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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 by using OnOffParameters to define the on/off state of the Flow, or by using InvestParameters to change the size of the Flow from a constant to an optimization variable.

Mathematical Patterns Used

Flow formulation uses the following modeling patterns:

Implementation

Python Class: Flow

Key Parameters: - size: Flow size \(\text{P}\) (can be fixed or variable with InvestParameters) - relative_minimum, relative_maximum: Relative bounds \(\text{p}^{\text{L}}_{\text{rel}}, \text{p}^{\text{U}}_{\text{rel}}\) - effects_per_flow_hour: Operational effects (costs, emissions, etc.) - invest_parameters: Optional investment modeling (see InvestParameters) - on_off_parameters: Optional on/off operation (see OnOffParameters)

See the Flow API documentation for complete parameter list and usage examples.

See Also