Load Modeling

HAEO supports two load types: constant (fixed power) and forecast (time-varying power).

Constant Load

Decision Variables

None - constant parameter.

Parameters

• \(P_{\text{constant}}\): Fixed power consumption (kW) - from power config

Constraints

\[ P_{\text{load}}(t) = P_{\text{constant}} \quad \forall t \]

Load power is fixed at all time steps.

Physical Interpretation

Represents baseline consumption: refrigerators, network equipment, standby power, always-on devices.

Forecast Load

Decision Variables

None - follows forecast parameter.

Parameters

• \(P_{\text{forecast}}(t)\): Forecasted power at time \(t\) (kW) - from forecast sensors

Constraints

\[ P_{\text{load}}(t) = P_{\text{forecast}}(t) \quad \forall t \]

Load follows forecast exactly.

Physical Interpretation

Represents time-varying consumption: HVAC, cooking, EV charging, occupancy-based loads.

Forecast accuracy directly impacts optimization quality.

Combined Usage

Typical systems use both load types: constant entries capture the baseline demand and forecast entries model time-varying usage. Total load at the balancing node equals the sum of all connected loads.

Configuration Impact

Load Type	Accuracy Needed	Best For
Constant	Rough estimate	Simple setup, stable consumption
Forecast	High accuracy	Variable loads, optimization value

Overestimating load: May cause infeasibility if supply can't meet.

Underestimating load: Real system may import more than optimized.

Related Documentation

• Load Configuration
• Forecast Load Configuration
• Modeling Overview
• Forecasts Guide