Grid Modeling¶

The grid element models bidirectional utility connection with time-varying pricing for import and export.

Model Formulation¶

Decision Variables¶

For each time step $t$:

$P_{\text{import}}(t)$: Power imported from grid (kW)
$P_{\text{export}}(t)$: Power exported to grid (kW)

Parameters¶

$p_{\text{import}}(t)$: Import price ($/kWh) - from import_price sensors
$p_{\text{export}}(t)$: Export price ($/kWh) - from export_price sensors
$P_{\text{import}}^{\max}$: Max import (kW) - from import_limit config (optional)
$P_{\text{export}}^{\max}$: Max export (kW) - from export_limit config (optional)

Constraints¶

Non-negativity¶

\[ P_{\text{import}}(t) \geq 0, \quad P_{\text{export}}(t) \geq 0 \]

Power Limits¶

If configured:

\[ P_{\text{import}}(t) \leq P_{\text{import}}^{\max}, \quad P_{\text{export}}(t) \leq P_{\text{export}}^{\max} \]

Cost Contribution¶

\[ C_{\text{grid}} = \sum_{t=0}^{T-1} \left( P_{\text{import}}(t) \cdot p_{\text{import}}(t) - P_{\text{export}}(t) \cdot p_{\text{export}}(t) \right) \cdot \Delta t \]

Import is positive cost. Export is negative cost (revenue).

Physical Interpretation¶

Import: Grid supplies power when generation (solar, battery) is insufficient.

Export: Grid absorbs excess power from solar or battery discharge.

Simultaneous import/export: Optimizer won't do this - it increases cost without benefit.

Unlimited grid: If no limits configured, grid can always balance power needs.

Configuration Impact¶

Parameter	Lower Value	Higher Value
Import limit	Risk infeasibility if too low	More flexibility, higher potential cost
Export limit	Wasted solar/battery if too low	More revenue potential
Import price	Lower grid costs	Incentivizes self-consumption
Export price	Less incentive to export	More revenue from exports

Time-varying prices: Enable optimization value through time-shifting with battery.

Flat pricing: Limited optimization benefit - battery only useful for solar storage.