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Inter-Component Constraints

Inter-component constraints are constraints that involve variables and parameters from multiple components in \(\mathcal{C}\). The inter-component constraints which are modeled within the framework are commodity balances, annual commodity inflow/outflow limits and shared potential constraints.

Commodity Balances

The constraints that provide the basic structure of the energy system are the commodity balances. They are defined for all commodities \(\text{g}\in\mathcal{G}\), at all locations in \(\text{l}\in\mathcal{L}\), if the commodity appears at that location in the model, and, there, for all periods and time steps \(\theta \in \Theta\).

The commodity appears at a location when the set

\[ \begin{aligned} &\mathcal{C}_\text{g,l} ~=~ \big\{ &&\text{c} ~\vert~ \forall~ \text{c}\in\mathcal{C}: \text{g}\in\mathcal{G}^\text{c}~\wedge~ \big(\text{l}\in\mathcal{L}_\text{c}~\lor \\ & &&(\exists~\text{l}^*\in\mathcal{L}: (\text{l},\text{l}^*)\in\mathcal{L}_\text{c}~\lor~(\text{l}^*,\text{l})\in\mathcal{L}_\text{c})\big)\big\} \end{aligned} \]

is not empty. In this case the commodity balance equation is given for all as

\[ \begin{aligned} &\sum\limits_{\text{c}~\in~\mathcal{C}_\text{g,l}} &&C_{\text{c,g,l,}\theta} ~=~ 0~. \end{aligned} \]

The definition of \(C_{\text{c,g,l,}\theta}\) is given in the component model extensions.

Shared Potential Constraints

As already explained in the Basic component model, two or more components can share a potential in an energy system. The framework ensures that for each location/connection where a shared potential is specified, the share on the maximum capacity of all components with the same identifier does not exceed 100%. Each component for which a maximum capacity is defined can be associated with the shared potential by setting the parameter \(\text{sharedPotentialID}_\text{c}=\text{sharedPotentialID}\) (default: \(\emptyset\)).

Let \(\mathcal{I}^\text{ID}\) be the set containing all shared potential IDs and let \(\mathcal{L}^\text{ID}\) be the set of locations or connections at which components compete for a maximum potential, respectively. The shared potential constraints are then given for all \(\text{i}\in\mathcal{I}^\text{ID}\) and all \(\text{l}\in\mathcal{L}^\text{ID}\) by

\[ \begin{aligned} &\sum\limits_{\text{c}~\in~\mathcal{C}^\text{i}} k_\text{c,l}/\text{K}^\text{max}_\text{c,l} ~\leq~ 1,\nonumber \\ &\text{with}~~\mathcal{C}^\text{i} = \left\{ \text{c} ~\vert~ \forall~ \text{c}\in\mathcal{C}: \text{sharedPotentialID}_\text{c}=\text{i} \right\}~. \end{aligned} \]