Mathematical notation for solph

Sets

\begin{tabular}{p{2cm}p{7cm}p{3cm}}\hline
     \textbf{Symbol}            & \textbf{Description}          & \textbf{Python-type of object in set}\\\hline
     \\
     $\mathcal{E}$        & Set of all Entities                                  & Entity\\
     $\mathcal{\vec{E}}$  & Set of all weighted edges $(e_i, e_j)$               & Tuple\\
     $\mathcal{E_B}$      & Set of all edges                                     & Bus \\
     $\mathcal{E_C}$      & Set of all components                                & Component\\
     $\mathcal{E}_{I}$    & Set of components with 1 input                       & Sink \\
     $\mathcal{E}_{O}$    & Set of components with 1 output                      & Source \\
     $\mathcal{E}_{IO}$   & Components with 1 input, 1 output $i_e \neq {o_{e,n}}$ & SimpleTransformer\\
     $\mathcal{E}_{IOO}$  & Components with 1 input, 2 outputs                   & SimpleCHP\\
     $\mathcal{E}_{S}$    & Components with 1 input, 1 output  $i_e = o_{e,n}$   & Storage\\
     $\mathcal{I}_e$      & All inputs of Entity $e$                             & Dict\\
     $\mathcal{O}_e$      & All outputs of Entity $e$                            & Dict\\
     $\mathcal{T}$        & Set of timesteps                                     & List \\
     \end{tabular}

Variables

\begin{tabular}{p{2cm}p{4cm}p{2cm}p{2cm}}\hline
     \textbf{Symbol}      & \textbf{Description}                      & \textbf{Possible Set}  & \textbf{Python variable}  \\\hline
     \\
     \multicolumn{4}{l}{\textbf{LP-models}}\\
     $w_{e_1, e_2}(t)$    & Weight of Edge $(e_1, e_2)$ at  $t$             & $(e_1, e_2) \in  \mathcal{\vec{E}}$   & \verb+w[e1,e2,t]+ \\
     $l_e(t)$             & Level of  component  $e$ at $t$                  & $e \in \mathcal{E}_S$     & \verb+cap[e,t]+     \\
     $g^{pos}_{e_{o,1}}(t)$ & Positive gradient between two sequential timesteps  & $e \in \mathcal{E}_C$     & \verb+grad_pos_var[e,t]+ \\
     $g^{neg}_{e_{o,1}}(t)$ & Negative gradient between two sequential timesteps  & $e \in \mathcal{E}_C$     & \verb+grad_neg_var[e,t]+ \\
     \\
     \multicolumn{4}{l}{\textbf{Dispatch-source only}}\\
     $w^{cut}_{e,o_e}(t)$ & Curtailment of value $w_{e, o_e}(t)$             &$e \in \mathcal{E}_O$     & \verb+curtailment_var[e1,e2,t]+ \\
     \\
     \multicolumn{4}{l}{\textbf{Investment models}}\\
     $\overline{w}^{add}_{o_e}$  & Optimized extension of bound $\overline{W}_{e, o_{e,1}}$    &$e \in \mathcal{E}_C$   &\verb+add_out[e]+ \\
     $\overline{l}^{add}_e$      & Optimized extension of bound $\overline{L}_e$               &$e \in \mathcal{E}_S$   &\verb+add_cap[e]+ \\
     \\
     \multicolumn{4}{l}{\textbf{MILP-models}}\\
     $y_e(t)$             & Binary status variable of component  $e$ at $t$  &$e \in \mathcal{E}_C$     & \verb+y[e,t]+         \\
     $z^{start}_e(t)$     & Binary startup variable of component $e$ at $t$ &$e \in \mathcal{E}_C$     & \verb+z_start[e,t]+   \\
     $z^{stop}_e(t)$      & Binary shutdown variable of component $e$ at $t$ &$e \in \mathcal{E}_C$    & \verb+z_stop[e,t]+   \\
     \end{tabular}

Parameters

Parameters will be notate with uppercase.

\begin{tabular}{p{2cm}p{5cm}p{4cm}p{1.5cm}}\hline
     \textbf{Symbol}            & \textbf{Description}                            & \textbf{Python variable} & \textbf{Python type} \\\hline

     $V_e$                      & Value of Component
                                  $e \in \{\mathcal{E}_o, \mathcal{E}_I\}$        & \verb+val+  & \\
     $V^{norm}_e$                      & Normend value of component
                                  $e \in \{\mathcal{E}_o, \mathcal{E}_I\}$        & \verb+val+  & \\
     $\eta_{i_e,o_{e,n}}$       & Efficiency at conversion of input $i_e$ to
                                  $n-$th output $o_{e,n}$ of component $e$        & \verb+eta+ & list\\
     $\overline{W}_{e_1, e_2}$  & Upper bound of variable $w_{e_1, e_2}$          & \verb+out_max+ / \verb+in_max+ & list\\
     $\underline{W}_{e_1, e_2}$ & Lower bound of variable  $w_{e_1, e_2}$         & \verb+out_min+ / \verb+in_min+ & list\\
     $\overline{L}_e$           & Upper bound of variable $l_e$                   & \verb+cap_max+       & float\\
     $\underline{L}_e$          & Lower bound of variable $l_e$                   & \verb+cap_min+       & float\\
     $C^{rate}_{e_i}$           & C-rate input of component $e$                   & \verb+c_rate_in+     & float\\
     $C^{rate}_{e_o}$           & C-rate output of component $e$                  & \verb+c_rate_out+    & float\\
     $\overline{O}^{global}_e$  & Global limit for all outputs of entity $e$      & \verb+sum_out_limit+ & float\\
     $\overline{G}^{pos}_{e_{o,1}}$ & Upper bound for positive gradient of 1st output     & \verb+grad_pos+ & float\\
     $\overline{G}^{neg}_{e_{o,1}}$ & Upper bound for negative gradient of 1st output     & \verb+grad_neg+ & float\\
     $C^{loss}_e$                 & Loss of energy per timestep                     & \verb+cap_loss+       & float \\
     $T^{min,off}_e$              & Minimum down-time of component $e$               & \verb+t_min_off+      & float \\
     $T^{min,on}_e$               & Minimum up-time of component $e$               & \verb+t_min_on+      & float \\
     \\
     \multicolumn{4}{l}{\textbf{Cost/Revenue parameters}}\\
     $C_{e,i}$                    & Costs for one unit inflow of Component $e$      & \verb+input_costs+   & list\\
     $C_{e,o}$                   & Costs for one unit outflow of Component $e$     & \verb+output_costs+ \verb+opex_var+ & list\\
     $R_{e,i}$                  & Revenues for one unit inflow of Component $e$   & \verb+input_revenues+ & list \\
     $R_{e,o_n}$                & Revenues for one unit outflow of the
                                  $n$-th output of Component $e$                  & \verb+output_revenues+ & list\\
     $C^{cut}_e$    & Costs for curtailment of variable  & \verb+curtailment_costs+ & float \\
     \end{tabular}