Flow

The flow_rate is the main optimization variable of the Flow. It's limited by the size of the Flow and relative bounds \eqref{eq:flow_rate}.

\[ \label{eq:flow_rate} \text P \cdot \text p^{\text{L}}_{\text{rel}}(\text{t}_{i}) \leq p(\text{t}_{i}) \leq \text P \cdot \text p^{\text{U}}_{\text{rel}}(\text{t}_{i}) \]

With:

• \(\text P\) being the size of the Flow
• \(p(\text{t}_{i})\) being the flow-rate at time \(\text{t}_{i}\)
• \(\text p^{\text{L}}_{\text{rel}}(\text{t}_{i})\) being the relative lower bound (typically 0)
• \(\text p^{\text{U}}_{\text{rel}}(\text{t}_{i})\) being the relative upper bound (typically 1)

With \(\text p^{\text{L}}_{\text{rel}}(\text{t}_{i}) = 0\) and \(\text p^{\text{U}}_{\text{rel}}(\text{t}_{i}) = 1\), equation \eqref{eq:flow_rate} simplifies to

\[ 0 \leq p(\text{t}_{i}) \leq \text P \]

This mathematical Formulation can be extended or changed when using OnOffParameters to define the On/Off state of the Flow, or InvestParameters, which changes the size of the Flow from a constant to an optimization variable.