Optimizing operations of multiple air-conditioning units

• US 10,161,649 B2
• Filed: 06/20/2014
• Issued: 12/25/2018
• Est. Priority Date: 06/20/2014
• Status: Active Grant

• Current Assignee: Mitsubishi Electric Research Laboratories, Inc. (Mitsubishi Electric Corporation)
• Original Assignee: Mitsubishi Electric Research Laboratories, Inc. (Mitsubishi Electric Corporation)
• Inventors: Raghunathan, Arvind U, Nikovski, Daniel Nikolaev
• Primary Examiner(s): Barnes-Bullock, Crystal J
• Application Number:
  US14/310,274
• Publication Number:
  US 20150370271A1
• Time in Patent Office: 1,649 Days
• Field of Search: 703 1
• CPC Class Codes: B60H 1/00807 the input being a specific way of measuring or calculating an air or coolant temperature
• CPC Class Codes: B60H 1/00814 Control systems or circuits characterised by their output, for controlling particular components of the heating, cooling or ventilating installation
• CPC Class Codes: B60H 1/00821 the components being ventilating, air admitting or air distributing devices
• CPC Class Codes: F24F 11/30 for purposes related to the operation of the system, e.g. for safety or monitoring
• CPC Class Codes: F24F 11/46 Improving electric energy efficiency or saving
• CPC Class Codes: F24F 11/54 using one central controller connected to several sub-controllers
• CPC Class Codes: F24F 11/58 using Internet communication
• CPC Class Codes: F24F 11/62 characterised by the type of control or by internal processing, e.g. using fuzzy logic, adaptive control or estimation of values
• CPC Class Codes: F24F 11/63 Electronic processing
• CPC Class Codes: F25B 13/00 Compression machines, plants or systems, with reversible cycle defrosting cycles F25B47/02
• CPC Class Codes: F25B 2600/01 Timing
• CPC Class Codes: F25B 2600/0251 with on-off operation
• CPC Class Codes: F25B 49/022 Compressor control arrangements
• CPC Class Codes: G05B 15/02 electric
• CPC Class Codes: G05D 23/19 characterised by the use of electric means G05D23/1393 takes precedence
• CPC Class Codes: G05D 23/193 sensing the temperaure in different places in thermal relationship with one or more spaces
• CPC Class Codes: G05D 23/1932 to control the temperature of a plurality of spaces
• CPC Class Codes: G05D 23/1934 each space being provided with one sensor acting on one or more control means
• CPC Class Codes: Y02T 10/88 Optimized components or subsystems, e.g. lighting, actively controlled glasses

Abstract

A method operates a set of heating, ventilation and air-conditioning (HVAC) units by optimizing jointly operations of the set of HVAC units subject to constraints to determine times of switching each HVAC unit ON and OFF and by controlling each HVAC unit according to the corresponding times of switching. The operation of each HVAC unit is represented by a continuous function. The constraints include a complementarity constraint for each HVAC unit, such that the complementarity constraint for the HVAC unit defines a discontinuity of the operation of the HVAC unit at corresponding times of switching.

Claims

1. A method for operating a set of heating, ventilation and air-conditioning (HVAC) units, comprising:

optimizing jointly operations of the set of HVAC units subject to constraints to determine time instants of switching each HVAC unit ON and OFF,

wherein the operation of switching ON each HVAC unit at each time instant is represented by a continuous function and a set of constraints for switching ON, such that the continuous function for switching ON is a deviation of a current time instant from the time instant of switching ON, and the set of the constraints include a difference of multipliers that are equal to the continuous function, and complementarity constraints between the multiplier variables and a state variable modeling of the switching ON for each HVAC unit;

wherein the operation of switching OFF of each HVAC unit at each time instant is represented by a continuous function and a set of constraints for switching OFF, such that the continuous function for switching OFF is a deviation of a current time instant from the time instant of switching OFF, and the set of constraints include a difference of multipliers that are equal to the continuous function, and complementarity constraints between multiplier variables and a state variable modeling of the switching OFF for each HVAC unit; and

controlling each HVAC unit according to the corresponding times of switching, wherein the steps are performed in a processor.

2. The method of claim 1, wherein the complementarity constraint defines that the operation of HVAC unit includes one switching from OFF to ON state and one switching from ON to OFF state within a period of time.

3. The method of claim 2, wherein the period of time is twenty four hours.

4. The method of claim 1, wherein the set of HVAC units are configured to operate within a building, further comprising:

modeling the building as a network of nodes connected by edges to produce a model of the building, wherein the nodes represent rooms and the edges represent walls between the rooms;

determining, using the model of the building, a model for operating the set of HVAC units including differential equations of dynamics of one or combination of temperatures and humidity in the rooms of the building; and

optimizing the operation of the set of HVAC units according to the model of the operation, wherein parameters of optimization include one or combination of a comfort of occupants in the building and the energy consumption of the set of HVAC units.

5. The method of claim 4, further comprising:

determining the model for the operation of the HVAC system for a period of time using one or combination of a weather forecast for the period of time, a heat load forecast for each HVAC unit for the period of time, an occupancy heat load forecast for each room for the period of time, and comfort requirements for each room for the period of time.

6. The method of claim 1, further comprising:

modeling the ON and OFF operations of the HVAC units using the complementarity constraints;

formulating an optimal control problem jointly optimizing the ON and OFF operations of the set of HVAC units;

discretizing the optimal control problem using an integration technique to produce a finite dimensional optimization problem; and

solving iteratively the finite dimensional optimization problem using a sparse linear algebra until convergence.

7. The method of claim 1, wherein the continuous function includes

−

(t−

τ

₁)−

λ

₁(t)+v₁(t)=0,

wherein τ

₁is a time to switch the HVAC unit ON, t is defined as the current time instant, and λ

₁(t), v₁(t) are multipliers for lower and upper bound constraints, wherein the complementarity constraint for the HVAC unit includes

z₁(t)≥

0⊥

λ

₁(t)≥

0

z₁(t)≤

1⊥

v₁(t)≥

0

wherein a variable z₁(t) models a state of the HVAC unit, the variable z₁(t) is one after the HVAC unit is ON and zero before the HVAC unit is ON, wherein the continuous function includes

−

(t−

τ

₂)−

λ

₂(t)+v₂(t)=0,

wherein τ

₂ is a time to switch the HVAC unit OFF, λ

₂(t), v₂(t) are Lagrange multipliers for the lower and the upper bound constraints, wherein the complementarity constraint for the HVAC unit includes

z₂(t)≥

0⊥

λ

₂(t)≥

0

z₂(t)≤

1⊥

v₂(t)≥

0,

wherein a variable z₂(t) models the state of the HVAC unit and equals one after the HVAC unit is switched OFF at the switch OFF time and equals zero before the switch OFF time, wherein the continuous function includes

z(t)=z₁(t)−

z₂(t),

wherein z(t) is a variable that equals one when the state of the HVAC unit is ON and equals zero when the state of the HVAC unit is OFF.

8. The method of claim 7, wherein the complementarity constraint includes

z_1,i(t)≥

z_2,i(t),

wherein a variable z_1,i(t) models a state of an i-th HVAC unit and equals one after the i-th HVAC unit is switched ON at the switch ON time of the i-th HVAC unit and equals zero before the switch ON time of the i-th HVAC unit, and wherein a variable z_2,i(t) models the state of an i-th HVAC unit and equals one after the i-th HVAC unit is switched OFF at the switch OFF time of the i-th HVAC unit and equals zero before the switch OFF time of the i-th HVAC unit.

9. The method of claim 8, wherein the complementarity constraint includes

10. The method of claim 1, wherein the continuous function includes

−

(t−

τ

₁)(τ

₂−

t)−

λ

(t)+v(t)=0,

wherein τ

₁ is a switch ON time of switching a HVAC unit ON, t is defined as the current time instant τ

₂ is a switch OFF time of switching the HVAC unit OFF, λ

(t), v(t) are Lagrange multipliers for lower and upper bound constraints, wherein the complementarity constraint for each HVAC unit includes

z(t)≥

0⊥

λ

(t)≥

0

z(t)≤

1⊥

v(t)≥

0,

wherein z(t) is a variable that equals one when the state of the HVAC unit is ON and equals zero when the state of the HVAC unit is OFF.

11. The method of claim 10, wherein the complementarity constraint includes

12. The method of claim 1, further comprising:

optimizing the operations of the HVAC units using iterative relaxation of the complementarity constraint.

13. The method of claim 12, wherein the complementarity constraint is relaxed according to a relaxation parameter, and wherein, for each iteration of the iterative relaxation, the relaxation parameter is reduced monotonically.

14. The method of claim 12, wherein a relaxation parameter is modified only when the complementarity constraint for a current value of the relaxation parameter is violated.

15. The method of claim 12, further comprising:

optimizing the operations of the HVAC units using an interior point method.

16. The method of claim 12, further comprising:

reformulating the complementarity constraint as an inequality, such that a product of the state variable modeling of the switching ON for each HVAC unit and the multiplier corresponding to its lower bound of zero or a product of a difference of the state variable modeling of the switching ON for each HVAC unit from one and the multiplier corresponding to the upper bound of one is less than a relaxation parameter; and

determining the times of the switching iteratively based on the inequality, wherein a value of the relaxation parameter is adaptively reduced for subsequent iterations;

reformulating the complementarity constraint as an inequality, such that a product of the state variable modeling of the switching OFF for each HVAC unit and the multiplier corresponding to its lower bound of zero or a product of a difference of the state variable modeling of the switching OFF for each HVAC unit from one and the multiplier corresponding to the upper bound of one is less than a relaxation parameter; and

determining the times of the switching iteratively based on the inequality, wherein a value of the relaxation parameter is adaptively reduced for subsequent iterations.

17. The method of claim 16, wherein the determining for a current iteration comprises:

determining the times of the switching based on values of the times of the switching determined during a previous iteration;

testing the inequality using values of the times of the switching of the current iteration; and

modifying the value of the relaxation parameter, if the inequality is violated.

18. The method of claim 17, wherein the optimizing uses an interior point method, wherein the relaxation parameter is proportional to a barrier parameter of the interior point method, and wherein the barrier parameter is monotonically reduced for each iteration.

19. The method of claim 16, further comprising:

determining the times of the switching iteratively using an interior point method based on a barrier problem.

20. A controller for operating a set of heating, ventilation and air-conditioning (HVAC) units according to corresponding times of switching, the controller comprising:

a processor for optimizing jointly operations of the set of HVAC units subject to constraints to determine time instants of switching each HVAC unit ON and OFF,

wherein the operation of switching ON each HVAC unit at each time instant is represented by a continuous function and a set of constraints for switching ON, wherein the continuous function for switching ON is a deviation of a current time instant from the time instant of switching ON, and the set of the constraints include a difference of multipliers that are equal to the continuous function, and complementarity constraints between the multiplier variables and a state variable modeling of the switching ON for each HVAC unit,

wherein the operation of switching OFF of each HVAC unit at each time instant is represented by a continuous function and a set of constraints for switching OFF, such that the continuous function for switching OFF is a deviation of a current time instant from the time instant of switching OFF, and the set of constraints include a difference of multipliers that are equal to the continuous function, and complementarity constraints between multiplier variables and a state variable modeling of the switching OFF for each HVAC unit and

controlling each HVAC unit according to the corresponding times of switching.

21. A method for operating a set of heating, ventilation and air-conditioning (HVAC) units, comprising:

optimizing jointly operations of the set of HVAC units subject to constraints to determine time instants of switching each HVAC unit ON and OFF,

wherein the operation of switching ON each HVAC unit at each time instant is represented by a continuous function and a set of constraints for switching ON, such that the continuous function for switching ON is a deviation of a current time instant from the time instant of switching ON, and the set of the constraints include a difference of multipliers that are equal to the continuous function, and complementarity constraints between the multiplier variables and a state variable modeling of the switching ON for each HVAC unit, such that the continuous function includes

−

(t−

τ

₁)−

λ

₁(t)=0,

 

wherein τ

₁ is a time instant to switch the HVAC unit ON, t is defined as the current time instant, and λ

₁(t), v₁(t) are multipliers for lower and upper bound constraints,

wherein the operation of switching OFF of each HVAC unit at each time instant is represented by a continuous function and a set of constraints for switching OFF, such that the continuous function for switching OFF is a deviation of a current time instant from the time instant of switching OFF, and the set of constraints include a difference of multipliers that are equal to the continuous function, and complementarity constraints between multiplier variables and a state variable modeling of the switching OFF for each HVAC unit, such that the continuous function includes

−

(t−

τ

₂)−

λ

₂(t)+v₂(t)=0,

 

wherein τ

₂ is a time instant to switch the HVAC unit OFF, t is defined as the current time instant, and λ

₂(t), v₂(t) are multipliers for lower and upper bound constraints; and

controlling each HVAC unit according to the corresponding times of switching, wherein the steps are performed in a processor.

22. A system for operating a set of heating, ventilation and air-conditioning (HVAC) units, comprising:

a processor is configured to optimize jointly operations of the set of HVAC units subject to constraints to determine time instants of switching each HVAC unit ON and OFF,

wherein the operation of switching ON each HVAC unit at each time instant is represented by a continuous function and a set of constraints for switching ON, such that the continuous function for switching ON is a deviation of a current time instant from the time instant of switching ON, and the set of the constraints include a difference of multipliers that are equal to the continuous function, and complementarity constraints between the multiplier variables and a state variable modeling of the switching ON for each HVAC unit, such that the continuous function includes

−

(t−

τ

₁)−

λ

₁(t)=0,

 

wherein τ

₁ is a time instant to switch the HVAC unit ON, t is defined as the current time instant, and λ

₁(t), v₁(t) are multipliers for lower and upper bound constraints,

wherein the operation of switching OFF of each HVAC unit at each time instant is represented by a continuous function and a set of constraints for switching OFF, such that the continuous function for switching OFF is a deviation of a current time instant from the time instant of switching OFF, and the set of constraints include a difference of multipliers that are equal to the continuous function, and complementarity constraints between multiplier variables and a state variable modeling of the switching OFF for each HVAC unit, such that the continuous function includes

−

(t−

τ

₂)−

λ

₂(t)=v₂(t)=0,

 

wherein τ

₂ is a time instant to switch the HVAC unit OFF, t is defined as the current time instant, and λ

₂(t), v₂(t) are multipliers for lower and upper bound constraints; and

control each HVAC unit according to the corresponding times of switching.