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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][flixopt.elements.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][flixopt.elements.Flow] API documentation for complete parameter list and usage examples.

See Also