Building energy system with stochastic model predictive control and demand charge incorporation

1 . A building energy system configured to serve energy loads of a building or campus, the system comprising:

equipment configured to consume, store, or discharge one or more energy resources purchased from a utility supplier, wherein at least one of the energy resources is subject to a demand charge; and

a controller configured to determine an optimal allocation of the energy resources across the equipment over a demand charge period, the controller configured to:

obtain a plurality of different alternative sets of representative loads and representative rates for the building or campus for a same future portion of the demand charge period;

generate a first objective function comprising at least (i) a first cost of purchasing the energy resources over the same future portion of the demand charge period based on first decision variables for the energy resources purchased during the same future portion of the demand charge period and the representative rates for a first alternative set of the plurality of different alternative sets (ii) a second cost of purchasing the energy resources over the same future portion of the demand charge period based on second decision variables for the energy resources purchased during the same future portion of the demand charge period and the representative rates for a second alternative set of the plurality of different alternative sets, and (iii) a demand charge term for the demand charge period based on a value for a peak demand target for an energy resource subject to the demand charge;

perform a first optimization using the first objective function to determine (i) first values for the first decision variables subject to first constraints based on the representative loads of the first alternative set (ii) second values for the second decision variables subject to second constraints based on the representative loads of the second alternative set, and iii) the value for the peak demand target subject to a plurality of constraints ensuring that the value for the peak demand target is greater than or equal to the first values and the second values over the demand charge period; and

control the equipment to achieve the optimal allocation of the one or more energy resources.

2 . The building energy system of claim 1 , wherein the controller is further configured to:

generate a second objective function comprising a cost of purchasing the energy resources over an optimization period different than the demand charge period;

use the peak demand target to implement a peak demand constraint that limits a maximum purchase of the one or more energy resources subject to the demand charge during the optimization period; and

perform a second optimization, subject to the peak demand constraint, to determine the optimal allocation of the energy resources across the equipment over the optimization period.

3 . The building energy system of claim 2 , wherein the controller is configured to implement the peak demand constraint as a soft constraint on the maximum purchase of the one or more energy resources subject to the demand charge.

4 . The building energy system of claim 2 , wherein the controller is configured to:

perform the second optimization a plurality of times, each of the second optimizations determining the optimal allocation of the energy resources for one of a plurality of optimization periods; and

use the same peak demand constraint to constrain each of the second optimizations.

5 . The building energy system of claim 2 , wherein the controller is configured to:

perform the first optimization such that first state values for one or more states of the system resulting from the first decision variables and second state values for the one or more states of the system resulting from the second decision variables are constrained to be equal at a beginning and end of the future portion of the demand charge period; and

generate a terminal constraint based on the equal values and perform the second optimization subject to the terminal constraint.

6 . The building energy system of claim 1 , wherein the peak demand target minimizes a risk attribute of the first objective function over the first cost, the second cost, and a one or more additional costs based on one or more sets of additional decision variables for the energy resources purchased during the same future portion of the demand charge period and the representative rates for one or more additional alternative sets of the plurality of different alternative sets, and wherein the risk attribute of the first objective function comprises at least one of a conditional value at risk, a value at risk, or an expected cost.

7 . The building energy system of claim 1 , wherein the first objective function comprises a frequency regulation revenue term that accounts for revenue generated by operating the equipment to participate in a frequency regulation program for an energy grid.

8 . The building energy system of claim 1 , wherein the controller is configured to obtain the representative loads and the representative rates by:

receiving user input defining loads and rates for a plurality of prospective alternative sets; and

at least one of:

sampling the representative loads and the representative rates from the user input defining the loads and rates; or

generating an estimated distribution of the loads and rates defined by the user input and sampling the representative loads and the representative rates from the estimated distribution.

9 . The building energy system of claim 1 , wherein the controller is configured to obtain the representative loads and the representative rates by:

receiving input defining loads and rates for a plurality of prospective alternative sets, each of the plurality of prospective alternative sets corresponding to a different time period used by a planning tool; and

sampling the representative loads and the representative rates from the loads and rates for a corresponding time period used by the planning tool.

10 . The building energy system of claim 1 , wherein the controller is configured to obtain the representative loads and the representative rates by:

storing a history of past alternative sets comprising actual values for historical loads and rates; and

at least one of:

sampling the representative loads and the representative rates from the history of past alternative sets; or

generating an estimated distribution of the historical loads and rates based on the history of past alternative sets and sampling the representative loads and the representative rates from the estimated distribution.

11 . The building energy system of claim 10 , wherein:

each of the historical loads and rates corresponds to different time periods; and

the controller is configured to:

indicate a time period of the different time periods by comparing characteristics of the different time periods to characteristics of the future portion of the demand charge period; and

sample the representative loads and the representative rates for the alternative sets from the historical loads and rates corresponding to the time period indicated.

12 . The building energy system of claim 1 , wherein the controller is configured to perform the first optimization such that first state values for one or more states of the system resulting from the first decision variables and second state values for the one or more states of the system resulting from the second decision variables are constrained to be equal at a beginning and end of the future portion of the demand charge period.

13 . A method for managing equipment in a building energy system over a demand charge period, the method comprising:

operating the equipment to consume, store, or discharge one or more energy resources purchased from a utility supplier, wherein at least one of the energy resources is subject to a demand charge;

obtaining a plurality of different alternative sets of representative loads and representative rates for a building or campus for a same future portion of the demand charge period;

generating a first objective function comprising at least (i) a first cost of purchasing the energy resources over the same future portion of the demand charge period based on first decision variables for the energy resources purchased during the same future portion of the demand charge period and the representative rates for a first alternative set of the plurality of different alternative sets (ii) a second cost of purchasing the energy resources over the same future portion of the demand charge period based on second decision variables for the energy resources purchased during the same future portion of the demand charge period and the representative rates for a second alternative set of the plurality of different alternative sets, and (iii) a demand charge term for the demand charge period based on a value for a peak demand target for an energy resource subject to the demand charge; and

performing a first optimization using the first objective function to determine (i) first values for the first decision variables subject to first constraints based on the representative loads of the first alternative set (ii) second values for the second decision variables subject to second constraints based on the representative loads of the second alternative set, and (iii) the value for the peak demand target subject to a plurality of constraints ensuring that the value for the peak demand target is greater than or equal to the first values and the second values over the demand charge period.

14 . The method of claim 13 , further comprising:

generating a second objective function comprising a cost of purchasing the energy resources over an optimization period;

using the peak demand target to implement a peak demand constraint that limits a maximum purchase of the at least one of the energy resources subject to the demand charge during the optimization period; and

performing a second optimization, subject to the peak demand constraint, to determine an optimal allocation of the energy resources across the equipment over the optimization period.

15 . The method of claim 14 , wherein the peak demand constraint is implemented as a soft constraint on the maximum purchase of the at least one of the energy resources subject to the demand charge.

16 . The method of claim 14 , further comprising:

performing the second optimization a plurality of times, each of the second optimizations determining the optimal allocation of the energy resources for one of a plurality of optimization periods; and

using the peak demand constraint to constrain each of the second optimizations.

17 . The method of claim 14 , wherein the first optimization is performed such that first state values for one or more states of the system resulting from the first decision variables and second state values for the one or more states of the system resulting from the second decision variables are constrained to be equal at a beginning and end of the future portion of the demand charge period; and

wherein the second optimization is performed subject to a terminal constraint, the terminal constraint generated based on the equal values.

18 . The method of claim 13 , wherein the peak demand target minimizes a risk attribute of the first objective function over the first cost, the second cost, and a one or more additional costs based on one or more sets of additional decision variables for the energy resources purchased during the same future portion of the demand charge period and the representative rates for one or more additional alternative sets of the plurality of different alternative sets, and wherein the risk attribute of the first objective function comprises at least one of a conditional value at risk, a value at risk, or an expected cost.

19 . The method of claim 13 , wherein the first objective function comprises a frequency regulation revenue term that accounts for revenue generated by operating the equipment to participate in a frequency regulation program for an energy grid.

20 . The method of claim 13 , wherein obtaining the representative loads and the representative rates comprises:

receiving user input defining loads and rates a plurality of prospective alternative sets; and

at least one of:

sampling the representative loads and the representative rates from the user input defining the loads and rates; or

generating an estimated distribution of the loads and rates defined by the user input and sampling the representative loads and the representative rates from the estimated distribution.

21 . The method of claim 13 , wherein obtaining the representative loads and the representative rates comprises:

receiving input defining loads and rates for a plurality of prospective alternative sets, each of the plurality of prospective alternative sets corresponding to a different time period used by a planning tool; and

sampling the representative loads and the representative rates from the loads and rates for a corresponding time period used by the planning tool.

22 . The method of claim 13 , wherein obtaining the representative loads and the representative rates comprises:

storing a history of past alternative sets comprising actual values for historical loads and rates; and

at least one of:

sampling the representative loads and the representative rates from the history of past alternative sets; or

generating an estimated distribution of the historical loads and rates based on the history of past alternative sets and sampling the representative loads and the representative rates from the estimated distribution.

23 . The method of claim 22 , wherein:

each of the historical loads and rates corresponds to different time periods;

the method comprises indicating a time period of the different time periods by comparing characteristics of the different time periods to characteristics of the future portion of the demand charge period; and

the representative loads and the representative rates are sampled for each alternative set from the historical loads and rates corresponding to the time period indicated.

24 . The method of claim 13 , wherein the first optimization is performed such that first state values for one or more states of the system resulting from the first decision variables and second state values for the one or more states of the system resulting from the second decision variables are constrained to be equal values at a beginning and end of the future portion of the demand charge period.