Model predictive control for heat transfer to fluids

1. A method for controlling a temperature of a fluid, the method comprising:

an minimizing energy required to heat the fluid, wherein the method includes a model predictive controller configured to achieve the minimizing using a objective function defined by

R opt ∝C rate [P 1 (R(i))+P 2 (R(i))], wherein:

R opt is an optimized fluid temperature set-point,

P 1 is the first power consumed by a first heating element to achieve a fluid temperature set-point (R(i)),

P 2 is the second power consumed by a second heating element to achieve the fluid temperature set-point (R(i)), and

C rate is an electricity rate;

changing the fluid temperature set-point; and heating the fluid utilizing the first heating element and the second heating element to the optimized fluid temperature set-point;

solving the objective function for the optimized fluid temperature set-point with the changed fluid temperature set-point;

repeating the changing and the solving until the minimizing is achieved;

adjusting at least one of the first power consumed by a first heating element or the second power consumed by a second heating element so that the fluid attains the optimized fluid temperature set-point; and heating the fluid utilizing the first heating element and the second heating element to the optimized fluid temperature set-point.

2. The method of claim 1 , wherein the objective function is also a function of a future fluid usage prediction, and the future fluid prediction is at least partially determined by historical fluid usage data.

3. The method of claim 2 , wherein the historical fluid usage data are determined by

defining a first time period (T);

defining a second time period (t) by dividing T by an integer value (N) such that T is divided into N equal and consecutive time intervals (t n ), wherein T restarts and repeats upon completion of the last t n ; and

collecting consecutive measurements of actual fluid usage data (F n ) for each consecutive t n as the historical usage data.

4. The method of claim 3 , further comprising storing on a data storage medium no more than N sets of consecutive measurements.

5. The method of claim 4 , wherein the historical fluid usage data comprises a measurement of least one of a fluid flow or a fluid temperature.

6. The method of claim 1 , wherein the first heating element and the second heating element comprise at least one of a resistive heating element or a heat pump.

7. The method of claim 1 , wherein the fluid is a liquid.

8. The method of claim 7 , wherein the liquid is water.

9. The method of claim 1 , wherein the optimized fluid temperature set-point ranges from about 0° F. to about 500° F.

10. A method for controlling a temperature of water utilizing a resistive heating element and a heat pump, the method comprising:

minimizing the sum of the first power consumed by a heat pump and a second power consumed by a resistive heating element, wherein the minimizing is achieved using an objective function defined by

R opt ∝C rate [P hp (R(i))+P elec (R(i))], wherein:

R opt is an optimized water temperature set-point for the water,

P 1 is the first power consumed by a heat pump to achieve a water temperature set-point (R(i)),

P 2 is the second power consumed by a resistive heating element to achieve the water temperature set-point (R(i)), and

C rate is an electricity rate;

changing the water temperature set-point;

solving the objective function for the optimized water temperature set-point with the changed water temperature set-point;

repeating the changing and the solving until the minimization is achieved; and

adjusting at least one of the resistive heating element or the heat pump to heat the water to the optimized water temperature set-point.

11. The method of claim 10 , wherein the objective function is also a function of a future water volume usage prediction, and the future water volume usage prediction is at least partially determined by historical water volume usage data.

12. The method of claim 11 , wherein the historical water usage data are determined by defining a first time period;

defining a second time period by dividing the first time period by an integer (N);

defining a third time period by dividing the second time period by an integer (I) to create N*I consecutive time intervals, wherein each time interval is about equal to the third time period; and

collecting consecutive measurements of actual water flow and water temperature data for each consecutive time interval as the historical usage data.

13. The method of claim 12 , wherein the first time period equals about 14 days, the second time period equals about 1 day for an N of about 14, and the third time period is about 30 minutes for an I of about 48.