Thermal Model of the Home

The model represents the house as a dynamic system that exchanges heat with its environment. It is simple enough to be identifiable, yet rich enough to be useful.

Model Structure

The house is modeled as a lumped thermal system (a first-order RC equivalent circuit) with four key components:

Indoor Air Temperature: The state variable we aim to control.
Effective Thermal Mass: Represents the ability of walls and furniture to store heat.
Heat Transfer to Outside: Describes how quickly the home loses heat.
Heating System Input: The power injected by the boiler.

Governing Equation (Conceptual)

The change in indoor temperature over time depends on the balance between heat input from the system and heat losses to the environment, modulated by the home's thermal inertia. The exact equations are intentionally abstracted to allow for future model extensibility.

Known Limitations

Spatial temperature gradients, occupancy effects, and solar gains are aggregated. These are accepted trade-offs for model stability and identifiability.