Source/Sink Component Model Extension

Components which generate or consume commodities across the energy system's boundary are modeled as so-called Source/Sink components. Examples for Source components are wind turbines or natural gas imports. Examples for Sink components are electricity demands or electricity exports. The Source/Sink component model extends the Basic component model. In the following, the set of all Source and Sink components is labeled \(\mathcal{C}^\text{srcSnk}\subseteq\mathcal{C}^\text{node}\).

Specification of Operation Variables and Associated Commodities

A Source/Sink component \(\text{c}\in\mathcal{C}^\text{srcSnk}\) only has one type of basic operation variables \(\mathcal{O}^\text{c}=\{\text{op}\}\). It is associated with one commodity \(\mathcal{G}^\text{c}=\{\text{g}\}\), \(\text{g}\in\mathcal{G}\), which is the commodity that the component generates or consumes. If a capacity is defined for this component, it is related to this commodity. For example, the capacity of a wind turbine is related to the electric power which it generates at full load, e.g. in MW\(_\text{el}\).

Specification of Commodity Balance Contributions

Contributions to the commodity balance equations are modeled for a component \(\text{c}\in\mathcal{C}_\text{srcSnk}\), for \(\text{g}\in\mathcal{G}_\text{c}\), for all \(\text{l}\in\mathcal{L}_\text{c}\) and for all \(\theta\in\Theta\) as

\[ \begin{aligned} &C_{\text{c,g,l,}\theta} ~=~ \text{sign}_\text{c} \cdot o_{\omega\text{,l,}\theta}, ~~\text{where} \\ &\text{sign}^\text{c} = \begin{cases} +1 &,~\text{if c is a }\mathit{Source}\text{ component, and} \\ -1 &,~\text{if c is a }\mathit{Sink}\text{ component}~. \end{cases} \end{aligned} \]

Specification of Objective Function Contributions

Parameter	Domain	Description
\(\hat{X}^{\text{opex}_\text{O}}_{\omega\text{,l}}\)	\(\mathbb{R}_0^+\) with \(\omega \in \Omega_\text{srcSnk}, l \in \mathcal{L}_\text{c}\)	expenditures per operation of component c
\(\hat{X}^{\text{g}}_{\omega\text{,l}}\)	\(\mathbb{R}_0^+\) with \(g \in \mathcal{G}_\text{c}, \omega \in \Omega_\text{srcSnk}, l \in \mathcal{L}_\text{c}\)	expenditures per unit of commodity g
\(\hat{V}^{\text{g}}_{\omega\text{,l}}\)	\(\mathbb{R}_0^+\) with \(g \in \mathcal{G}_\text{c}, \omega \in \Omega_\text{srcSnk}, l \in \mathcal{L}_\text{c}\)	revenues per unit of commodity g

The cost factor \(\text{F}^\text{O}_{\omega\text{,l}}\) is for a Source/Sink component \(\text{c}\in\mathcal{C}^\text{srcSnk}\) given as

\[ \begin{aligned} &~~\text{F}^\text{O}_{\omega \text{,l}} = \big(\hat{X}^{\text{opex}_\text{O}}_{\omega\text{,l}} + \hat{X}^{\text{g}}_{\omega\text{,l}} + \hat{V}^{\text{g}}_{\omega\text{,l}} ~\big)~. \end{aligned} \]

Thus, operational cost as well as a cost and revenue for the associated generated or consumed commodity can be considered with the parameters \(\hat{X}^{\text{opex}_\text{O}}_{\omega\text{,l}}\in\mathbb{R}^{\geq0}\), \(\hat{X}^{\text{g}}_{\omega\text{,l}}\in\mathbb{R}^{\geq0}\) and \(\hat{V}^{\text{g}}_{\omega\text{,l}}\in\mathbb{R}^{\leq0}\) respectively.