustrate that additional balanced modes, beyond PV, arise from the moisture. To support and motivate the discussion, we consider balanced–unbalanced decompositions arising from a simplified Boussinesq numerical simulation and a hemispheric-sized channel simulation using the Weather Research and Forecasting (WRF) Model. One important role of the balanced moist modes is in the inversion principle that is used to recover the moist balanced flow: rather than traditional PV inversion that involves only the PV variable, it is PV-and- M inversion that is needed, involving M variables that describe the moist balanced modes. In examples of PV-and- M inversion, we show that one can decompose all significant atmospheric variables, including total water or water vapor, into balanced (vortical mode) and unbalanced (inertio-gravity wave) components. The moist inversion, thus, extends the traditional dry PV inversion to allow for moisture and phase changes. In addition, we illustrate that the moist balanced modes are essentially conserved quantities of the flow, and they act qualitatively as additional PV-like modes of the system that track balanced moisture.
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Multiphase Distribution Locational Marginal Prices: Approximation and Decomposition
We propose a multiphase distribution locational marginal price (DLMP) model. Compared to existing DLMP models in the literature, the proposed model has three distinctive features: i) It provides a linear approximation of relevant DLMP components which captures the global behavior of nonlinear functions; ii) it decomposes into most general components, i.e., energy, loss, congestion, voltage violations; and iii) it incorporates both wye and delta grid connections along with unbalanced loadings. The developed model is tested on a benchmark IEEE 13-bus unbalanced distribution system with the inclusion of distributed generators (DGs).
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- Award ID(s):
- 1851602
- NSF-PAR ID:
- 10079397
- Publisher / Repository:
- IEEE
- Date Published:
- ISBN:
- 978-1-5386-7703-2
- Subject(s) / Keyword(s):
- Distribution Locational Marginal Prices (DLMPs), Approximation, Distributed Generators (DGs)
- Format(s):
- Medium: X
- Location:
- Portland, OR
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/PESGM.2018.8585925
