Thermodynamic model generation and implementation using observed HVAC and/or enclosure characteristics
Techniques for determining and using a thermodynamic model that characterizes a thermodynamic response of an enclosure conditioned by an HVAC system are disclosed. To determine a thermodynamic model, temperature information when the HVAC system operates in a first state may first be received. A response interval may then be determined where the response interval indicates an estimated time between when the HVAC system begins operating in the first state and when the temperature within the enclosure begins to change in a direction associated with the first state. Weighting factors corresponding to basis functions may then be determined, where the weighted basis functions characterize the temperature trajectory of the enclosure in response to the HVAC system operating in the first state. The basis functions may include a first basis function that is evaluated from a time that the HVAC system begins operating in the first state until a time when the response interval ends, and a second basis function that is evaluated beginning at the time when the response interval ends.
1. A method of determining a thermodynamic model of an enclosure associated with a heating, ventilation, and air conditioning (HVAC) system, the method comprising:
receiving temperature information for a period of time during which the HVAC system operates in a first state, the temperature information defining a temperature trajectory of the enclosure during the period of time;
determining, by a computer system, a response interval that indicates an estimated time between when the HVAC system begins operating in the first state and when the temperature within the enclosure begins to change in a direction associated with the first state;
determining, by the computer system and using the temperature information, a plurality of weighting factors corresponding to a respective plurality of basis functions, the weighted combination of basis functions forming the thermodynamic model and characterizing the temperature trajectory of the enclosure in response to the HVAC system operating in the first state, wherein the plurality of basis functions comprises:
a first basis function that is evaluated from a time that the HVAC system begins operating in the first state until a time when the response interval ends, wherein the first basis function represents an effect of a previous HVAC cycle on a current HVAC cycle; and
a second basis function that is evaluated beginning at the time when the response interval ends until the HVAC stops operating in the first state, wherein the second basis function represents an effect of the HVAC system operating in the first state during a current HVAC cycle and includes an effectiveness factor that represents an effectiveness of the HVAC system with respect to differences in a temperature outside of the enclosure and a temperature inside of the enclosure; and
causing, by the computer system, the HVAC system to operate in the first state using the thermodynamic model of the enclosure in response to the HVAC system operating in the first state.
2. The method of claim 1 , wherein the response interval is empirically determined based on previous HVAC cycles of the HVAC system operating in the first state.
3. The method of claim 1 , wherein the response interval is empirically determined based on data received from other enclosures.
4. The method of claim 1 , wherein the plurality of basis functions further comprises a third basis function that represents an effect of sunlight on the enclosure.
5. The method of claim 4 , wherein the third basis function is evaluated during the response interval and after the response interval ends.
6. The method of claim 4 , wherein:
the first state comprises a drift state wherein the HVAC system does not actively heat or cool the enclosure; and
the plurality of basis functions further comprises a fourth basis function that represents an effect of a temperature differential between an outdoor temperature and an indoor temperature.
7. A thermostat for controlling operations of an HVAC system in an enclosure, the thermostat comprising:
HVAC control circuitry operable to actuate one or more elements of the HVAC system;
one or more sensors for measuring environmental characteristics associated with the enclosure; and
one or more processors coupled to the HVAC control circuitry and the one or more sensors, the one or more processors operable to cause the thermostat to perform operations including:
receiving, via the one or more sensors, temperature information for a period of time during which the HVAC system operates in a first state, the temperature information defining a temperature trajectory of the enclosure during the period of time;
determining a response interval that indicates an estimated time between when the HVAC system begins operating in the first state and when the temperature within the enclosure begins to change in a direction associated with the first state;
determining, using the temperature information, a plurality of weighting factors corresponding to a respective plurality of basis functions, the weighted combination of basis functions forming the thermodynamic model and characterizing the temperature trajectory of the enclosure in response to the HVAC system operating in the first state, wherein the plurality of basis functions comprises:
a first basis function that is evaluated from a time that the HVAC system begins operating in the first state until a time when the response interval ends, wherein the first basis function represents an effect of a previous HVAC cycle on a current HVAC cycle; and
a second basis function that is evaluated beginning at the time when the response interval ends until the HVAC stops operating in the first state, wherein the second basis function represents an effect of the HVAC system operating in the first state during a current HVAC cycle and includes an effectiveness factor that represents an effectiveness of the HVAC system with respect to differences in a temperature outside of the enclosure and a temperature inside of the enclosure; and
causing, by the computer system, the HVAC system to operate in the first state using the thermodynamic model of the enclosure in response to the HVAC system operating in the first state.
8. The thermostat of claim 7 , further comprising wireless communication circuitry that sends one or more of the plurality of weighting factors and/or an HVAC effectiveness factor to a thermostat management server.
9. The thermostat of claim 8 , wherein the wireless communication circuitry further sends a length of the response interval to the thermostat management server.
10. The thermostat of claim 7 , wherein the one or more processors are further operable to cause the thermostat to perform operations including characterizing an aspect of the HVAC system based on one or more of the plurality of weighting factors and/or an HVAC effectiveness factor.
11. The thermostat of claim 10 , further comprising a user interface that provides an indication associated with the aspect of the HVAC system characterized by the one or more processors.
12. The thermostat of claim 7 , wherein the plurality of weighting factors are determined using a local time-of-day and information provided by the one or more sensors.
13. A tangible, non-transitory, computer-readable storage medium including instructions that, when executed by one or more processors, cause the one or more processors to perform operations including:
receiving temperature information for a period of time during which the HVAC system operates in a first state, the temperature information defining a temperature trajectory of the enclosure during the period of time;
determining a response interval that indicates an estimated time between when the HVAC system begins operating in the first state and when the temperature within the enclosure begins to change in a direction associated with the first state;
determining, using the temperature information, a plurality of weighting factors corresponding to a respective plurality of basis functions, the weighted combination of basis functions forming the thermodynamic model and characterizing the temperature trajectory of the enclosure in response to the HVAC system operating in the first state, wherein the plurality of basis functions comprises:
a first basis function that is evaluated from a time that the HVAC system begins operating in the first state until a time when the response interval ends, wherein the first basis function represents an effect of a previous HVAC cycle on a current HVAC cycle; and
a second basis function that is evaluated beginning at the time when the response interval ends until the HVAC stops operating in the first state, wherein the second basis function represents an effect of the HVAC system operating in the first state during a current HVAC cycle and includes an effectiveness factor that represents an effectiveness of the HVAC system with respect to differences in a temperature outside of the enclosure and a temperature inside of the enclosure; and
causing, by the computer system, the HVAC system to operate in the first state using the thermodynamic model of the enclosure in response to the HVAC system operating in the first state.
14. The storage medium of claim 13 , wherein each of the plurality of basis functions characterizes at least a portion of the temperature trajectory.
15. The storage medium of claim 13 , wherein the effectiveness factor is higher for small differences in outside and inside temperature and lower for large differences in outside and inside temperature.
16. The storage medium of claim 13 , wherein the effectiveness factor is determined empirically based on previous HVAC cycles.
17. The storage medium of claim 13 , wherein the operations further include:
identifying a demand-response event period;
predicting a thermodynamic behavior of the enclosure during at least a portion of the demand-response event period based on the weighting factors and the basis functions; and
controlling the HVAC system during the demand-response event period based at least in part on the predicted thermodynamic behavior of the enclosure.