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LinearConverter

LinearConverters define a ratio between incoming and outgoing Flows.

\[ \label{eq:Linear-Transformer-Ratio} \sum_{f_{\text{in}} \in \mathcal F_{in}} \text a_{f_{\text{in}}}(\text{t}_i) \cdot p_{f_\text{in}}(\text{t}_i) = \sum_{f_{\text{out}} \in \mathcal F_{out}} \text b_{f_\text{out}}(\text{t}_i) \cdot p_{f_\text{out}}(\text{t}_i) \]

With:

  • \(\mathcal F_{in}\) and \(\mathcal F_{out}\) being the set of all incoming and outgoing flows
  • \(p_{f_\text{in}}(\text{t}_i)\) and \(p_{f_\text{out}}(\text{t}_i)\) being the flow-rate at time \(\text{t}_i\) for flow \(f_\text{in}\) and \(f_\text{out}\), respectively
  • \(\text a_{f_\text{in}}(\text{t}_i)\) and \(\text b_{f_\text{out}}(\text{t}_i)\) being the ratio of the flow-rate at time \(\text{t}_i\) for flow \(f_\text{in}\) and \(f_\text{out}\), respectively

With one incoming Flow and one outgoing Flow, this can be simplified to:

\[ \label{eq:Linear-Transformer-Ratio-simple} \text a(\text{t}_i) \cdot p_{f_\text{in}}(\text{t}_i) = p_{f_\text{out}}(\text{t}_i) \]

where \(\text a\) can be interpreted as the conversion efficiency of the LinearTransformer.

Piecewise Concersion factors

The conversion efficiency can be defined as a piecewise linear approximation. See Piecewise for more details.