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notation.tex
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notation.tex
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\section*{Notation}
\addcontentsline{toc}{section}{Notation}
\begin{tabular}{ l l }
Sets & \\
$ \cG $ & Generators \\
$ \cD $ & Demand Nodes \\
$ \cB $ & Buses \\
$ \cS $ & Scenarios \\
$ \cN $ & Nodes of Scenario Tree\\
$\rho \left( n \right) $ & Predecessor of node $ n \in \cN $ \\
$ \cV $ & Vertices $ = \cG \cup \cD \cup \cB $ \\
$ \cE $ & Edges, $ \cE \subseteq (\cV \times \cV )$ \\
$ \cT $ & Time stages\\
& \\
Parameters & \\
$X_e $ & Reactance of edge $e \in \cE$ \\
$ \overline{P}_i $ & Upper bounds on power produced at $ i \in \cG $ \\
$ \underline{P}_i $ & Lower bounds on power produced at $ i \in \cG $ \\
$ U_{e} $ & Nominal Capacity of line $e \in \cE$ \\
$ R_{en} $ & Effective capacity of $e \in \cE$ at node $n \in \cN$ \\
& \\
Variables & \\
$f_{ijn}$ & Flow in direction $(i,j) \in \cE$ at node $ n \in \cN $ \\
$p_{in} $ & Power at generator $i \in \cG$ at node $n \in \cN$ \\
$\theta_{in} $ & Phase angle at vertex $i \in \cV$ at node $n \in \cN$ \\
$d_{in} $ & Power at vertex $i \in \cV$ at node $n \in \cN$ \\
$z_{ijn} $ & $ \mbox{if edge } (i,j) \in \cE \mbox{ is available at node } n \in \cN $ \\
$y_{in} $ & $ \mbox{if generator } i \in \cG \mbox{ is on at node } n \in \cN $ \\
\end{tabular}