Systems and methods for controlling energy use in a building management system using energy budgets

1. A method for controlling power consumption of a building HVAC system, the method comprising:

using a controller of the HVAC system to calculate a deferred power usage resulting from a setpoint trajectory for a first time period;

finding a target deferred power usage for a second time period subsequent to the first time period;

finding a linear operator that transforms the deferred power usage for the first time period into the target deferred power usage; and

applying the linear operator to the setpoint trajectory for the first time period to create a setpoint trajectory for the second time period.

2. The method of claim 1 , wherein using a controller of the HVAC system to calculate the deferred power usage comprises:

observing a power usage resulting from the setpoint trajectory for the first time period;

estimating a hypothetical power usage resulting from a constant setpoint for the first time period; and

calculating the deferred power usage by subtracting the observed power usage from the estimated hypothetical power usage.

3. The method of claim 1 , wherein the first time period is a demand limiting period of a first day and the second time period is a demand limiting period of a second day subsequent to the first day.

4. The method of claim 1 , wherein the setpoint trajectory for the first time period is a temperature setpoint trajectory; and

wherein applying the linear operator to the setpoint trajectory for the first time period comprises operating the HVAC system using open loop control while a measured temperature of the building is within a predetermined temperature range.

5. The method of claim 1 , wherein finding the linear operator that transforms the deferred power usage for the first time period into the target deferred power usage comprises:

defining the linear operator as a weighted sum of multiple terms comprising at least one of an integral of the deferred power usage and a derivative of the deferred power usage;

calculating relative weights for each of the multiple terms of the linear operator by minimizing a function of a difference between the linear operator and the target deferred power usage.

6. The method of claim 5 , wherein calculating the relative weights comprises:

finding a set of output basis vectors for the multiple terms of the linear operator based on samples of the deferred power usage;

finding a set of input basis vectors for a setpoint derivative for the first time period based on samples of the setpoint derivative; and

scaling the input basis vectors so each has an average value equal to an average setpoint derivative.

7. The method of claim 1 , wherein finding the target deferred power usage for the second time period comprises:

finding a total deferred energy usage during the first time period and an energy storage period prior to the first time period;

dividing the total deferred energy usage over the first time period;

finding an average power usage during parts of the first time period that have a constant energy cost; and

performing an optimization routine to minimize the total cost of the deferred power usage for each period of constant energy cost during the first time period.

8. The method of claim 7 , wherein finding the target deferred power usage for the second time period further comprises:

transforming at least one constraint on a measured temperature of the building to a constraint on the deferred power usage;

wherein the optimization routine minimizes the total energy cost subject to the constraint on deferred power usage.

9. The method of claim 1 , further comprising:

using a capacitive model to estimate thermal energy storage in the building; and

adjusting the setpoint trajectory for the second time period using the capacitive model.

10. The method of claim 1 , wherein creating the setpoint trajectory for the second time period comprises accounting for variations in the power usage resulting from a non-constant setpoint by isolating power usage resulting from a constant setpoint.

11. A controller a building HVAC system, the controller comprising:

a processing circuit configured to calculate a deferred power usage resulting from a setpoint trajectory for a first time period;

wherein the processing circuit is configured to find a target deferred power usage for a second time period subsequent to the first time period;

wherein the processing circuit is configured to find a linear operator that transforms the deferred power usage for the first time period into the target deferred power usage; and

wherein the processing circuit is configured to apply the linear operator to the setpoint trajectory for the first time period to create a setpoint trajectory for the second time period.

12. The controller of claim 11 , wherein the deferred power usage is calculated by:

observing a power usage resulting from the setpoint trajectory for the first time period;

estimating a hypothetical power usage resulting from a constant setpoint for the first time period; and

calculating the deferred power usage by subtracting the observed power usage from the estimated hypothetical power usage.

13. The controller of claim 11 , wherein the first time period is a demand limiting period of a first day and the second time period is a demand limiting period of a second day subsequent to the first day.

14. The controller of claim 11 , wherein the setpoint trajectory is a temperature setpoint trajectory; and

wherein the linear operator is applied to the setpoint trajectory by operating the HVAC system using open loop control while a measured temperature of the building is within a predetermined temperature range.

15. The controller of claim 11 , wherein the linear operator that transforms the deferred power usage for the first time period into the target deferred power usage is found by:

defining the linear operator as a weighted sum of multiple terms comprising at least one of an integral of the deferred power usage and a derivative of the deferred power usage;

calculating relative weights for each of the multiple terms of the linear operator by minimizing a function of a difference between the linear operator and the target deferred power usage.

16. The controller of claim 15 , wherein the relative weights is calculated by:

finding a set of output basis vectors for the multiple terms of the linear operator based on samples of the deferred power usage;

finding a set of input basis vectors for a setpoint derivative for the first time period based on samples of the setpoint derivative; and

scaling the input basis vectors so each has an average value equal to an average setpoint derivative.

17. The method of claim 11 , wherein the target deferred power usage for the second time period is found by:

finding a total deferred energy usage during the first time period and an energy storage period prior to the first time period;

dividing the total deferred energy usage over the first time period;

finding an average power usage during parts of the first time period that have a constant energy cost; and

performing an optimization routine to minimize the total cost of the deferred power usage for each period of constant energy cost during the first time period.

18. The controller of claim 17 , wherein the target deferred power usage for the second time period is found by:

transforming at least one constraint on a measured temperature of the building to a constraint on the deferred power usage;

wherein the optimization routine minimizes the total energy cost subject to the constraint on deferred power usage.

19. The controller of claim 11 , wherein the processing circuit is configured to:

use a capacitive model to estimate thermal energy storage in the building; and

adjust the setpoint trajectory for the second time period using the capacitive model.

20. The controller of claim 11 , wherein the setpoint trajectory for the second time period is created by accounting for variations in the power usage resulting from a non-constant setpoint by isolating power usage resulting from a constant setpoint.