Generating and implementing thermodynamic models of a structure

1. A thermostat for controlling a heating, ventilation, and air conditioning (HVAC) system in a structure, the thermostat comprising:

HVAC control circuitry operable to actuate one or more elements of the HVAC system;

a communications component;

one or more sensors for measuring characteristics of the structure; and

a processor coupled to the HVAC control circuitry and the one or more sensors that is configured to perform operations including:

storing temperature information from the one or more sensors and time stamps for the temperature information;

causing the HVAC control circuitry to actuate an HVAC function to transition a temperature inside the structure from a first temperature to a second temperature;

populating a thermodynamic model that predicts a temperature trajectory of the temperature of the air inside the structure in response to actuation of the HVAC function, wherein:

the thermodynamic model comprises a plurality of basis functions that together characterize the temperature trajectory of the air inside the structure in response to the actuation of the HVAC function;

the thermodynamic model comprises a plurality of weighting factors corresponding to the plurality of basis functions; and

the plurality of basis functions comprises a basis function comprising an expression that models an effect of a rate of temperature change that was occurring in the structure prior to actuating the HVAC function and which exponentially decays from a time that the HVAC function is actuated until a time when steady-state activity overcomes early-cycle activity;

fitting the plurality of weighting factors of the thermodynamic model to a portion of the temperature information and time stamps for the temperature information corresponding to times when the HVAC function was actuated; and

predicting the temperature trajectory of the air inside the structure using the thermodynamic model.

2. The thermostat of claim 1 , wherein the processor is further configured to create the thermodynamic model where the plurality of basis functions further comprises a basis function for a current stage effect component that characterizes an effect that a current stage has on the temperature trajectory of the air inside the structure.

3. The thermostat of claim 2 , wherein the processor is further configured to create the thermodynamic model where the current stage effect component begins at zero, reaches a maximum after a certain period of time, and diminishes thereafter.

4. The thermostat of claim 1 , wherein the processor is further configured to fit the plurality of weighting factors using weather forecast and a clock signal received through the communications component.

5. The thermostat of claim 1 , wherein the processor is further configured to cause the HVAC control circuitry to actuate the HVAC function by switching the HVAC function from a first state characterized by a relatively low energy consumption, to a second state characterized by a relatively high energy consumption.

6. The thermostat of claim 1 , wherein the expression used by the processor that models the effect of the rate of temperature change that was occurring in the structure prior to actuating the HVAC function comprises:

(

1

-

1

1

+

e

-

γ

⁡

(

t

cycle

-

t

steady

-

state

)

)

·

r

;

wherein r represents the rate of temperature change that was occurring in the structure prior to actuating the HVAC function;

wherein γ represents a constant value;

wherein t cycle represent a time elapsed since actuating the HVAC function; and

wherein t steady-state represents a time.

7. The thermostat of claim 6 , wherein the processor is further configured to create the thermodynamic model where the current stage effect component begins at zero, reaches a maximum at 2×t steady-state , and diminishes thereafter.

8. The thermostat of claim 1 , wherein the plurality of basis functions further comprises a basis function characterizing an effect of a difference between an outdoor temperature and an indoor temperature.

9. The thermostat of claim 1 , wherein the operations the processor is configured to perform further include estimating a temperature of the structure by:

setting an initial temperature of the structure to an indoor temperature at a first time; and

for each of a plurality of times after the first time, determining the temperature of the structure as a weighted combination of a previous indoor temperature and a previous outdoor temperature.

10. The thermostat of claim 1 , the wherein the plurality of basis functions further comprises a basis function characterizing an effect of a difference in a temperature of the structure and an indoor temperature.

11. The thermostat of claim 1 , wherein the plurality of basis functions further comprises a basis function characterizing an effect of a time-of-day approximating an effect of sunlight.

12. The thermostat of claim 11 , wherein the basis function characterizing the effect of the time-of-day approximating the effect of sunlight comprises a sinusoidal term having a period of 24 hours.

13. The thermostat of claim 1 , wherein the plurality of basis functions further comprises a basis function comprising a constant representing energy changes not affected by environmental factors.

14. The thermostat of claim 1 , wherein the operations the processor is configured to perform further include:

using a required level of specificity for the thermodynamic model.

15. The thermostat of claim 14 , wherein the operations the processor is configured to perform further include:

searching a plurality of existing thermodynamic models for one or more candidate thermodynamic models that satisfy the required level of specificity for the thermodynamic model.

16. The thermostat of claim 15 , wherein creating the thermodynamic model that predicts the temperature trajectory of the air inside the structure in response to the actuation of the HVAC function comprises:

failing to identify one or more candidate models; and

in response to failing to identify the one or more candidate models, generating the thermodynamic model.

17. The thermostat of claim 1 , wherein the processor is configured to predict the temperature trajectory of the air inside the structure by calculating a time-wise series of temperature changes beginning at a current indoor temperature.