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[Model Element Name]

Brief description of this model element's role in the optimization problem (1-2 sentences). Focus on what decisions the optimizer makes regarding this element.

Model Layer element

This page documents a Model Layer element—the building blocks of HAEO's linear programming formulation. Model Layer elements are composed by Device Layer elements through the adapter layer.

Model Formulation

This section describes the mathematical optimization model for this element. Present the formulation in standard optimization notation.

Parameters

List all parameters (inputs) required by this element's model. Distinguish between configuration-derived parameters and sensor-derived data.

Parameter Dimensions Source Description
\(p_{\text{max}}\) scalar Configuration Maximum power capacity
\(f_{t}\) \(T\) Sensor Forecasted values at each time period

Decision Variables

List all decision variables this element introduces to the optimization problem. Use consistent mathematical notation.

Variable Dimensions Domain Description
\(x_{t}\) \(T\) \(\mathbb{R}_{\geq 0}\) Description of what this variable represents
\(y_{t}\) \(T\) \(\{0, 1\}\) Binary decision variable description

Constraints

List all constraints this element contributes to the optimization problem. Present each constraint with its mathematical formulation and a brief explanation.

Constraint Name

\[ \text{mathematical formulation} \]

Brief explanation of what this constraint ensures and why it's necessary.

Cost Contribution

Describe this element's contribution to the objective function. Explain the economic interpretation.

\[ \text{Cost} = \sum_{t \in T} c_t \cdot x_t \]

Where \(c_t\) represents the cost coefficient at time \(t\).

Physical Interpretation

Provide a conceptual explanation of how the mathematical model relates to real-world behavior. Focus on intuition, not detailed calculations.

Example Scenarios

Describe typical operating scenarios and how the model captures them:

Scenario Name: Brief description of the scenario and how the model responds.

Model Assumptions

List key assumptions made in the formulation:

  • Assumption one and its implications
  • Assumption two and its implications

Limitations

Note any real-world behaviors not captured by the model:

  • Limitation one and when it matters
  • Limitation two and potential workarounds

Next Steps

Template Instructions

When using this template:

  1. Replace element.py in the source code link with the actual model filename (e.g., battery.py)
  2. Curate Next Steps cards to show 3-4 most relevant actions for readers of this page
  3. Link to related Model Layer elements and relevant user-facing documentation
  4. Do NOT enumerate which Device Layer elements use this model (that's reverse enumeration)