Patent Publication Number: US-11042924-B2

Title: Building controller for optimizing equipment upgrades with design of experiments

Description:
BACKGROUND 
     A building, facility, or central plant includes various types of equipment. The equipment may be used to heat the building, cool the building, store energy, etc. The equipment may include chillers, air handler units, boilers, thermal energy storage units, and any other piece of equipment that can be used in a building, facility, or central plant. The equipment may be available for purchase in various sizes, various capacities, with various software options, with various equipment upgrades, etc. There may be a large number of possible purchase options for a single piece of equipment. Further, when determining to purchase multiple pieces of building equipment, the number of possible purchases may become very large. 
     When considering upgrades for building equipment, known as facility improvement measures (FIMS), a large number of possible selections can be made regarding the equipment. Each selection may correspond to one potential upgrade that can be made. In some cases, the number of possible selections is infinite (e.g., if there is no limit to the number of potential sizes that can be selected). If multiple equipment selections are considered concurrently, the number of possible combinations of equipment selections may be exponentially larger than the number of possible selections. 
     In conventional systems, each potential combination of equipment upgrades is evaluated (e.g., by a controller or building management system) and compared to the other potential combinations to determine which combination is predicted to optimize the performance of the building or facility. However, when the number of potential combinations is large, determining the optimal upgrades and/or building equipment purchases may take a long time and/or may be impossible to determine by brute force. 
     SUMMARY 
     One implementation of the present disclosure is a building management system. The building management system includes building equipment operable to affect a variable state or condition of a building and a controller. The controller is configured to identify one or more facility improvement measures (FIMS), each of the FIMS representing a potential upgrade or addition to the building equipment. The controller is further configured to perform a design of experiments analysis to determine a plurality of combinations of the FIMS, each combination includes one or more of the FIMS and a level for each FIM in the combination. The controller is configured to generate an objective function based on the combinations of the FIMS. The objective function indicates an economic value as a function of the FIMS and optimize the objective function to determine an optimal combination of the FIMS. 
     In some embodiments, the FIMS determined by the controller include each possible combination of each FIM and each FIM level. The controller can be configured to select one or more levels for each FIM based on an output response of the FIM. 
     In some embodiments, the controller is configured to determine an output response for each FIM. The output response may indicate a type of relationship between the FIM and an operating cost resulting from the FIM. The controller can be configured to select two distinct levels for a particular FIM in response to determining that the output response of the particular FIM is binary, select two distinct levels for the particular FIM in response to determining that the output response of the particular FIM is linear, and select three distinct levels for the particular FIM in response to determining that the output response of the particular FIM is quadratic. 
     In some embodiments, the controller is configured to generate a baseline model based on information associated with the building equipment. The baseline model may represent an operating cost of the building equipment prior to implementing the FIMS. 
     The controller can be configured to generate the objective function based on an operating expense model of the FIMS. The operating expense model can represent an operating cost of the FIMS. In some embodiments, the controller is configured to generate the operating expense model by determining an operating cost for each combination of the FIMS and performing a regression with the operating costs. 
     In some embodiments, the controller is configured to generate an operating expense model for each of the combinations of the FIMS. The operating expense model may indicate a cost of operating the building equipment after implementing the FIMS. 
     In some embodiments, the controller is configured to generate a baseline model that indicates a cost of operating the building equipment prior to implementing the FIMS and determine a benefit of each of the combinations of the FIMS based on a difference between the cost indicated by the baseline model and the cost indicated by the operational expense model. 
     In some embodiments, the controller is configured to determine a capital expense function for each of the FIMS and generate a capital expense model by summing each of the capital expense functions. The capital expense model may represent a purchase cost of the FIMS. 
     The controller can be configured to generate the objective function further based on a capital expense model and an operating expense model. The capital expense model may represent a purchase cost of the FIMS and the operating expense model represents an operating cost of the FIMS. 
     In some embodiments, the objective function is a net present value (NPV) function. The difference between the baseline model and the operating expense model and the capital expense model may be arguments in the NPV function. In some embodiments, the controller is configured to optimize the NPV function to identify FIMS which result in an optimal NPV or internal rate of return (IRR). 
     Another implementation of the present disclosure is a method for optimizing upgrades to building equipment in a building management system. The method includes identifying one or more facility improvement measures (FIMS), each of the FIMS representing a potential upgrade or addition to the building equipment. The building equipment is operable to affect a variable state or condition of a building. The method further includes performing a design of experiments analysis to determine a plurality of combinations of the FIMS, each combination includes one or more of the FIMS and a level for each FIM in the combination. The method includes generating an objective function based on the combinations of the FIMS. The objective function indicates an economic value as a function of the FIMS and optimizing the objective function to determine an optimal combination of the FIMS. 
     In some embodiments, the combinations of the FIMS includes each possible combination of each FIM and each FIM level. The method may further include selecting one or more levels for each FIM based on an output response of the FIM. 
     In some embodiments, the method further includes determining an output response for each FIM. The output response may indicate a type of relationship between the FIM and an operating cost resulting from the FIMS. The method may include selecting two distinct levels for a particular FIM in response to determining that the output response of the FIM is binary, selecting two distinct levels for the particular FIM in response to determining that the output response of the FIM is linear, and selecting three distinct levels for the particular FIM in response to determining that the output response of the FIM is quadratic. 
     The method may further include generating a baseline model based on information associated with the building equipment. The baseline model may represent an operating cost of the building equipment prior to implementing the FIMS. 
     In some embodiments, generating the objective function is based on an operating expense model of the FIMS. The operating expense model may represent an operating cost of the FIMS. In some embodiments, the method further includes generating the operating expense model by determining an operating cost for each combination of the FIMS and performing a regression with the operating costs. 
     In some embodiments, the method further includes generating a baseline model that predicts a cost of operating the building equipment prior to implementing the FIMS and determining a benefit of each of the combinations of the FIMS based on a difference between the cost predicted by the baseline model and the cost predicted by the operational expense model. 
     In some embodiments, the generating the objective function is further based on a capital expense model and an operating expense model. The capital expense model may represent a purchase cost of the FIMS and the operating expense model represents an operating cost of the FIMS. In some embodiments, the method further includes generating the capital expense model by determining a capital expense function for each of the combinations of the FIMS and summing each of the capital expense functions. 
     In some embodiments, the objective function is a net present value (NPV) function and the difference between the baseline model and the operating expense model and the capital expense are arguments in the NPV function. In some embodiments, the method further includes optimizing the NPV function to identify FIMS which result in an optimal NPV or internal rate of return (IRR). 
     Another implementation of the present disclosure is a building management system. The building management system includes building equipment operable to affect a variable state or condition of a building and a controller. The controller is configured to identify one or more facility improvement measures (FIMS), each of the FIMS representing a potential upgrade or addition to the building equipment and perform a design of experiments analysis to determine a plurality of combinations of the FIMS, the combinations of the FIMS includes each possible combination of the FIMS and one or more levels for each FIM. The controller is further configured to determine an output response for each FIM. The output response indicates a type of relationship between the FIM and an operating cost resulting from the FIM and select the one or more levels for each FIM in the combinations based on the output response. The controller is further configured to generate a baseline model that predicts a cost of operating the building equipment prior to implementing any of the FIMS. The controller is configured to generate the operating expense model by determining an operating cost for each combination of the FIMS and performing a regression with the operating costs. The operating expense model represents an operating cost of the FIMS and generate a capital expense model. The capital expense model represents a purchase cost of the FIMS. The controller is further configured to generate an objective function based on the baseline model, the operating expense model, and the capital expense model. The objective function indicates an economic value for the FIMS and optimize the objective function to determine an optimal combination of the FIMS. 
     In some embodiments, the controller is configured to select two distinct levels for a particular FIM in the combination in response to determining that the output response of the FIM is binary. The controller can be configured to select two distinct levels for the particular FIM in the combination in response to determining that the output response of the FIM is linear and select three distinct levels for the particular FIM in the combination in response to determining that the output response of the FIM is quadratic. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Various objects, aspects, features, and advantages of the disclosure will become more apparent and better understood by referring to the detailed description taken in conjunction with the accompanying drawings, in which like reference characters identify corresponding elements throughout. In the drawings, like reference numbers generally indicate identical, functionally similar, and/or structurally similar elements. 
         FIG. 1  is a drawing of a building equipped with a HVAC system, according to an exemplary embodiment. 
         FIG. 2  is a block diagram of a waterside system that may be used in conjunction with the building of  FIG. 1 , according to an exemplary embodiment. 
         FIG. 3  is a block diagram of an airside system that may be used in conjunction with the building of  FIG. 1 , according to an exemplary embodiment. 
         FIG. 4  is a block diagram of a building controller generating outputs from inputs with design of experiments, according to an exemplary embodiment. 
         FIG. 5  is a table of the inputs and the outputs of  FIG. 4 , according to an exemplary embodiment. 
         FIG. 6  is a block diagram of the building controller of  FIG. 4  in greater detail, according to an exemplary embodiment. 
         FIG. 7  is a block diagram of components of the building controller of  FIG. 4  and  FIG. 6  in greater detail, according to an exemplary embodiment. 
         FIG. 8  is a flow diagram of a process for using design of experiments to determine optimal FIMS with the building controller of  FIGS. 4 and 6-7 , according to an exemplary embodiment. 
         FIG. 9  is an example of FIMS, FIM levels, FIM level combinations, and an operating cost for each FIM level combination that can be determined by the building controller of  FIGS. 4 and 6-7 , according to an exemplary embodiment. 
         FIG. 10  is a set of two plots which illustrate the effect of an input on an output where the input has predefined levels, according to an exemplary embodiment. 
         FIG. 11  is an interactions plot illustrating an effect which combinations of inputs may have on an output, according to an exemplary embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Overview 
     Referring generally to the FIGURES, systems and methods for determining equipment upgrades for a building with a building controller utilizing design of experiments are shown, according to various exemplary embodiments. The building controller may be configured to use the design of experiments method to efficiently and effectively determine what improvements should be made to a facility and/or building. An upgrade to a facility or building may have a large number of possible sizes and/or selections. For example, when considering to upgrade a thermal energy storage (TES) tank, a large number of possible tank sizes must be considered. In addition to the TES tank upgrade, a second upgrade may be simultaneously considered which may be upgrading the size of a chiller. Again the number of various sizes for a chiller may be large. Further, a third upgrade to a facility may be the purchase of variable speed drives (VSDS) for compressors of the building. 
     The most effective way for the building controller to select an optimal TES tank size, a chiller size, and whether or not to purchase VSDS for compressors of the building is to analyze the upgrades in combination rather than in isolation. However, when analyzing the various upgrades in combination, the number of possible upgrade selections becomes exponentially large. For example, if there are 100 different TES tank sizes, 600 different chiller sizes, and 2 selections for the VSDS, this means there are 100*600*2=120,000 different possible combinations to consider. Having a controller exhaustively test all 120,000 different possible combinations is not efficient and may take a long time (e.g., a predefined number of processor cycles). 
     A building controller may use design of experiments to appropriately model the upgrades or improvements rather than exhaustively test each combination of each size and level of each upgrade or improvement. By using design of experiments, the building controller can select a predefined amount of levels to test and generate models for the equipment upgrades based on the selected levels. This may allow the building controller to determine optimal equipment upgrades faster (e.g., with less processor cycles) than exhaustively testing each possible combination of equipment upgrades. 
     Building Management System and HVAC System 
     Referring now to  FIGS. 1-3 , an exemplary building management system (BMS) and HVAC system in which the systems and methods of the present invention can be implemented are shown, according to an exemplary embodiment. Referring particularly to  FIG. 1 , a perspective view of a building  10  is shown. Building  10  is served by a BMS. A BMS is, in general, a system of devices configured to control, monitor, and manage equipment in or around a building or building area. A BMS can include, for example, a HVAC system, a security system, a lighting system, a fire alerting system, any other system that is capable of managing building functions or devices, or any combination thereof. 
     The BMS that serves building  10  includes an HVAC system  100 . HVAC system  100  can include a plurality of HVAC devices (e.g., heaters, chillers, air handling units, pumps, fans, thermal energy storage, etc.) configured to provide heating, cooling, ventilation, or other services for building  10 . For example, HVAC system  100  is shown to include a waterside system  120  and an airside system  130 . Waterside system  120  can provide a heated or chilled fluid to an air handling unit of airside system  130 . Airside system  130  can use the heated or chilled fluid to heat or cool an airflow provided to building  10 . An exemplary waterside system and airside system which can be used in HVAC system  100  are described in greater detail with reference to  FIGS. 2-3 . 
     HVAC system  100  is shown to include a chiller  102 , a boiler  104 , and a rooftop air handling unit (AHU)  106 . Waterside system  120  can use boiler  104  and chiller  102  to heat or cool a working fluid (e.g., water, glycol, etc.) and can circulate the working fluid to AHU  106 . In various embodiments, the HVAC devices of waterside system  120  can be located in or around building  10  (as shown in  FIG. 1 ) or at an offsite location such as a central plant (e.g., a chiller plant, a steam plant, a heat plant, etc.). The working fluid can be heated in boiler  104  or cooled in chiller  102 , depending on whether heating or cooling is required in building  10 . Boiler  104  can add heat to the circulated fluid, for example, by burning a combustible material (e.g., natural gas) or using an electric heating element. Chiller  102  can place the circulated fluid in a heat exchange relationship with another fluid (e.g., a refrigerant) in a heat exchanger (e.g., an evaporator) to absorb heat from the circulated fluid. The working fluid from chiller  102  and/or boiler  104  can be transported to AHU  106  via piping  108 . 
     AHU  106  can place the working fluid in a heat exchange relationship with an airflow passing through AHU  106  (e.g., via one or more stages of cooling coils and/or heating coils). The airflow can be, for example, outside air, return air from within building  10 , or a combination of both. AHU  106  can transfer heat between the airflow and the working fluid to provide heating or cooling for the airflow. For example, AHU  106  can include one or more fans or blowers configured to pass the airflow over or through a heat exchanger containing the working fluid. The working fluid can then return to chiller  102  or boiler  104  via piping  110 . 
     Airside system  130  can deliver the airflow supplied by AHU  106  (i.e., the supply airflow) to building  10  via air supply ducts  112  and can provide return air from building  10  to AHU  106  via air return ducts  114 . In some embodiments, airside system  130  includes multiple variable air volume (VAV) units  116 . For example, airside system  130  is shown to include a separate VAV unit  116  on each floor or zone of building  10 . VAV units  116  can include dampers or other flow control elements that can be operated to control an amount of the supply airflow provided to individual zones of building  10 . In other embodiments, airside system  130  delivers the supply airflow into one or more zones of building  10  (e.g., via supply ducts  112 ) without using intermediate VAV units  116  or other flow control elements. AHU  106  can include various sensors (e.g., temperature sensors, pressure sensors, etc.) configured to measure attributes of the supply airflow. AHU  106  can receive input from sensors located within AHU  106  and/or within the building zone and can adjust the flow rate, temperature, or other attributes of the supply airflow through AHU  106  to achieve setpoint conditions for the building zone. 
     Referring now to  FIG. 2 , a block diagram of a waterside system  200  is shown, according to an exemplary embodiment. In various embodiments, waterside system  200  can supplement or replace waterside system  120  in HVAC system  100  or can be implemented separate from HVAC system  100 . When implemented in HVAC system  100 , waterside system  200  can include a subset of the HVAC devices in HVAC system  100  (e.g., boiler  104 , chiller  102 , pumps, valves, etc.) and can operate to supply a heated or chilled fluid to AHU  106 . The HVAC devices of waterside system  200  can be located within building  10  (e.g., as components of waterside system  120 ) or at an offsite location such as a central plant. 
     In  FIG. 2 , waterside system  200  is shown as a central plant having a plurality of subplants  202 - 212 . Subplants  202 - 212  are shown to include a heater subplant  202 , a heat recovery chiller subplant  204 , a chiller subplant  206 , a cooling tower subplant  208 , a hot thermal energy storage (TES) subplant  210 , and a cold thermal energy storage (TES) subplant  212 . Subplants  202 - 212  consume resources (e.g., water, natural gas, electricity, etc.) from utilities to serve the thermal energy loads (e.g., hot water, cold water, heating, cooling, etc.) of a building or campus. For example, heater subplant  202  can be configured to heat water in a hot water loop  214  that circulates the hot water between heater subplant  202  and building  10 . Chiller subplant  206  can be configured to chill water in a cold water loop  216  that circulates the cold water between chiller subplant  206  building  10 . Heat recovery chiller subplant  204  can be configured to transfer heat from cold water loop  216  to hot water loop  214  to provide additional heating for the hot water and additional cooling for the cold water. Condenser water loop  218  can absorb heat from the cold water in chiller subplant  206  and reject the absorbed heat in cooling tower subplant  208  or transfer the absorbed heat to hot water loop  214 . Hot TES subplant  210  and cold TES subplant  212  can store hot and cold thermal energy, respectively, for subsequent use. 
     Hot water loop  214  and cold water loop  216  can deliver the heated and/or chilled water to air handlers located on the rooftop of building  10  (e.g., AHU  106 ) or to individual floors or zones of building  10  (e.g., VAV units  116 ). The air handlers push air past heat exchangers (e.g., heating coils or cooling coils) through which the water flows to provide heating or cooling for the air. The heated or cooled air can be delivered to individual zones of building  10  to serve the thermal energy loads of building  10 . The water then returns to subplants  202 - 212  to receive further heating or cooling. 
     Although subplants  202 - 212  are shown and described as heating and cooling water for circulation to a building, it is understood that any other type of working fluid (e.g., glycol, CO2, etc.) can be used in place of or in addition to water to serve the thermal energy loads. In other embodiments, subplants  202 - 212  can provide heating and/or cooling directly to the building or campus without requiring an intermediate heat transfer fluid. These and other variations to waterside system  200  are within the teachings of the present invention. 
     Each of subplants  202 - 212  can include a variety of equipment configured to facilitate the functions of the subplant. For example, heater subplant  202  is shown to include a plurality of heating elements  220  (e.g., boilers, electric heaters, etc.) configured to add heat to the hot water in hot water loop  214 . Heater subplant  202  is also shown to include several pumps  222  and  224  configured to circulate the hot water in hot water loop  214  and to control the flow rate of the hot water through individual heating elements  220 . Chiller subplant  206  is shown to include a plurality of chillers  232  configured to remove heat from the cold water in cold water loop  216 . Chiller subplant  206  is also shown to include several pumps  234  and  236  configured to circulate the cold water in cold water loop  216  and to control the flow rate of the cold water through individual chillers  232 . 
     Heat recovery chiller subplant  204  is shown to include a plurality of heat recovery heat exchangers  226  (e.g., refrigeration circuits) configured to transfer heat from cold water loop  216  to hot water loop  214 . Heat recovery chiller subplant  204  is also shown to include several pumps  228  and  230  configured to circulate the hot water and/or cold water through heat recovery heat exchangers  226  and to control the flow rate of the water through individual heat recovery heat exchangers  226 . Cooling tower subplant  208  is shown to include a plurality of cooling towers  238  configured to remove heat from the condenser water in condenser water loop  218 . Cooling tower subplant  208  is also shown to include several pumps  240  configured to circulate the condenser water in condenser water loop  218  and to control the flow rate of the condenser water through individual cooling towers  238 . 
     Hot TES subplant  210  is shown to include a hot TES tank  242  configured to store the hot water for later use. Hot TES subplant  210  can also include one or more pumps or valves configured to control the flow rate of the hot water into or out of hot TES tank  242 . Cold TES subplant  212  is shown to include cold TES tanks  244  configured to store the cold water for later use. Cold TES subplant  212  can also include one or more pumps or valves configured to control the flow rate of the cold water into or out of cold TES tanks  244 . 
     In some embodiments, one or more of the pumps in waterside system  200  (e.g., pumps  222 ,  224 ,  228 ,  230 ,  234 ,  236 , and/or  240 ) or pipelines in waterside system  200  include an isolation valve associated therewith. Isolation valves can be integrated with the pumps or positioned upstream or downstream of the pumps to control the fluid flows in waterside system  200 . In various embodiments, waterside system  200  can include more, fewer, or different types of devices and/or subplants based on the particular configuration of waterside system  200  and the types of loads served by waterside system  200 . 
     Referring now to  FIG. 3 , a block diagram of an airside system  300  is shown, according to an exemplary embodiment. In various embodiments, airside system  300  can supplement or replace airside system  130  in HVAC system  100  or can be implemented separate from HVAC system  100 . When implemented in HVAC system  100 , airside system  300  can include a subset of the HVAC devices in HVAC system  100  (e.g., AHU  106 , VAV units  116 , ducts  112 - 114 , fans, dampers, etc.) and can be located in or around building  10 . Airside system  300  can operate to heat or cool an airflow provided to building  10  using a heated or chilled fluid provided by waterside system  200 . 
     In  FIG. 3 , airside system  300  is shown to include an economizer-type air handling unit (AHU)  302 . Economizer-type AHUs vary the amount of outside air and return air used by the air handling unit for heating or cooling. For example, AHU  302  can receive return air  304  from building zone  306  via return air duct  308  and can deliver supply air  310  to building zone  306  via supply air duct  312 . In some embodiments, AHU  302  is a rooftop unit located on the roof of building  10  (e.g., AHU  106  as shown in  FIG. 1 ) or otherwise positioned to receive both return air  304  and outside air  314 . AHU  302  can be configured to operate exhaust air damper  316 , mixing damper  318 , and outside air damper  320  to control an amount of outside air  314  and return air  304  that combine to form supply air  310 . Any return air  304  that does not pass through mixing damper  318  can be exhausted from AHU  302  through exhaust damper  316  as exhaust air  322 . 
     Each of dampers  316 - 320  can be operated by an actuator. For example, exhaust air damper  316  can be operated by actuator  324 , mixing damper  318  can be operated by actuator  326 , and outside air damper  320  can be operated by actuator  328 . Actuators  324 - 328  can communicate with an AHU controller  330  via a communications link  332 . Actuators  324 - 328  can receive control signals from AHU controller  330  and can provide feedback signals to AHU controller  330 . Feedback signals can include, for example, an indication of a current actuator or damper position, an amount of torque or force exerted by the actuator, diagnostic information (e.g., results of diagnostic tests performed by actuators  324 - 328 ), status information, commissioning information, configuration settings, calibration data, and/or other types of information or data that can be collected, stored, or used by actuators  324 - 328 . AHU controller  330  can be an economizer controller configured to use one or more control algorithms (e.g., state-based algorithms, extremum seeking control (ESC) algorithms, proportional-integral (PI) control algorithms, proportional-integral-derivative (PID) control algorithms, model predictive control (MPC) algorithms, feedback control algorithms, etc.) to control actuators  324 - 328 . 
     Still referring to  FIG. 3 , AHU  302  is shown to include a cooling coil  334 , a heating coil  336 , and a fan  338  positioned within supply air duct  312 . Fan  338  can be configured to force supply air  310  through cooling coil  334  and/or heating coil  336  and provide supply air  310  to building zone  306 . AHU controller  330  can communicate with fan  338  via communications link  340  to control a flow rate of supply air  310 . In some embodiments, AHU controller  330  controls an amount of heating or cooling applied to supply air  310  by modulating a speed of fan  338 . 
     Cooling coil  334  can receive a chilled fluid from waterside system  200  (e.g., from cold water loop  216 ) via piping  342  and can return the chilled fluid to waterside system  200  via piping  344 . Valve  346  can be positioned along piping  342  or piping  344  to control a flow rate of the chilled fluid through cooling coil  334 . In some embodiments, cooling coil  334  includes multiple stages of cooling coils that can be independently activated and deactivated (e.g., by AHU controller  330 , by BMS controller  366 , etc.) to modulate an amount of cooling applied to supply air  310 . 
     Heating coil  336  can receive a heated fluid from waterside system  200  (e.g., from hot water loop  214 ) via piping  348  and can return the heated fluid to waterside system  200  via piping  350 . Valve  352  can be positioned along piping  348  or piping  350  to control a flow rate of the heated fluid through heating coil  336 . In some embodiments, heating coil  336  includes multiple stages of heating coils that can be independently activated and deactivated (e.g., by AHU controller  330 , by BMS controller  366 , etc.) to modulate an amount of heating applied to supply air  310 . 
     Each of valves  346  and  352  can be controlled by an actuator. For example, valve  346  can be controlled by actuator  354  and valve  352  can be controlled by actuator  356 . Actuators  354 - 356  can communicate with AHU controller  330  via communications links  358 - 360 . Actuators  354 - 356  can receive control signals from AHU controller  330  and can provide feedback signals to controller  330 . In some embodiments, AHU controller  330  receives a measurement of the supply air temperature from a temperature sensor  362  positioned in supply air duct  312  (e.g., downstream of cooling coil  334  and/or heating coil  336 ). AHU controller  330  can also receive a measurement of the temperature of building zone  306  from a temperature sensor  364  located in building zone  306 . 
     In some embodiments, AHU controller  330  operates valves  346  and  352  via actuators  354 - 356  to modulate an amount of heating or cooling provided to supply air  310  (e.g., to achieve a setpoint temperature for supply air  310  or to maintain the temperature of supply air  310  within a setpoint temperature range). The positions of valves  346  and  352  affect the amount of heating or cooling provided to supply air  310  by cooling coil  334  or heating coil  336  and may correlate with the amount of energy consumed to achieve a desired supply air temperature. AHU controller  330  can control the temperature of supply air  310  and/or building zone  306  by activating or deactivating coils  334 - 336 , adjusting a speed of fan  338 , or a combination of both. 
     Still referring to  FIG. 3 , airside system  300  is shown to include a building management system (BMS) controller  366  and a client device  368 . BMS controller  366  can include one or more computer systems (e.g., servers, supervisory controllers, subsystem controllers, etc.) that serve as system level controllers, application or data servers, head nodes, or master controllers for airside system  300 , waterside system  200 , HVAC system  100 , and/or other controllable systems that serve building  10 . BMS controller  366  can communicate with multiple downstream building systems or subsystems (e.g., HVAC system  100 , a security system, a lighting system, waterside system  200 , etc.) via a communications link  370  according to like or disparate protocols (e.g., LON, BACnet, etc.). In various embodiments, AHU controller  330  and BMS controller  366  can be separate (as shown in  FIG. 3 ) or integrated. In an integrated implementation, AHU controller  330  can be a software module configured for execution by a processor of BMS controller  366 . 
     In some embodiments, AHU controller  330  receives information from BMS controller  366  (e.g., commands, setpoints, operating boundaries, etc.) and provides information to BMS controller  366  (e.g., temperature measurements, valve or actuator positions, operating statuses, diagnostics, etc.). For example, AHU controller  330  can provide BMS controller  366  with temperature measurements from temperature sensors  362 - 364 , equipment on/off states, equipment operating capacities, and/or any other information that can be used by BMS controller  366  to monitor or control a variable state or condition within building zone  306 . 
     Client device  368  can include one or more human-machine interfaces or client interfaces (e.g., graphical user interfaces, reporting interfaces, text-based computer interfaces, client-facing web services, web servers that provide pages to web clients, etc.) for controlling, viewing, or otherwise interacting with HVAC system  100 , its subsystems, and/or devices. Client device  368  can be a computer workstation, a client terminal, a remote or local interface, or any other type of user interface device. Client device  368  can be a stationary terminal or a mobile device. For example, client device  368  can be a desktop computer, a computer server with a user interface, a laptop computer, a tablet, a smartphone, a PDA, or any other type of mobile or non-mobile device. Client device  368  can communicate with BMS controller  366  and/or AHU controller  330  via communications link  372 . 
     Systems and Methods for Optimizing Building Equipment 
     Referring now to  FIG. 4 , a system  400  is shown using design of experiments to generate one or more outputs from one or more inputs. System  400  is shown to include a building controller  402 . Building controller  402  can be a computer system (e.g., one or more processors coupled to one or more memory devices). In some embodiments, building controller  402  is a computer system and/or controller running METASYS®, VERASYS®, and/or other building management software. In some embodiments, building controller  402  is at least one of or a combination of a controller, a thermostat, a sensor, and/or an actuator that can process data. In some embodiments, building controller  402  is a Network Automation Engine (NAE), a Network Integration Engine (NIE), an Advanced Field Equipment Controller (FAC), a Network Control Engine (NCE) and/or any other network engine and/or controller. In various embodiments, building controller  402  is a laptop computer, a desktop computer, a server, and/or any other computing device. 
     Building controller  402  may be a building controller for a building (e.g., building  10 ), a campus, a facility, a central plant, etc. In some embodiments, building controller  402  is located in a building such as an office, a school, a factory, a hospital, etc. where building controller  402  may be configured to control an environmental condition such as temperature or humidity among performing other functions. In various embodiments, building controller  402  may be a building controller for a central plant. The central plant may serve one or more buildings by heating and/or cooling the buildings. When referred to herein, “building,” “facility,” or “building or facility,” may refer to any building, a facility, or central plant. 
     Building controller  402  is shown to use inputs B 1   404 , C 1   406 , and C 2   408 . The inputs B 1   404 , C 1   406 , and C 2   408  may be inputs to a process or inputs used to generate a model by building controller  402 . In some embodiments, inputs B 1   404 , C 1   406 , and C 2   408  are generated by building controller  402 . For example, building controller  402  may be configured to determine one or more equipment upgrades for a building or facility. These upgrades may be FIMS. FIMS may be purchases of various equipment and/or software. For example FIMS may include, software purchases (e.g., METASYS®), various equipment upgrades or add-ons (e.g., a variable speed drive), increasing a tank size for and/or purchasing TES and/or a TES tank, increasing the size of and/or purchasing a new boiler, increasing the size of and/or purchasing a new chiller, etc. Building controller  402  may identify three possible FIMS, B 1   404 , C 1   406 , and C 2   408  which may correspond to possible equipment and/or software updates. Input B 1   404  may correspond to the purchase of a variable speed drive for a compressor of a building or facility, C 1   406  may correspond to a tank size of a TES, while C 2   408  may correspond to chiller size of a chiller. Building controller  402  is further shown to generate output Y 1   410 . Y 1   410  may be a particular operating expense or a model of operating expenses based on the three FIMS, B 1   404 , C 1   406 , and C 2   408 . 
     Building controller  402  can select a finite amount of levels for each input. In some embodiments, building controller  402  may identify and/or predict the effect which an input, B 1   404 , C 1   406 , and/or C 2   408  will have on output Y 1   410 . If the effect the input will have on the output is linear, building controller  402  can be configured to assign the input two levels. If the effect the input will have on the output is quadratic, building controller  402  may assign the input three levels. In this regard, a continuous input, such as TES tank size, may be represented as two or three discrete tank sizes, a small size, a medium size, and a large size. If an input only have two possible inputs, such as B 1   404  which may be to either make a purchase of a variable speed drive or not to make a purchase of a variable speed drive, building controller  402  can be configured to assign two levels to the input since the input is a binary input. 
     In some embodiments, building controller  402  generates output Y 1   410  based on inputs B 1   404 , C 1   406 , and C 2   408  and the various levels for each input assigned by building controller  402 . Input B 1   404  is shown to include two levels, a low level and a high level. Input B 1   404  may be a binary input, that is, an input which has two levels, a high level and a low level, an on state and an off state. Similar to input B 1   404 , input C 1   406  is shown to have two levels. However, input C 1   406  may not be a binary input, but may rather be a continuous input. A continuous input may be an input which has more than two input states and/or is continuous rather than discrete. For example, input C 1   406  may contain all values from 0 to 10. However, building controller  402  may characterize input C 1   406  as an input with two discrete values if building controller  402  determines that output Y 1   410  has a linear response to input C 1   406 . Input C 1   406  may have a linear response if Y 1   410  has a linear relationship to input C 1   406 . Because building controller  402  may characterize input C 1   406  as a linear input, building controller  402  may assign two distinct levels to input C 1 , a low level and a high level. In some embodiments, the low level of input C 1   406  may correspond to a particular value of possible C 1   406  values (e.g., 2 in a range of inputs between 0 and 10) while the high level of input C 1   406  may correspond to a particular value of possible C 1   406  values (e.g., 8 in a range of inputs between 0 and 10). 
     C 2   408  may be a continuous input characterized by building controller  402  as having three distinct levels, a low level, a medium level, and a high level. Building controller  402  can be configured to determine if input C 2   408  has a quadratic response. A quadratic response may mean that input C 2   408  causes output Y 1   410  to respond in a quadratic manner to input values of C 2   408 . Building controller  402  can be configured to assign the low level, the medium level, and the high level of input C 2   408  to distinct levels (e.g., 2, 5, and 8 if C 2   408  has a range of inputs from 0-10) in response to determining that output Y 1   410  has a quadratic response to input C 2   408 . 
     Building controller  402  is shown to generate output Y 1   410 . Building controller  402  can generate output Y 1   410  based on inputs B 1   404 , C 1   406 , and C 2   408 . Further, building controller  402  can generate output Y 1   410  based on the various levels and combinations of the levels of inputs B 1   404 , C 1   406 , and C 2   408 . Output Y 1   410  generated by building controller  402  is shown to include 12 distinct values. In this regard, the number of outputs generated by building controller  402  from inputs B 1   404 , C 1   406 , and C 2   408  is finite. 
     Using the combination of levels of the inputs allows building controller  402  to perform a limited and non-exhaustive analysis of inputs B 1   404 , C 1   406 , and C 2   408  to generate output Y 1   410 . For example, the two levels of B 1   404 , C 1   406 , and the three levels of C 2   408  allow for twelve possible combinations of inputs and thus twelve values for output Y 1   410  (e.g., 3*2*2=12). However, if input C 1   406  and C 2   408  were not given distinct and limited levels, the number of values for output Y 1   410 , and hence the number of calculations necessary to generate output Y 1   410 , may exponentially increase. For example, if the two levels of C 1   406  and the three levels of C 2   408  are both taken from a range of 0-10, the number of outputs for Y 1   410  would be 200 (i.e., 10*10*2=200). 
     Building controller  402  can be configured to generate a model for Y 1   410  based on the twelve values of output Y 1   410 . In various embodiments, the model may be generated based on a regression and/or any other analysis technique. The result of the regression may be a model which represents the output Y 1   410  as a function of input B 1   404 , C 1   406 , and C 2   408 . Building controller  402  can be configured to perform various types of regression such as linear regression, multiple linear regression (MLR), logistic regression, polynomial regression, stepwise regression, etc. Building controller  402  can be configured to utilize MLR to create a linear model of a non-linear system (e.g., inputs B 1   404 , C 1   406 , C 2   408 , and output Y 1   410 ) by using least squares fitting. 
     Building controller  402  can be configured to generate output Y 1   420  by using MLR. For example, building controller  402  can be configured to generate the following equation to represent Y 1   410 . In some embodiments, generating the equation below involves determining values for and a with least squares fitting which result in the smallest amount of error between the input x, and the output Ŷ. In the following equation, Ŷ may represent Y 1   420 , β may represent a vector of constants generated by the MLR, x may represent a vector of predictor variables (e.g., inputs B 1   404 , C 1   406 , C 2   408 ) while a may be a constant generated by the MLR.
 
 Ŷ=βx+a   Equation 1
 
     In some embodiments, x, the value representing a vector of the predictor variables, may be an equation of predictor variables. For example, the following equation represents a particular predictor variable, x 1 , as a function of two predictor variables, x B1  and x C1  which may be inputs B 1   404  and input C 1   406 .
 
 x   1 =( x   B1 )( x   C1 )  Equation 2
 
     In some embodiments, the model for output Y 1   410  can be analyzed by building controller  402  to determine if the model is accurate. In some embodiments, the building controller  402  can be configured to generate and use a statistical p-value to determine if the model for output Y 1   420  is accurate. In various embodiments, building controller  402  can be configured to generate and use a coefficient of variation root mean squared error (CVRMSE) value to determine if the model for output Y 1   420  is accurate. Building controller  402  can determine the statistical p-value and the CVRMSE value to determine if the model for output Y 1   410  in terms of inputs B 1   404 , C 1   406 , and C 2   408  is accurate. If the statistical p-value indicates that some of the inputs to the model for output Y 1   410  are not significant, building controller  402  can be configured to discard the insignificant input and re-generate the model for output Y 1   410 . Similarly, building controller  402  can be configured to determine the CVRMSE value to determine the accuracy of the fit of the model for output Y 1   410 . In response to determining that the model for output Y 1   410  is not accurate, building controller  402  can be configured to identify new inputs for the model and re-generate the model for output Y 1   420  based on the additional inputs. 
     The following equation shows a relationship which building controller  402  can be configured to utilize to determine a CVRMSE value for a model for output Y 1   420 , wherein RMSE is root mean squared error and y is the mean of the output of the model for output Y 1   420 . 
     
       
         
           
             
               
                 
                   CVRMSE 
                   = 
                   
                     RMSE 
                     
                       y 
                       _ 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   3 
                 
               
             
           
         
       
     
     Referring now to  FIG. 5 , table  500  illustrating the various combination of the levels of input B 1   404 , input C 1   406 , and input C 2   408  that generate outputs Y 1   410  are shown, according to an exemplary embodiment. Table  500  illustrates the twelve possible combinations of inputs B 1   404 , input C 1   406 , and input C 2   408 . Even through C 1   406  and C 2   408  may have possible inputs exponentially greater than two and three levels and/or even an infinite number of possible inputs, building controller  402  can still generate output values (i.e., Y 1   410 ) which can be used to model output Y 1   410  is terms of the levels that building controller  402  can be configured to define for input B 1   404 , input C 1   406  and input C 2   408 . 
     In this regard, a model for inputs in which some inputs have an infinite number of possible levels can be generated. Further, the number of calculations are reduced proportionally to the number of combinations. In this regard, building controller  402  can generate output Y 1   410  and/or a model for output Y 1   410  faster than an exhaustive calculation approach (e.g., a brute force approach). This may result in faster computing times and less energy consumption as compared to the exhaustive calculation approaches. 
     Referring now to  FIG. 6 , a block diagram of a building management system (BMS)  600  is shown, according to an exemplary embodiment. In some embodiments, BMS  600  is configured to monitor and control building equipment  602  in an online operational environment. For example, BMS  600  can include a METASYS® building management system, a VERASYS® building management system, a central plant optimization system, an energy optimization system, and/or other types of online systems configured to perform real-time control of building equipment  602 . In other embodiments, BMS  600  can be implemented as an offline planning tool configured to simulate the operation of a building or central plant over a predetermined time period (e.g., a day, a month, a week, a year, etc.) for planning, budgeting, and/or design considerations. For example, BMS  600  may use building loads and utility rates to determine an optimal allocation of energy resources across building equipment  602  to minimize cost over a simulation period. However, BMS  600  may not be responsible for real-time control of building equipment  602 . Throughout this disclosure, the term “building management system” is used to describe both the online implementation and the offline implementation. 
     In  FIG. 6 , building controller  402  is shown in greater detail. Building controller  402  is shown to communicate with building equipment  602 . Building equipment  602  may be and/or include the various equipment described with reference to  FIGS. 1-3  (e.g., heaters, chillers, air handling units, pumps, fans, thermal energy storage, etc.) that can be configured to effect environmental changes in a building (e.g., building  10 ). For example, building equipment  602  may be and/or include boiler  104 , chiller  102 , AHU  106 , VAV unit  116 , subplants  202 - 212 , various thermostats, sensors, controllers (e.g., controllers similar to building controller  402 ), and/or any other computing device and/or HVAC device and/or controller. Building controller  402  can be configured to receive data from building equipment  602  and provide control signals to building equipment  602 . In some embodiments, building controller  402  operates building equipment  602  to affect a variable state or condition within the building. 
     Building equipment  602  may store data indicative of various metrics of building equipment  602  and/or other equipment coupled to building equipment  602 . In this regard, the data stored by building equipment  602  may be used to determine an operating cost of a particular piece of building equipment and/or a building (e.g., building  10 ) as a whole. Data such as power consumption  602   a , load metrics  602   b  (e.g., hot loads, cold loads, etc.), specifications  602   c , and schedules  602   d  (e.g., dispatch schedules) can be used to generate the operating cost of the particular piece of building equipment and/or the building or facility as a whole. Building equipment  602  may be configured to communicate data  602   a - 602   d  to building controller  402  automatically, periodically, or based on a request and/or query from building controller  402 . 
     Building controller  402  is shown to include network interface  604  and processing circuit  605 . Building controller  402  can be configured to receive data  602   a - 602   d  from building equipment  602 . Further, building controller  402  can be configured to query building equipment  602  for data  602   a - 602   d . In various embodiments, network interface  604  connects building controller  402  to various building and non-building networks. In this regard, network interface  604  may include various transmitters, network components, connectors, etc. In some embodiments, building controller  402  is configured to store data  602   a - 602   d  in memory (e.g., memory  608 . In this regard, building controller  402  may not be configured to retrieve and/or receive some and/or all of data  602   a - 602   d  from building equipment  602 . 
     Network interface  604  may allow building controller  402  to communicate with various devices, systems, and servers of system  200 . Network interface  604  may allow building controller  402  to communicate with various components of building  10  and/or building equipment  602 . In some embodiments, network interface  604  may allow building controller  402  to communicate with a Wi-Fi network, a wired Ethernet network, a Zigbee network, a Bluetooth network, and/or any other wireless network. Network interface  604  may allow building controller  402  to communicate via a local area network or a wide area network (e.g., the Internet, a building WAN, etc.) that may use a variety of communications protocols (e.g., BACnet, IP, LON, etc.). In some embodiments, network interface  604  may allow building controller  402  to communicate via RS485 communication, RS232 communication, USB communication, fire wire communication, and/or any other communication type. 
     Processing circuit  605  is shown to include processor  606  and memory  608 . Processor  606  can be a general purpose or specific purpose processor, an application specific integrated circuit (ASIC), one or more field programmable gate arrays (FPGAs), a group of processing components, or other suitable processing components. Processor  606  may be configured to execute computer code and/or instructions stored in memory  608  or received from other computer readable media (e.g., CDROM, network storage, a remote server, etc.). 
     Memory  608  can include one or more devices (e.g., memory units, memory devices, storage devices, etc.) for storing data and/or computer code for completing and/or facilitating the various processes described in the present disclosure. Memory  608  can include random access memory (RAM), read-only memory (ROM), hard drive storage, temporary storage, non-volatile memory, flash memory, optical memory, or any other suitable memory for storing software objects and/or computer instructions. Memory  608  can include database components, object code components, script components, or any other type of information structure for supporting the various activities and information structures described in the present disclosure. Memory  608  can be communicably connected to processor  606  via processing circuit  605  and can include computer code for executing (e.g., by processor  606 ) one or more processes described herein. 
     Memory  608  is shown to include FIM model generator  610 . FIM model generator  610  can be configured to identify one or more facility improvement measures (FIMS) and generate a model based on the FIMS. A FIM may be any improvement that can be made to a facility (e.g., building  10 ). A non-exhaustive list of FIMS may be purchasing a building controller for a facility, upgrading a tank size of a chiller, purchasing a variable frequency drive (VFD) for a compressor, etc. These FIMS may increase or decrease the performance of the facility. Further, each upgrade and/or purchase may cost a predefined amount. 
     FIM model generator  610  can determine one or more levels (e.g., sizes) for each FIM. Further, FIM model generator  610  can determine an exhaustive list of combinations of each FIM and each FIM level. An example of FIM levels would be that purchasing a piece of equipment or not purchasing a piece of equipment. This FIM would have two levels, purchase the equipment or do not purchase equipment. However, a FIM such as a chiller may have an large and/or infinite number of chiller sizes. FIM model generator  610  can be configured to select a finite number of levels for the chiller size. FIM model generator  610  can be configured to characterize each FIM as a binary input, a linear continuous input, a quadratic continuous input, etc. In some embodiments, the FIMS may be inputs such as input B 1   404 , input C 1   406 , and input C 2   408 . In this regard, FIM model generator  610  can be configured to select one or more levels for each FIM and generate FIM combinations, an exhaustive number of combinations for each level of each FIM. The FIM combinations can be understood with reference to  FIG. 5  which illustrates a table of exhaustive combinations of levels of input B 1   404 , C 1   406 , and C 2   408  and/or  FIG. 9  which illustrates combinations of FIM levels. 
     FIM model generator  610  may provide the FIM combinations to an operational expense (OPX) model generator  612  and the selected FIMS to a capital expense (CAPX) model generator  614 . OPX model generator  612  can be configured to generate an OPX model. OPX model generator  612  may generate the OPX model based on the FIM combinations received from FIM model generator  610 . In this regard, OPX model generator  612  may be configured to predict an operating cost for each combination of FIM levels (described in greater detail with reference to  FIG. 7 ). OPX model generator  612  can be configured to generate the OPX model by performing a regression (e.g., a multi-linear regression) on the operating expenses of each combination of FIM levels. For example, the equation below illustrates a potential model which FIM model generator  610  can be configured to generate. The OPX model below (Equation 4) illustrates the predicted operating expense Ŷ OPX  for FIMS which include X Tank  representing tank sizes of a TES, X Chiller  represents sizes for a chiller, X Year  represents years so that load growth can be incorporated into the model and utility price escalation, while β 0 -β 7  represent constants generated by the regression:
 
 Ŷ   OPX =β 0 +β 1   X   Tank +β 2 ( X   Tank ) 2 +β 3   X   Chiller +β 4 ( X   Chiller ) 2 +β 5   X   Year +β 6 ( X   Year ) 2 +β 7 ( X   Year )( X   Chiller )  Equation 4
 
     Generating an OPX model with OPX model generator  612  (e.g., Equation 4) based on selected combinations of levels of FIMS may be faster than exhaustively generating the OPX model based on an exhaustive number of combinations of each FIM. However, even though the OPX model is generated based on the selected levels of combinations of the FIMS, the OPX model represents any and all possible FIM level (e.g., continuous inputs that have not been converted into discrete multi-level inputs). 
     The OPX model can be generated from a discrete number of possible combinations. For example, the FIMS, tank, chiller, and year in Equation 4 may each be represented by discrete levels that when exhaustively combined, may have a discrete number of operating costs. The tank FIM may have three possible sizes, the chiller FIM may have 3 possible sizes, while the year may also have three possible sizes. The exhaustive combination of FIMS and FIM levels may be 27 since 3*3*3=27. A discrete operating cost may be generated by OPX model generator  612  for each of the 27 levels. By taking the 27 discrete operating costs and performing a regression on the operating costs, an OPX model, such as Equation 4, can be generated. The OPX model may represent operating expense costs of FIMS beyond the 27 possible combinations. For example, the tank, chiller, and year may have an infinite number of possible sizes within a predefined ranges, that is, they are continuous. This extrapolation and interpolation of operating costs facilitated by the regression and represented by the OPX model that OPX model generator  612  can be configured to generate can represent any possible size or level for each FIM and is not limited to the discrete levels selected for each FIM that are used to generate the OPX model. 
     In some embodiments, OPX model generator  612  can be configured to determine if inputs to an OPX model generated by OPX model generator  612  need to be added and/or removed. In this regard, OPX model generator  612  can be configured analyze the OPX model and determine metrics for the quality of the model. OPX model generator  612  can be configured to determine a statistical p-value for each input to the OPX model and a CVRMSE value for the model. In response to determining that the statistical p-value indicates that one or more inputs to the OPX model are insignificant (e.g., less significant than a predefined amount), OPX model generator  612  can be configured to remove the input from the OPX model and generate a new OPX model. Further, in response to determining that the CVRMSE value is above a predefined amount, OPX model generator  612  can be configured to determine that more inputs need to be incorporated into the OPX model and a new OPX model should be generated based on one or more additional inputs. By generating an OPX model and then iteratively updating the OPX model, OPX model generator  612  can be configured to iteratively improve the quality of the OPX model until various metrics (e.g., a statistical p-value and a CVRMSE value) indicate that the OPX model is acceptable. 
     CAPX model generator  614  can be configured to generate a capital expense (CAPX) model. The CAPX model may represent a capital expense and/or an initial cost of a particular FIM. For example, buying a particular piece of equipment (e.g., a variable speed drive for a compressor) used in a building or facility may have a flat cost (e.g., $100, $500, $1k etc.) associated with the purchase (e.g., the cost of purchasing the equipment). In various embodiments, a continuous input such as a size of a TES may have a cost proportional to and/or otherwise a function of the size of the TES. In this regard, CAPX model generator  614  can be configured to store and/or retrieve a price and/or price function representative of a particular FIM. The equation below illustrates the general form for the CAPX model that may be generated by CAPX model generator  614 . The CAPX model may be understood as a summation of all the cost functions of all the FIMS and in this regard, CAPX model generator  614  can be configured to sum all of the cost functions of all the FIMS to generate the CAPX model. In the equation below, C CAPX  represents the capital expense and/or the CAPX model, n represents the number of FIMS, while ƒ i (X i ) represents the cost function for each FIM: 
     
       
         
           
             
               
                 
                   
                     C 
                     CAPX 
                   
                   = 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       n 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         f 
                         i 
                       
                       ⁡ 
                       
                         ( 
                         
                           X 
                           i 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   5 
                 
               
             
           
         
       
     
     An example of a CAPX model is the equation below. In the equation below, three FIMS were being considered and as such, the CAPX model, C CAPX , is the summation of three terms. In the example, three FIMS are being considered which are a TES tank, a chiller, and a variable speed drive upgrade to a compressor. C Tank  represents the cost of a tank proportional to the size of the tank while X Tank  represents the size of the tank. C Chiller represents the cost of the chiller proportional to the size of the chiller while C Chiller represents the size of the chiller. Finally, C VSD , represents the price of the variable speed drive for the compressor. It is being assumed that the variable speed drive has a flat price, that is, it is being considered as a binary input to the CAPX model.
 
 C   CAPX   =C   Tank   X   Tank   +C   Chiller   X   Chiller   +C   VSD   Equation 6
 
     Baseline model generator  616  can be configured to generate a baseline model. In some embodiments, the baseline model represents an operating cost of a building (e.g., building  10 ) in its current state, that is, without any FIMS. In this regard, baseline model generator  616  can be configured to communicate with building equipment  602  via network interface  604  and retrieve information regarding building equipment  602  (e.g., power consumption  602   a , load metrics  602   b , specifications  602   c , schedules  602   d ). Based on power consumption  602   a , load metrics  602   b , specifications  602   c , and schedules  602   d , baseline model generator  616  can be configured to determine a predicted operating cost of the building or facility. Baseline model generator  616  can be configured to further generate the baseline model based on hot loads and cold loads of various equipment of a building and/or a building, electrical consumption of the equipment and/or the building or facility, the effect which weather (e.g., predicted weather) has on the efficiency of the building equipment, utility rates, etc. In some embodiments, baseline model generator  616  can be configured store and utilize various equipment and building models to generate the baseline model. These equipment and building models, in combination with power consumption  602   a , load metrics  602   b , specifications  602   c , and/or schedules  602   d , and various other variables can be used to predict the power consumption of a piece of equipment and/or the building or facility over a time period (e.g., one month, one year, etc.). The predicted power consumption can be used in combination with utility rates to determine the cost of operating the building or facility. Various examples of using building and equipment models to determine an operating cost (e.g., the functions performed by baseline model generator) can be found in U.S. patent application Ser. No. 14/634,609 filed Feb. 27, 2015, the entirety of which is incorporated by reference herein. 
     Baseline model generator  616  can be configured to generate power consumption of a piece of equipment and/or the building or facility based on the power consumption of the equipment and/or building or facility at one or more points in time. Baseline model generator  616  can be configured to generate the baseline model based on the one or more data points representing the operating cost of the building or facility at the discrete points in time. Baseline model generator  616  can be configured to generate the baseline model by performing a regression (e.g., MLR) on the data points. 
     Baseline model generator  616  can be configured to generate the baseline model to be accurate to the operating cost of the building or facility to a predefined amount (e.g., matches annual operation within +/−5% and/or monthly operating cost within +/−7%). The following equation represents a baseline model. Ŷ Baseline  represents the baseline model, β 0 -β 2  represent constants generated by baseline model generator  616 , and Year represents a year after a starting time (e.g., 1 year, 2 years, etc.) after the baseline model is generated:
 
 Ŷ   Baseline =β 0 β 1 (Year)+β 2 (Year) 2   Equation 7
 
     Objective function generator  618  can be configured to generate an objective function. Objective function generator  618  can be configured to generate the objective function based on the baseline model received from the baseline model received from baseline model generator  616 , the CAPX model received from CAPX model generator  614 , and/or the OPX model received from OPX model generator  612 . In various embodiments, objective function generator  618  can be configured to use one or more models which relate the baseline model, the CAPX model, and/or the OPX model to a predefined variable. The predefined variable may be an internal rate of return (IRR), a net present value (NPV), and/or any other metric. 
     In some embodiments, the CAPX model, the OPX model, and the baseline are terms in a model representing NPV. The equation below represents NPV where NPV is the net present value, C 0  is an initial expenditure, C t  are cashflows, and r is a discount rate applied to all future cashflows and T is the lifespan. 
     
       
         
           
             
               
                 
                   NPV 
                   = 
                   
                     
                       - 
                       
                         C 
                         0 
                       
                     
                     + 
                     
                       
                         ∑ 
                         
                           t 
                           = 
                           1 
                         
                         T 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           C 
                           t 
                         
                         
                           
                             ( 
                             
                               1 
                               + 
                               r 
                             
                             ) 
                           
                           t 
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   8 
                 
               
             
           
         
       
     
     Objective function generator  618  can be configured to utilize equation 8 in terms of the CAPX model, the OPX model, and the baseline model. Objective function generator  618  can be configured to perform the following substitutions into equation 8. 
     
       
         
           
             
               
                 
                   
                     
                       C 
                       0 
                     
                     = 
                     
                       C 
                       CAPX 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       C 
                       t 
                     
                     = 
                     
                       
                         
                           Y 
                           ^ 
                         
                         
                           Baseline 
                           , 
                           t 
                         
                       
                       - 
                       
                         
                           Y 
                           ^ 
                         
                         
                           OPX 
                           , 
                           t 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     NPV 
                     = 
                     
                       
                         - 
                         
                           C 
                           CAPX 
                         
                       
                       + 
                       
                         
                           ∑ 
                           
                             t 
                             = 
                             1 
                           
                           T 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             
                               
                                 Y 
                                 ^ 
                               
                               
                                 Baseline 
                                 , 
                                 t 
                               
                             
                             - 
                             
                               
                                 Y 
                                 ^ 
                               
                               
                                 OPX 
                                 , 
                                 t 
                               
                             
                           
                           
                             
                               ( 
                               
                                 1 
                                 + 
                                 r 
                               
                               ) 
                             
                             t 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equations 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   9 
                   ⁢ 
                   –11 
                 
               
             
           
         
       
     
     Optimizer  620  can be configured to optimize the objective function. In this regard, optimize  620  can be configured to use the objective function to determine optimal FIMS. Optimizer is shown to be configured to receive the objective function from objective function generator  618 . In some embodiments, the optimizer may maximize and/or minimize a particular parameter and/or parameters of the objective function. In this regard, optimizer  620  can be configured to determine optimal FIMS (e.g., an optimal TES tank size, an optimal chiller size, etc.). In various embodiments, the optimizer identifiers optimal FIMS that will optimize a NPV, an IRR, and/or any other metric. In some embodiments, optimizer  620  uses various constraints when performing the optimization. For example, optimizer  620  can be configured to use a maximum and/or minimum equipment size and/or capacity (e.g., equipment size of a FIM) and/or a maximum and/or minimum payback period when optimizing the objective function. In some embodiments, optimizer  620  can be configured to user mixed integer linear programming (MILP) to optimize the objective function (e.g., maximize, minimize, or otherwise optimize, IRR and NPV). Further, optimizer  620  can be configured to use a branch and bound algorithm to optimize the objective function. 
     In some embodiments, optimizer  620  can be configured to modify and/or update the baseline model, the OPX model, the CAPX model, and/or the objective function before identifying the optimal FIMS. For example, in some embodiments, optimizer  620  may implement various investment constraints. For example, a particular FIM may have a minimum capital expense cost. In this regard, optimizer  620  can be configured to update the CAPX model and/or the objective function based on the following relationship, where {acute over (ƒ)} i ({acute over (X)} i ) is the cost function for a particular FIM (i.e., the FIM indexed) while C min  is the minimum capital expense cost. 
     
       
         
           
             
               
                 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       n 
                     
                     ⁢ 
                     
                       
                         
                           f 
                           
                             
                                 
                             
                             ⁢ 
                             ′ 
                           
                         
                         i 
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             X 
                             
                               
                                   
                               
                               ⁢ 
                               ′ 
                             
                           
                           i 
                         
                         ) 
                       
                     
                   
                   ≥ 
                   
                     C 
                     min 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   12 
                 
               
             
           
         
       
     
     Because each FIM is represented by one or more discrete levels, optimizer  620  can be configured to perform a discrete normalization on a data set. The equation for the normalization is below where X′ is the normalized data set, X min  is the minimum data point of the data set, X max  is the maximum data point of the data set, a is the lower bound of the normalization, b is the maximum value of the normalization, while X is the data set before being normalized. Since the design levels are discrete and non-continuous, optimizer  620  can be configured to perform a discrete normalization on each data set. The equation for doing this is shown below. 
     
       
         
           
             
               
                 
                   
                     X 
                     ′ 
                   
                   = 
                   
                     a 
                     + 
                     
                       
                         
                           ( 
                           
                             X 
                             - 
                             
                               X 
                               min 
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             b 
                             - 
                             a 
                           
                           ) 
                         
                       
                       
                         ( 
                         
                           
                             X 
                             max 
                           
                           - 
                           
                             X 
                             min 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   13 
                 
               
             
           
         
       
     
     In some embodiments, optimizer  620  can be configured to determine b by finding the greatest common divisor of the range of available FIM levels. In addition to scaling the input values for the FIMS, optimizer  620  can be configured to adjust the CAPX model. The equation for adjusting the CAPX model is shown below where ƒ i (X i ) is the cost function for a particular FIM while ƒ′ i (X′ i ) is the adjusted cost function. 
     
       
         
           
             
               
                 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       n 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         f 
                         i 
                       
                       ⁡ 
                       
                         ( 
                         
                           X 
                           i 
                         
                         ) 
                       
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       n 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         f 
                         i 
                         ′ 
                       
                       ⁡ 
                       
                         ( 
                         
                           X 
                           i 
                           ′ 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   14 
                 
               
             
           
         
       
     
     Optimizer  620  can be configured to generate the following equation and use the equation to optimize the objective function. Based on the normalized predictor variables generated by optimizer  620  via the normalization, optimizer  620  can be configured to update the OPX model. In this regard, a regression (e.g., multi-linear regression) may be performed to update the OPX model. 
     
       
         
           
             
               
                 
                   
                     
                       f 
                       ′ 
                     
                     ⁡ 
                     
                       ( 
                       
                         X 
                         ′ 
                       
                       ) 
                     
                   
                   = 
                   
                     C 
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             
                               ( 
                               
                                 
                                   X 
                                   ′ 
                                 
                                 - 
                                 a 
                               
                               ) 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   X 
                                   max 
                                 
                                 - 
                                 
                                   X 
                                   min 
                                 
                               
                               ) 
                             
                           
                           
                             ( 
                             
                               b 
                               - 
                               a 
                             
                             ) 
                           
                         
                         + 
                         
                           X 
                           min 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   15 
                 
               
             
           
         
       
     
     Building controller  402  is shown to include user interface  622 . User interface  622  may be a touch screen display configured to receive input from a user and display images and text to a user. In some embodiments, user interface  622  is at least one or a combination of a resistive touch screen and a capacitive touch screen (e.g., projective capacitive touch screen). In some embodiments, user interface  622  is a monitor, a keyboard, a mouse, and/or any other device which may be coupled and/or remotely connected to building controller  402  that is configured to display output from and receive input for building controller  402 . 
     User interface  622  can be configured to allow a user to view various results generated by the various components of memory  608  (e.g., the OPX model, the FIM combinations, the FIMS, the baseline model, the objective function, the results of optimizer  620 , etc.). In this regard, user interface  622  can be configured to display information such as table  900  as described with reference to  FIG. 9 , plots  1002  and  1004  as described with reference to  FIG. 10 , and plots  1102  as described with reference to  FIG. 11 . Further, user interface  622  can receive various inputs from user interface  622  regarding the various models generated. For example, user interface  622  may allow a user to enter, select, and/or manually generate a baseline model, the FIM combinations, the FIMS, form various combinations between the baseline model and the FIM combinations and/or FIMS, the CAPX model, various cost functions for the FIMS, response types for FIMS (e.g., binary, linear, quadratic, etc.), FIM levels, etc. Further, user interface  622  can allow a user to change and/or various models (e.g., FIM combinations, OPX model, FIMS, CAPX model, objective function, baseline model) without building controller  402  having to regenerate the models. The user interface  622  can be configured to allow a user to manually select and/or override which variables are significant in the OPX model. The user interface  622  can be configured to allow a user to substitute one FIM for another, add or remove FIMS, etc. 
     Referring now to  FIG. 7 , various components of memory  608  are shown in greater detail, according to an exemplary embodiment. In  FIG. 7 , OPX model generator  612 , CAPX model generator  614 , and FIM model generator  610  are shown as described with reference to  FIG. 6 . FIM model generator  610  is shown to generate FIMS and FIM combinations. FIM model generator  610  is shown to be configured to provide the FIMS to CAPX model generator  614  and the FIM combinations to OPX model generator  612 . 
     FIM model generator  610  is shown to include existing equipment identifier  702 , equipment upgrade module  704 , FIM identifier  706 , and combination generator  708 . Existing equipment identifier  702  can be configured to communicate with building equipment  602 . In this regard, existing equipment identifier  702  can be configured to determine what existing equipment is in a particular building or facility (e.g., building  10 ). Existing equipment identifier  702  can be configured to receive various identifiers from building equipment  602  which existing equipment identifier  702  can be configured to use to identify existing equipment. In various embodiments, existing equipment identifier  702  may communicate to a database and/or retrieve a list that may be stored by building controller  402  to determine the existing equipment. Existing equipment identifier  702  can be configured to communicate an indication of the existing equipment to FIM identifier  706 . 
     Equipment upgrade module  704  can be configured to store and/or maintain a data structure (e.g., a list) identifying equipment upgrades. In this regard, equipment upgrade module  704  may communicate with a network (e.g., the Internet) via network interface  604 . In some embodiments, equipment upgrade module  704  can be configured to communicate with various servers and/or equipment manufacturers and/or entities selling equipment to determine if there are equipment upgrades for pieces of equipment identified by existing equipment identifier  702  and/or if building  10  can utilize the purchase of a new piece of equipment. Equipment upgrade module  704  is shown to communicate various indications of equipment and/or equipment upgrades that are available for purchase to FIM identifier  706 . 
     FIM identifier  706  can be configured to generate, identify, and/or select one or more FIMS. FIM identifier can be configured to provide the FIMS to CAPX model generator  614  and combination generator  708 . FIM identifier  706  can be configured to receive user input, an indication of existing equipment, and an indication of equipment that is available for purchase. FIM identifier  706  may determine a set of FIMS based on the user input, the indication of existing equipment, and the indication of equipment that is available for purchase. In some embodiments, FIM identifier  706  can be configured to receive one or more requested FIMS via user input. In this regard, a user may identify a specific FIM that they are interested (e.g., a particular building equipment purchase, purchase and/or upgrade of a chiller, etc.). 
     In addition to determining one or more FIMS, FIM identifier  706  can be configured to select one or more levels for the identified FIMS. In this regard, FIM identifier  706  can be configured to determine if the response of a particular FIM is binary, linear, and/or quadratic. The response of a particular FIM may be the relationship between the FIM and the operating cost model. In this regard, FIM identifier  706  may store a response (e.g., binary, linear, and/or quadratic) in FIM response  707 . FIM response  707  may store a response type for various system upgrades. For example, the purchase and/or upgrade of a particular chiller may be a quadratic response while the purchase and/or upgrade of TES may always be linear. FIM identifier  706  can be configured to use the existing equipment indication and the equipment available for upgrade and/or purchase with the FIM response  707  to determine if the FIMS need to be binary, quadratic, or linear. In some embodiments, FIM identifier  706  may be coupled to user interface  622 . In this regard, a user may manually select whether a particular is binary, linear, and/or quadratic via user interface  622  which FIM identifier  706  can be configured to receive and implement. 
     If FIM identifier  706  determines that a FIM is binary, it may assign the FIM two distinct levels (e.g., Low and High). If FIM identifier  706  determines that a FIM is linear, it may assign two distinct FIM levels (Low and High). In response to determining that a FIM is linear, FIM identifier can be configured to determine two levels for the linear FIM. FIM identifier  706  can be configured to use a FIM size range to determine a high level and a low level for the linear FIM. In some embodiments, FIM identifier  706  can be configured to set the high level as an upper half FIM average of the FIM size range and the lower level as a lower half FIM average of the FIM size range. In some embodiments, if the FIM is a new purchase, FIM identifier  706  can be configured to use the largest possible FIM purchase size and the smallest possible FIM purchase size to determine the FIM size range. In some embodiments, if the FIM is an upgrade to and/or a replacement of existing building equipment, FIM identifier  706  can be configured to determine the FIM size range with the current FIM size and the largest possible FIM size. 
     In response to determining that a FIM is quadratic, FIM identifier can be configured to determine three levels for the quadratic FIM. FIM identifier  706  can be configured to use a FIM size range to determine a high level, a medium level, and a low level for the quadratic FIM. In some embodiments, FIM identifier  706  can be configured to set the high level as an upper half FIM average of the FIM size range, the medium level as the average of the FIM size range, and the low level as a lower half FIM average of the FIM size range. In some embodiments, if the FIM is a new purchase, FIM identifier  706  can be configured to use the largest possible FIM purchase size and the smallest possible FIM purchase size as the FIM size range. In some embodiments, if the FIM is an upgrade to and/or a replacement of existing building equipment, FIM identifier  706  can be configured to use the current FIM size and the largest possible FIM size as the size range. 
     In various embodiments, the FIM size ranges can be set and/or adjusted via user input (e.g., user interface  622 ). In some embodiments, a user may indicate what a maximum size is and/or a minimum size for a FIM. Further, a user may be able to manually select a FIM level (e.g., low level, medium level, and high level) directly via user interface  622 . 
     Combination generator  708  can be configured to generate combinations of each FIM and each FIM level. In this regard, FIM combination generator  708  can be configured to exhaustively generate the combinations for each FIM and each FIM level. An example of the result of FIM combinations generated by combination generator  708  is shown in  FIG. 5  or table  900  as described with reference to  FIG. 9 . In  FIG. 5 , each possible combination of levels for input B 1   404 , C 1   406 , and C 2   408  is identified. Combination generator  708  can be configured to generate a data structure, FIM combinations, which includes each combination of each FIM. For example, if there are three FIMS and each FIM has two levels, combination generator  708  will generate six FIM level combinations (e.g., 2*2*2=6). In another case, if there are three FIMS and one FIM has two levels and two FIMS each have three levels, combination generator  708  would generate 18 FIM level combinations (e.g., 2*3*3=18). Combination generator  708  can be configured to provide cost predictor  710  and generator  714  the FIM combinations it generates. 
     OPX model generator  612  is shown to include cost predictor  710 , building and equipment models database  712 , and generator  714 . Cost predictor  710  is shown to receive the FIM combinations generated by combination generator  708 . Cost predictor  710  can be configured to predict an operating cost for each FIM combination. Cost predictor  710  can be configured to use various equipment and/or building models to predict the operating cost of each FIM combination. In some embodiments, the building and/or equipment models are retrieved and/or received from building and equipment models database  712 . Further, cost predictor  710  may use various weather predictions and utility costs to predict the operating cost. Cost predictor  710  can be configured to provide the operating cost of each FIM to generator  714 . An example of the operating costs may be the output values of Y 1   410  (i.e., value 1-value 12) shown in  FIG. 5 . Values 1-12 represent an output value of Y 1   410  for each combination of inputs B 1   404 , C 1   406 , and C 2   408 . Further, an example of the operating costs may be operating costs  908  of table  900  as described with further reference to  FIG. 9 . In  FIG. 9 , table  900  shows operating cost  908  for each combination of tank size  902 , year  904 , and chiller size  906 . 
     Various examples of using building and equipment models to determine an operating cost (e.g., the functions performed by cost predictor  710  and building and equipment models database  712 ) can be found in U.S. patent application Ser. No. 14/634,609 filed Feb. 27, 2015. In some embodiments, cost predictor  710  can be configured to determine one or more optimal setpoints and/or operating settings for building equipment  602  based on the building models, the equipment models, energy consumption predictions, etc. These setpoints and settings may result in energy efficiency, lower run times, etc. for building equipment that is installed and operating in a building or facility. The operating cost generated by cost predictor  710  may be highly accurate (e.g., accurate to a predefined amount) since the operating cost predicted by cost predictor  710  may be based on building or equipment models that are specific to a particular building. The OPX model generated by generator  714  may be highly accurate (e.g., accurate to a predefined amount) since the operating costs received from cost predictor  710  may be highly accurate. Cost predictor  710  can be configured to predict an energy consumption amount for a building and/or building equipment (e.g., building equipment  602 ) and determine an operating cost by multiplying the energy consumption amount by an energy cost. The energy cost may be the cost of a utility (e.g., electricity, water, gas, etc.). 
     In addition to generating the OPX model and the operating cost based on building and equipment models, baseline model generator  616 , as described with reference to  FIG. 6 , can be configured to generate the baseline model based on the equipment and building models. For example, the baseline model may be highly accurate (e.g., accurate above a predefined amount) since the baseline model may be generated based on building models, equipment models, and building equipment energy efficient setpoints and operating settings, etc. Similar to cost predictor  710 , baseline model generator  616  can be configured to determine a predicted energy amount for building equipment and/or a building based on the building models, the equipment models, optimal setpoints and equipment settings, etc. This predicted energy amount may be multiplied by an energy cost of a particular utility (e.g., electricity, water, gas, etc.). 
     Still referring to  FIG. 7 , generator  714  can be configured to generate the OPX model. Generator  714  can be configured to generate the OPX model based on the FIM combinations received from combination generator  708  and the operating cost for each FIM combination received from cost predictor  710 . The OPX model can be an equation similar to the OPX model described in Equation 4. The different FIM levels or the various possible sizes or values for the FIMS may be the dependent variables in the OPX model while the predicted operating cost of the OPX model may be the dependent variable. In various embodiments, generator  714  can be configured to perform a regression (e.g., an MLR) on the FIM combinations and the operating costs to determine the OPX model. 
     Referring now to  FIG. 8 , a process  800  for using design of experiments to determine optimal facility improvements, according to an exemplary embodiment. Building controller  402  can be configured to perform process  800 . Further, the various components of building controller  402  can be configured to perform each and/or some of the steps of process  800 . In step  802 , baseline model generator  616  can generate a baseline model. Baseline model generator  616  may retrieve information regarding equipment in a building. In this regard, baseline model generator  616  can retrieve power consumption  602   a , load metrics  602   b , specifications  602   c , and/or schedules  602   d . Based on power consumption  602   a , load metrics  602   b , specifications  602   c , and schedules  602   d , baseline model generator  616 , various equipment and building models, utility rates, and/or weather data (e.g., weather predictions), baseline model generator  616  can determine a prediction of the power consumption of a piece of equipment, equipment in a building, and/or the building over a time period (e.g., one month, one year, etc.). In some embodiments, baseline model generator  616  can determine the power consumption of a building and/or piece of equipment at one or more discrete points (e.g., data points representing energy consumption and/or operating costs) in time and perform a regression on the data points to determine the baseline model. 
     In step  804 , FIM model generator  610 , or components of FIM model generator  610 , such as FIM identifier  706 , can determine one or more FIMS and/or levels for each FIM. FIM identifier  706  can receive user input via user interface  622  such as an indication of existing equipment in a building, can retrieve an indication of existing equipment and/or equipment that is available for purchase and/or via the Internet, based on a data structure stored by FIM model generator  61 , and/or by communicating with building equipment (e.g., equipment  602 ). FIM identifier  706  can determine one or more FIMS based on the indication of existing equipment and/or the indication of equipment that is available for purchase and/or upgrade. 
     In step  804 , FIM identifier  706  can determine one or more levels for the FIMS. FIM identifier  706  may determine a response (e.g., binary, linear, and/or quadratic) for each FIM. FIM identifier  706  can use the existing equipment indication and/or equipment available for upgrade and/or purchase to determine if each FIM has a binary, quadratic, or linear response. In some embodiments, FIM identifier  706  can determine the response based on an indication of the response for each FIM stored by FIM identifier  706  and/or based on user input via user interface  622 . If FIM identifier  706  determines that a FIM is binary, it may assign the FIM two distinct levels (e.g., Low and High). If FIM identifier  706  determines that a FIM is linear, it may assign two distinct FIM levels (e.g., Low and High). Further, if FIM identifier  706  determines that a FIM is quadratic, it may assign the FIM three distinct FIM levels (e.g., Low, Medium, and High). In step  804 , combination generator  708  can generate combinations of each FIM and each FIM level based on the FIMS and FIM levels identified by FIM identifier  706 . In this regard, FIM combination generator  708  can exhaustively generate combinations of each FIM, and each FIM level. 
     In step  806 , CAPX model generator  614  can generate a CAPX model based on the FIMS determined in step  804 . The CAPX model may represent a capital expense and/or an initial cost of a particular FIM and/or a combination of all the FIMS. CAPX model generator  614  may store and/or retrieve a price and/or price function representative of a particular FIM and sum the cost functions of all the FIMS identified by CAPX model generator  614  to generate the CAPX model. 
     In step  808 , FIM model generator  610  can adjust the FIMS, the FIM levels, and the FIM combinations. In this regard, FIM model generator  610  present the FIMS, the FIM levels, and/or the FIM level combinations to a user via user interface  622 , and/or any other method for communicating to a user. This may allow the user to review the FIMS, the FIM levels, and/or the FIM level combinations and make various changes to the FIMS. For example, a user may want to add a FIM, remove a FIM, change the levels of a FIM if the user believes a FIM is linear rather than quadratic as identified by FIM model generator  610 , etc. If the FIMS and/or FIM levels are adjusted, the process returns to step  804 . In this regard, steps  804  and  806  are performed to generate new FIM level combinations and/or a new capital expense model based on the adjustments to the FIMS and/or the FIM levels as in step  808 . 
     In step  810 , OPX model generator  612  can generate an operating expense model based on the FIM level combinations. OPX model generator  612  may determine an operating cost for each combination of FIM levels. In some embodiments, OPX model generator  612  generates the OPX model based on a regression of the operating expenses of each combination of FIM levels. In some embodiments, cost predictor  710  determines the operating cost for each FIM combination based on various equipment models, building models, weather predictions, utility rates, etc. Generator  714  can generate the OPX model based on the FIM combinations determined in step  804  and the operating cost for each FIM combination determined by cost predictor  710 . In various embodiments, generator  714  can perform a regression (e.g., an MLR) on the FIM combinations and the operating cost for each FIM combination to determine the OPX model. 
     In step  812 , OPX model generator  612  can determine if inputs to the OPX model need to be added and/or removed. In this regard, OPX model generator  612  can analyze the OPX model. In some embodiments, OPX model generator  612  determines a statistical p-value for each input to the OPX model. If the statistical p-value indicates that one or more inputs to the OPX model are insignificant (e.g., less significant than a predefined amount), OPX model generator  612  can perform step  814 . In some embodiments, OPX model generator  612  can determine if the fit of the OPX model is appropriate by calculating a CVRMSE value for the model. If the CVRMSE value calculated is above a predefined amount, OPX model generator  612  may determine that more inputs need to be incorporated into the OPX model and process  800  may advance to step  814 . 
     In step  814 , OPX model generator  612  can remove the insignificant inputs from the OPX model as determined by the statistical p-values. Further, OPX model generator  612  can add one or more inputs to the FIM model which may not have been originally considered based on the CVRMSE value. Process  800  can continue to step  810  where the OPX model is generated. In this regard, steps  810 ,  812 , and  814  may be performed iteratively to generate an OPX model in which each input to the OPX model is significant to a predefined amount and the CVRMSE value for the OPX model is below a predefined amount. 
     In step  816 , objective function generator  618  can generate an objective function based on the OPX model, the CAPX model, and/or the baseline model. In some embodiments, the objective function generated by objective function generator  618  is a NPV function wherein objective function generator  618  uses the OPX model, the CAPX model, and the baseline model as inputs to the NPV function. For example, Equation 9 represents the NPV function while equations 10 and 11 represent the substitution into Equation 9 that objective function generator  618  can perform. The difference between the baseline model and the OPX model may indicate the savings and/or economic benefit to the FIMS (Equation 11). Equation 12 represents the NPV function generated by objective function generator  618  in terms of the CAPX model, the OPX model, and the baseline. 
     
       
         
           
             
               
                 
                   
                     NPV 
                     = 
                     
                       
                         - 
                         
                           C 
                           0 
                         
                       
                       + 
                       
                         
                           ∑ 
                           
                             t 
                             = 
                             1 
                           
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                         ⁢ 
                         
                             
                         
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                               ( 
                               
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                               ) 
                             
                             t 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       C 
                       0 
                     
                     = 
                     
                       C 
                       CAPX 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       C 
                       t 
                     
                     = 
                     
                       
                         
                           Y 
                           ^ 
                         
                         
                           Baseline 
                           , 
                           t 
                         
                       
                       - 
                       
                         
                           Y 
                           ^ 
                         
                         
                           OPX 
                           , 
                           t 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     NPV 
                     = 
                     
                       
                         - 
                         
                           C 
                           CAPX 
                         
                       
                       + 
                       
                         
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                             = 
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                               ) 
                             
                             t 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equations 
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     In step  818 , optimizer  620  can be configured to optimize the objective function. Optimizer  620  may maximize and/or minimize a particular parameter and/or parameters of the objective function. In this regard, optimizer  620  determines optimal FIMS for a building and/or facility. In various embodiments, the optimizer  620  determines FIMS that maximize and/or minimize a NPV, an IRR, and/or any other metric. In step  818 , optimizer  620  may use various constraints when performing the optimization such as a maximum and/or minimum equipment size and/or capacity (e.g., equipment size of a FIM) and/or a maximum and/or minimum payback period. In some embodiments, optimizer  620  uses various methods to optimize the objective function such as mixed integer linear programming. 
     Referring now to  FIG. 9 , a table  900  of FIMS, FIM levels, FIM combinations, and an operating cost for each FIM combination is shown, according to an exemplary embodiment. Building controller  402  can be configured to generate the FIMS, FIM levels, and FIM combinations shown in table  900 . In table  900 , three FIMS are shown. The FIMS are tank size  902  (e.g., tank size for TES), year  904  (e.g., the time after upgrading a FIM), and chiller size  906 . The three FIMS may be FIMS that are determined by FIM model generator  610  and/or FIM identifier  706 . As can be seen, each FIM has three levels, small, medium, and large. This indicates that each FIM is assumed to be quadratic by FIM identifier  706 . FIM identifier  706  can be configured to determine the response for each FIM and in this example, has determined and/or has been instructed that tank size  902 , year  904 , and chiller size  906  should be modeled as quadratic. 
     Operating cost  908  illustrates the operating cost of each FIM level combination. For example, for a small tank size  902 , a small year  904 , and a small chiller size  906 , the operating cost  908  is $9,000,280. However, for a medium tank size  902 , a large year  904 , and a medium chiller size  906  the operating cost is $13,825,434. Twenty seven separate operating costs  908  are shown for the twenty seven FIM level combinations shown in table  900  (i.e., 3*3*3=27). 
     In some embodiments, the operating cost  908  for each FIM level combination can be determined by OPX model generator  612 . From this data, operating cost  908 , OPX model generator  612  can be configured to generate the OPX model. In various embodiments, OPX model generator  612  can perform a regression with the operating cost  908  (e.g., linear regression, multi-linear regression, etc.). 
     Referring now to  FIG. 10 , two interaction plots,  1002  and  1004  are shown, according to an exemplary embodiment. In plot  1002 , the output (e.g., operating cost) is shown with respect to a single input, chillers. In this case, three sizes are being considered for the chiller, size 1, size 2, and size 3. Plot  1004  shows the same output isolated with respect to TES size. Three sizes for the TES are shown. The three levels being considered for the TES size are level 1, level 2, and level 3. 
     Based on the slope of the graphs in plots  1002  and  1004 , the effect that chiller size and TES size have on the output can be seen. A low slope may indicate that an input (e.g., chiller size or TES size) has a low effect on the output while a higher slope may indicate the input may have a greater effect on the output. In this regard, building controller  402  can be configured to generate plots (e.g., plots  1002  and  1004 ) which illustrate the effect which various inputs may have on an output. Building controller  402  can be configured to cause user interface  622  and/or terminal screen to display the various plots so that a user may select and/or otherwise understand the effect which input size and/or level has on an output. 
     Referring now to  FIG. 11 , plots  1102  are shown to illustrate the interactions between two inputs, according to an exemplary embodiment. Plots  1102  indicate whether the combination of one or more variables enhance or degrade the output and/or allow a system and/or user to identify which inputs are necessary for properly modeling a system. Plots  1102  may illustrate the effect which one input has on a second input. Plot  1104  illustrates the relationship between the output and three sizes of a TES and three sizes for a chiller. The chiller sizes, indicated by the solid, dotted, and dashed lines in plot  1104  are all relatively parallel. The more parallel the lines, the less effect the inputs have on each other. Because the lines are relatively parallel, it can be assumed that the effect between the TES size and the chiller size is mild. Similarly, in plot  1106 , the TES sizes, represented by the solid, dotted, and dashed lines, are shown with respect to chiller sizes. Again, the lines in plot  1106  are parallel. Building controller  402  can be configured to generate plots  1104  and  1106  to visually illustrate the effect which various inputs in combination may have on a single output. Building controller  402  can be configured to cause user interface  622  and/or terminal screen to display the plots  1102  so that a user may select and/or otherwise understand the effect which inputs have on each other. 
     Configuration of Exemplary Embodiments 
     The construction and arrangement of the systems and methods as shown in the various exemplary embodiments are illustrative only. Although only a few embodiments have been described in detail in this disclosure, many modifications are possible (e.g., variations in sizes, dimensions, structures, shapes and proportions of the various elements, values of parameters, mounting arrangements, use of materials, colors, orientations, etc.). For example, the position of elements may be reversed or otherwise varied and the nature or number of discrete elements or positions may be altered or varied. Accordingly, all such modifications are intended to be included within the scope of the present disclosure. The order or sequence of any process or method steps may be varied or re-sequenced according to alternative embodiments. Other substitutions, modifications, changes, and omissions may be made in the design, operating conditions and arrangement of the exemplary embodiments without departing from the scope of the present disclosure. 
     The present disclosure contemplates methods, systems and program products on any machine-readable media for accomplishing various operations. The embodiments of the present disclosure may be implemented using existing computer processors, or by a special purpose computer processor for an appropriate system, incorporated for this or another purpose, or by a hardwired system. Embodiments within the scope of the present disclosure include program products comprising machine-readable media for carrying or having machine-executable instructions or data structures stored thereon. Such machine-readable media can be any available media that can be accessed by a general purpose or special purpose computer or other machine with a processor. By way of example, such machine-readable media can comprise RAM, ROM, EPROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to carry or store desired program code in the form of machine-executable instructions or data structures and which can be accessed by a general purpose or special purpose computer or other machine with a processor. When information is transferred or provided over a network or another communications connection (either hardwired, wireless, or a combination of hardwired or wireless) to a machine, the machine properly views the connection as a machine-readable medium. Thus, any such connection is properly termed a machine-readable medium. Combinations of the above are also included within the scope of machine-readable media. Machine-executable instructions include, for example, instructions and data which cause a general purpose computer, special purpose computer, or special purpose processing machines to perform a certain function or group of functions. 
     Although the figures show a specific order of method steps, the order of the steps may differ from what is depicted. Also two or more steps may be performed concurrently or with partial concurrence. Such variation will depend on the software and hardware systems chosen and on designer choice. All such variations are within the scope of the disclosure. Likewise, software implementations could be accomplished with standard programming techniques with rule based logic and other logic to accomplish the various connection steps, processing steps, comparison steps and decision steps.