WO2021016264A1

WO2021016264A1 - Model predictive maintenance system with financial analysis functionality

Info

Publication number: WO2021016264A1
Application number: PCT/US2020/042916
Authority: WO
Inventors: Mohammad N. Elbsat; Michael J. Wenzel; Jingduo Fan
Original assignee: Johnson Controls Technology Company
Priority date: 2019-07-22
Filing date: 2020-07-21
Publication date: 2021-01-28

Abstract

A model predictive maintenance system for building equipment. The system includes one or more processing circuits including one or more processors and memory storing instructions that, when executed by the one or more processors, cause the one or more processors to perform operations. The operations include performing an optimization of an objective function that defines a present value of a total cost of operating the building equipment and performing maintenance on the building equipment as a function of operating decisions and maintenance decisions for the building equipment for time steps within a time period. The total cost includes one or more costs incurred during one or more future time steps of the time period. The operations include operating the building equipment and performing maintenance on the building equipment in accordance with decisions defined by the result of the optimization.

Description

MODEL PREDICTIVE MAINTENANCE SYSTEM WITH FINANCIAL ANALYSIS

FUNCTIONALITY

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

[0001] This application claims the benefit of and priority to U.S. Patent Application No. 16/518,548 filed July 22, 2019, which is a continuation-in-part of U.S. Patent Application No. 16/457,314 filed June 28, 2019, which is a continuation-in-part of U.S. Patent

Application No. 15/895,836 filed February 13, 2018, which claims the benefit of and priority to U.S. Provisional Patent Application No. 62/511,113 filed May 25, 2017. U.S. Patent Application No. 16/518,548 is also a continuation-in-part of U.S. Patent Application No. 15/426,962 filed February 7, 2017. The entire disclosures of all five (5) of these patent applications are incorporated by reference herein.

BACKGROUND

[0002] The present disclosure relates generally to a maintenance system for building equipment and more particularly to a maintenance system that uses a predictive

optimization technique to determine an optimal maintenance strategy for the building equipment.

[0003] Building equipment is typically maintained according to a maintenance strategy for the building equipment. One type of maintenance strategy is run-to-fail. The run-to-fail strategy allows the building equipment to run until a failure occurs. During this running period, only minor operational maintenance tasks (e.g., oil changes) are performed to maintain the building equipment.

[0004] Another type of maintenance strategy is preventative maintenance. The preventative maintenance strategy typically involves performing a set of preventative maintenance tasks recommended by the equipment manufactured. The preventative maintenance tasks are usually performed at regular intervals (e.g., every month, every year, etc.) which may be a function of the elapsed time of operation and/or the run hours of the building equipment. SUMMARY

[0005] One implementation of the present disclosure is a model predictive maintenance system for building equipment, according to some embodiments. The system includes one or more processing circuits including one or more processors and memory storing instructions that, when executed by the one or more processors, cause the one or more processors to perform operations, according to some embodiments. The operations include performing an optimization of an objective function that defines a present value of a total cost of operating the building equipment and performing maintenance on the building equipment as a function of operating decisions and maintenance decisions for the building equipment for time steps within a time period, according to some embodiments. The total cost includes one or more costs incurred during one or more future time steps of the time period, according to some embodiments. The operations include operating the building equipment and performing maintenance on the building equipment in accordance with decisions defined by a result of the optimization, according to some embodiments.

[0006] In some embodiments, the objective function defines the present value as a function of a constant interest rate for the time steps within the time period.

[0007] In some embodiments, the objective function defines the present value as a function of an interest rate that varies over the time period.

[0008] In some embodiments, the objective function further defines a second present value of a total cost of replacing the building equipment as a function of replacement decisions for the building equipment for the time steps within the time period. The total cost of replacing the building equipment includes a cost of replacing the building equipment incurred during a future time step of the time period, according to some embodiments.

[0009] In some embodiments, the objective function further defines a risk cost associated with a failure risk of the building equipment at the time steps of the time period. The risk cost is determined based on a degradation model of the building equipment, according to some embodiments.

[0010] In some embodiments, the present value is a net present value of operating and maintaining the building equipment over the time period. The optimization is performed to minimize the net present value, according to some embodiments. [0011] In some embodiments, the operations further include updating the present value based on closed-loop feedback of the building equipment. The closed-loop feedback of the building equipment is used to update at least one of an efficiency of the building equipment or a reliability of the building equipment, according to some embodiments. The

optimization is performed based on the efficiency of the building equipment and the reliability of the building equipment, according to some embodiments.

[0012] Another implementation of the present disclosure is a method for performing model predictive maintenance of building equipment, according to some embodiments. The method includes performing an optimization of an objective function that defines a present value of a total cost of operating the building equipment and performing maintenance on the building equipment as a function of operating decisions and maintenance decisions for the building equipment for time steps within a time period, according to some embodiments. The total cost includes one or more costs incurred during one or more future time steps of the time period, according to some embodiments. The method includes operating the building equipment and performing maintenance on the building equipment in accordance with decisions defined by a result of the optimization, according to some embodiments.

[0013] In some embodiments, the objective function defines the present value as a function of a constant interest rate for the time steps within the time period.

[0014] In some embodiments, the objective function defines the present value as a function of an interest rate that varies over the time period.

[0015] In some embodiments, the objective function further defines a second present value of a total cost of replacing the building equipment as a function of replacement decisions for the building equipment for the time steps within the time period. The total cost of replacing the building equipment includes a cost of replacing the building equipment incurred during a future time step of the time period, according to some embodiments.

[0016] In some embodiments, the objective function further defines a risk cost associated with a failure risk of the building equipment at the time steps of the time period. The risk cost is determined based on a degradation model of the building equipment, according to some embodiments.

[0017] In some embodiments, the present value is a net present value of operating and maintaining the building equipment over the time period. The optimization is performed to minimize the net present value, according to some embodiments. [0018] In some embodiments, the method includes updating the present value based on closed-loop feedback of the building equipment. The closed-loop feedback of the building equipment used to update at least one of an efficiency of the building equipment or a reliability of the building equipment, according to some embodiments. The optimization is performed based on the efficiency of the building equipment and the reliability of the building equipment, according to some embodiments.

[0019] Another implementation of the present disclosure is a controller for performing model predictive maintenance of building equipment, according to some embodiments. The controller includes one or more processors, according to some embodiments. The controller includes one or more non-transitory computer-readable media storing instructions that, when executed by the one or more processors, cause the one or more processors to perform operations, according to some embodiments. The operations include performing an optimization of an objective function that defines a present value of a total cost of operating the building equipment and performing maintenance on the building equipment as a function of operating decisions and maintenance decisions for the building equipment for time steps within a time period, according to some embodiments. The total cost includes one or more costs incurred during one or more future time steps of the time period, according to some embodiments. The operations include operating the building equipment and performing maintenance on the building equipment in accordance with decisions defined by a result of the optimization, according to some embodiments.

[0020] In some embodiments, the objective function defines the present value as a function of a constant interest rate for the time steps within the time period.

[0021] In some embodiments, the objective function defines the present value as a function of an interest rate that varies over the time period.

[0022] In some embodiments, the objective function further defines a second present value of a total cost of replacing the building equipment as a function of replacement decisions for the building equipment for the time steps within the time period. The total cost of replacing the building equipment includes a cost of replacing the building equipment incurred during a future time step of the time period, according to some embodiments.

[0023] In some embodiments, the objective function further defines a risk cost associated with a failure risk of the building equipment at the time steps of the time period. The risk cost is determined based on a degradation model of the building equipment, according to some embodiments.

[0024] In some embodiments, the present value is a net present value of operating and maintaining the building equipment over the time period. The optimization is performed to minimize the net present value, according to some embodiments.

[0025] Those skilled in the art will appreciate that the summary is illustrative only and is not intended to be in any way limiting. Other aspects, inventive features, and advantages of the devices and/or processes described herein, as defined solely by the claims, will become apparent in the detailed description set forth herein and taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0026] FIG. 1 is a drawing of a building equipped with a HVAC system, according to some embodiments embodiment.

[0027] FIG. 2 is a block diagram of a waterside system which can be used to serve the heating or cooling loads of the building of FIG. 1, according to some embodiments.

[0028] FIG. 3 is a block diagram of an airside system which can be used to serve the heating or cooling loads of the building of FIG. 1, according to some embodiments.

[0029] FIG. 4 is a block diagram of a building management system (BMS) which can be used to monitor and control the building of FIG. 1, according to some embodiments.

[0030] FIG. 5 is a block diagram of another BMS which can be used to monitor and control the building of FIG. 1, according to some embodiments.

[0031] FIG. 6 is a block diagram of a building system including a model predictive maintenance (MPM) system that monitors equipment performance information from connected equipment installed in the building, according to some embodiments.

[0032] FIG. 7 is a schematic diagram of a chiller which may be a type of connected equipment that provides equipment performance information to the MPM system of FIG. 6, according to some embodiments.

[0033] FIG. 8 is a block diagram illustrating the MPM system of FIG. 6 in greater detail, according to some embodiments. [0034] FIG. 9 is a block diagram illustrating a high level optimizer of the MPM system of FIG. 6 in greater detail, according to some embodiments.

[0035] FIG. 10 is a flowchart of a process for operating the MPM system of FIG. 6, according to some embodiments.

[0036] FIG. 11 is a block diagram of the MPM system of FIG. 8 in greater detail, according to some embodiments.

[0037] FIG. 12 is a block diagram further illustrating the high level optimizer of FIG. 9, according to some embodiments.

[0038] FIG. 13 is a graph illustrating differences in a total predicted cost of performing a maintenance activity on building equipment due to an interest rate, according to some embodiments.

[0039] FIG. 14 is a flow diagram of a process for generating an optimal maintenance and replacement strategy for building equipment that accounts for interest rates, according to some embodiments.

DETAILED DESCRIPTION

Overview

[0040] Referring generally to the FIGURES, a model predictive maintenance (MPM) system and components thereof are shown, according to various exemplary embodiments. The MPM system can be configured to determine an optimal maintenance strategy for building equipment. In some embodiments, the optimal maintenance strategy is a set of decisions which optimizes the total cost associated with purchasing, maintaining, and operating the building equipment over the duration of an optimization period (e.g., 30 weeks, 52 weeks, 10 years, 30 years, etc.). The decisions can include, for example, equipment purchase decisions, equipment maintenance decisions, and equipment operating decisions. The MPM system can use a model predictive control technique to formulate an objective function which expresses the total cost as a function of these decisions, which can be included as decision variables in the objective function. The MPM system can optimize (e.g., minimize) the objective function using any of a variety of optimization techniques to identify the optimal values for each of the decision variables.

[0041] One example of an objective function which can be optimized by The MPM system is shown in the following equation:

where C_op,i is the cost per unit of energy (e.g., $/kWh) consumed by the building equipment at time step i of the optimization period, P_op,i is the power consumption (e.g., kW) of the building equipment at time step i, Dt is the duration of each time step i , C_main,i is the cost of maintenance performed on the building equipment at time step i, B_main,i is a binary variable that indicates whether the maintenance is performed, C_cap,i is the capital cost of purchasing a new device of the building equipment at time step i , B_cap,i is a binary variable that indicates whether the new device is purchased, and h is the duration of the horizon or optimization period over which the optimization is performed.

[0042] The first term in the objective function j represents the operating cost of the building equipment over the duration of the optimization period. In some embodiments, the cost per unit of energy C_op,i is received from a utility as energy pricing data. The cost C_op,i may be a time-varying cost that depends on the time of day, the day of the week (e.g., weekday vs. weekend), the current season (e.g., summer vs. winter), or other time-based factors. For example, the cost C_op,i may be higher during peak energy consumption periods and lower during off-peak or partial-peak energy consumption periods.

[0043] In some embodiments, the power consumption P_op,i is based on the heating or cooling load of the building. The heating or cooling load can be predicted by the MPM system as a function of building occupancy, the time of day, the day of the week, the current season, or other factors that can affect the heating or cooling load. In some embodiments, the MPM system uses weather forecasts from a weather service to predict the heating or cooling load. The power consumption P_op,i may also depend on the efficiency hi of the building equipment. For example, building equipment that operate at a high efficiency may consume less power P_op,i to satisfy the same heating or cooling load relative to building equipment that operate at a low efficiency.

[0044] Advantageously, the MPM system can model the efficiency of the building equipment at each time step i as a function of the maintenance decisions B_main,i and the equipment purchase decisions B_cap,i. For example, the efficiency for a particular device may start at an initial value h₀ when the device is purchased and may degrade over time such that the efficiency hi decreases with each successive time step i. Performing maintenance on a device may reset the efficiency hi to a higher value immediately after the maintenance is performed. Similarly, purchasing a new device to replace an existing device may reset the efficiency hi to a higher value immediately after the new device is purchased. After being reset, the efficiency may continue to degrade over time until the next time at which maintenance is performed or a new device is purchased.

[0045] Performing maintenance or purchasing a new device may result in a relatively lower power consumption P_op,i during operation and therefore a lower operating cost at each time step i after the maintenance is performed or the new device is purchased. In other words, performing maintenance or purchasing a new device may decrease the operating cost represented by the first term of the objective function j. However, performing maintenance may increase the second term of the objective function j and purchasing a new device may increase the third term of the objective function j. The objective function j captures each of these costs and can be optimized by the MPM system to determine the optimal set of maintenance and equipment purchase decisions (i.e., optimal values for the binary decision variables B_main,i and B_cap,i ) over the duration of the optimization period.

[0046] In some embodiments, the MPM system uses equipment performance information received as a feedback from the building equipment to estimate the efficiency and/or the reliability of the building equipment. The efficiency may indicate a relationship between the heating or cooling load on the building equipment and the power consumption of the building equipment. The MPM system can use the efficiency to calculate the corresponding value of P_op,i. The reliability may be a statistical measure of the likelihood that the building equipment will continue operating without fault under its current operating conditions. Operating under more strenuous conditions (e.g., high load, high temperatures, etc.) may result in a lower reliability, whereas operating under less strenuous conditions (e.g., low load, moderate temperatures, etc.) may result in a higher reliability. In some embodiments, the reliability is based on an amount of time that has elapsed since the building equipment last received maintenance and/or an amount of time that has elapsed since the building equipment was purchased or installed.

[0047] In some embodiments, the MPM system generates and provides equipment purchase and maintenance recommendations. The equipment purchase and maintenance recommendations may be based on the optimal values for the binary decision variables B_main,i and B_cap,i determined by optimizing the objective function j. For example, a value of B_main,25 = 1 for a particular device of the building equipment may indicate that maintenance should be performed on that device at the 25^th time step of the optimization period, whereas a value of B_main,25 = 0 may indicate that the maintenance should not be performed at that time step. Similarly, a value of B_cap,25 = 1 may indicate that a new device of the building equipment should be purchased at the 25^th time step of the optimization period, whereas a value of B_cap,25 = 0 may indicate that the new device should not be purchased at that time step.

[0048] Advantageously, the equipment purchase and maintenance recommendations generated by the MPM system are predictive recommendations based on the actual operating conditions and actual performance of the building equipment. The optimization performed by the MPM system weighs the cost of performing maintenance and the cost of purchasing new equipment against the decrease in operating cost resulting from such maintenance or purchase decisions in order to determine the optimal maintenance strategy that minimizes the total combined cost j. In this way, the equipment purchase and maintenance recommendations generated by the MPM system may be specific to each group of building equipment in order to achieve the optimal cost j for that specific group of building equipment. The equipment-specific recommendations may result in a lower overall cost j relative to generic preventative maintenance recommendations provided by an equipment manufacturer (e.g., service equipment every year) which may be sub-optimal for some groups of building equipment and/or some operating conditions.

[0049] For estimations made by the MPM system to be accurate, the MPM system account for a time value of money if estimating various costs. The time value of money can refer to how a value of money (and/or another cost) can change over time. For example, if a 5% interest rate is estimated over a next year, $1.00 at a current time can be worth $1.05 at the next year due to a decrease in value of money. The value of money can

increase/decrease for a variety of reasons. As a few examples, the value of money may increase/decrease due to changing federal interest rates, inflation/deflation, etc.

[0050] Interest rates can be incorporated with the objective function j optimized by the MPM system. An example of the objective function j optimized by the MPM system without interest rates can be shown by the following equation:

where c_op,k (d_k ) is an operational cost dependent on a state of degradation d_k, c_main,k is a cost of maintenance at a time step k of a horizon or an optimization period, c_replace,k is a cost of maintenance at a time step k of the horizon or optimization period, m_k is a binary vector representing which maintenance actions are taken at time step k , p_fail,k (dk) is a vector of probabilities of failure for each tracked component of the system during the time step k and dependent on the degradation state d_k, and c_fail,k is a vector of costs of failure for each of the tracked components of the system. The probability of failure p_fail,k (dk) ^can be multiplied by the costs of failure c_fail,k (repair cost and opportunity cost) to form a risk term in the cost function.

[0051] The objective function j shown above can be augmented to include a time cost of money at each time step k of the optimization period. For example, the MPM system can optimize the following objective function j:

where a_k is a time cost of money at time step k. In particular, a_k can be given by the following:

where r is an interest rate. As shown, a_k can assume a constant interest rate such that the interest rate does not change over the horizon or optimization period. However, a time- varying interest rate can be used to calculate a_{k .} Specifically, a_k with time-varying interest rates can be given by the following:

where r_i is an interest rate at a time step i such that i £ k. In other words, a_k with time- varying interest rates can be calculated as a product of each interest rate for each time step through time step k. In this case, a_k can be provided for each time step during the optimization period based on interest rates from a first time step through time step k.

[0052] Advantageously, integration of the interest rate into the objective function j can be independent of what optimization method (e.g., integer programming, mixed integer linear programming, stochastic optimization, convex programming, dynamic programming, etc.) is used. In this way, the interest rates can be captured in the objective function j without a need for separate implementation dependent on an optimization method used. These and other features of the MPM system are described in detail below.

Building HVAC Systems and Building Management Systems

[0053] Referring now to FIGS. 1-5, several building management systems (BMS) and HVAC systems in which the systems and methods of the present disclosure can be implemented are shown, according to some embodiments. In brief overview, FIG. 1 shows a building 10 equipped with a HVAC system 100. FIG. 2 is a block diagram of a waterside system 200 which can be used to serve building 10. FIG. 3 is a block diagram of an airside system 300 which can be used to serve building 10. FIG. 4 is a block diagram of a BMS which can be used to monitor and control building 10. FIG. 5 is a block diagram of another BMS which can be used to monitor and control building 10.

Building and HVAC System

[0054] 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.

[0055] The BMS that serves building 10 includes a 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 may provide a heated or chilled fluid to an air handling unit of airside system 130. Airside system 130 may 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.

[0056] HVAC system 100 is shown to include a chiller 102, a boiler 104, and a rooftop air handling unit (AHU) 106. Waterside system 120 may use boiler 104 and chiller 102 to heat or cool a working fluid (e.g., water, glycol, etc.) and may 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 may 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 may 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.

[0057] AHU 106 may 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 may 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 may then return to chiller 102 or boiler 104 via piping 110.

[0058] Airside system 130 may deliver the airflow supplied by AHU 106 (i.e., the supply airflow) to building 10 via air supply ducts 112 and may 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 may receive input from sensors located within AHU 106 and/or within the building zone and may adjust the flow rate, temperature, or other attributes of the supply airflow through AHU 106 to achieve setpoint conditions for the building zone. Waterside System

[0059] Referring now to FIG. 2, a block diagram of a waterside system 200 is shown, according to some embodiments. In various embodiments, waterside system 200 may 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 may 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.

[0060] 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 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 may 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 may store hot and cold thermal energy, respectively, for subsequent use.

[0061] Hot water loop 214 and cold water loop 216 may 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 thermal energy loads of building 10. The water then returns to subplants 202-212 to receive further heating or cooling.

[0062] 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, C02, etc.) can be used in place of or in addition to water to serve thermal energy loads. In other embodiments, subplants 202-212 may 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 disclosure.

[0063] 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.

[0064] 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.

[0065] 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 may 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 may 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.

[0066] 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.

Airside System

[0067] Referring now to FIG. 3, a block diagram of an airside system 300 is shown, according to some embodiments. In various embodiments, airside system 300 may 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 may operate to heat or cool an airflow provided to building 10 using a heated or chilled fluid provided by waterside system 200.

[0068] 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 may receive return air 304 from building zone 306 via return air duct 308 and may 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.

[0069] 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 may communicate with an AHU controller 330 via a communications link 332.

Actuators 324-328 may receive control signals from AHU controller 330 and may 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.

[0070] 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 may 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.

[0071] Cooling coil 334 may receive a chilled fluid from waterside system 200 (e.g., from cold water loop 216) via piping 342 and may 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.

[0072] Heating coil 336 may receive a heated fluid from waterside system 200(e.g., from hot water loop 214) via piping 348 and may 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.

[0073] 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 may communicate with AHU controller 330 via communications links 358-360. Actuators 354-356 may receive control signals from AHU controller 330 and may 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 may also receive a measurement of the temperature of building zone 306 from a temperature sensor 364 located in building zone 306.

[0074] 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 330 may 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.

[0075] 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 may 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. [0076] 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 may 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.

[0077] 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 may communicate with BMS controller 366 and/or AHU controller 330 via

communications link 372.

Building Management Systems

[0078] Referring now to FIG. 4, a block diagram of a building management system (BMS) 400 is shown, according to some embodiments. BMS 400 can be implemented in building 10 to automatically monitor and control various building functions. BMS 400 is shown to include BMS controller 366 and a plurality of building subsystems 428. Building subsystems 428 are shown to include a building electrical subsystem 434, an information communication technology (ICT) subsystem 436, a security subsystem 438, a HVAC subsystem 440, a lighting subsystem 442, a lift/escalators subsystem 432, and a fire safety subsystem 430. In various embodiments, building subsystems 428 can include fewer, additional, or alternative subsystems. For example, building subsystems 428 may also or alternatively include a refrigeration subsystem, an advertising or signage subsystem, a cooking subsystem, a vending subsystem, a printer or copy service subsystem, or any other type of building subsystem that uses controllable equipment and/or sensors to monitor or control building 10. In some embodiments, building subsystems 428 include waterside system 200 and/or airside system 300, as described with reference to FIGS. 2-3.

[0079] Each of building subsystems 428 can include any number of devices, controllers, and connections for completing its individual functions and control activities. HVAC subsystem 440 can include many of the same components as HVAC system 100, as described with reference to FIGS. 1-3. For example, HVAC subsystem 440 can include a chiller, a boiler, any number of air handling units, economizers, field controllers, supervisory controllers, actuators, temperature sensors, and other devices for controlling the temperature, humidity, airflow, or other variable conditions within building 10. Lighting subsystem 442 can include any number of light fixtures, ballasts, lighting sensors, dimmers, or other devices configured to controllably adjust the amount of light provided to a building space. Security subsystem 438 can include occupancy sensors, video surveillance cameras, digital video recorders, video processing servers, intrusion detection devices, access control devices and servers, or other security-related devices.

[0080] Still referring to FIG. 4, BMS controller 366 is shown to include a

communications interface 407 and a BMS interface 409. Interface 407 may facilitate communications between BMS controller 366 and external applications (e.g., monitoring and reporting applications 422, enterprise control applications 426, remote systems and applications 444, applications residing on client devices 448, etc.) for allowing user control, monitoring, and adjustment to BMS controller 366 and/or subsystems 428. Interface 407 may also facilitate communications between BMS controller 366 and client devices 448. BMS interface 409 may facilitate communications between BMS controller 366 and building subsystems 428 (e.g., HVAC, lighting security, lifts, power distribution, business, etc.).

[0081] Interfaces 407, 409 can be or include wired or wireless communications interfaces (e.g., jacks, antennas, transmitters, receivers, transceivers, wire terminals, etc.) for conducting data communications with building subsystems 428 or other external systems or devices. In various embodiments, communications via interfaces 407, 409 can be direct (e.g., local wired or wireless communications) or via a communications network 446 (e.g., a WAN, the Internet, a cellular network, etc.). For example, interfaces 407, 409 can include an Ethernet card and port for sending and receiving data via an Ethernet-based

communications link or network. In another example, interfaces 407, 409 can include a Wi Fi transceiver for communicating via a wireless communications network. In another example, one or both of interfaces 407, 409 can include cellular or mobile phone

communications transceivers. In one embodiment, communications interface 407 is a power line communications interface and BMS interface 409 is an Ethernet interface. In other embodiments, both communications interface 407 and BMS interface 409 are Ethernet interfaces or are the same Ethernet interface.

[0082] Still referring to FIG. 4, BMS controller 366 is shown to include a processing circuit 404 including a processor 406 and memory 408. Processing circuit 404 can be communicably connected to BMS interface 409 and/or communications interface 407 such that processing circuit 404 and the various components thereof can send and receive data via interfaces 407, 409. Processor 406 can be implemented as a general purpose processor, an application specific integrated circuit (ASIC), one or more field programmable gate arrays (FPGAs), a group of processing components, or other suitable electronic processing components.

[0083] Memory 408 (e.g., memory, memory unit, storage device, etc.) can include one or more devices (e.g., RAM, ROM, Flash memory, hard disk storage, etc.) for storing data and/or computer code for completing or facilitating the various processes, layers and modules described in the present application. Memory 408 can be or include volatile memory or non-volatile memory. Memory 408 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 application. According to some embodiments, memory 408 is communicably connected to processor 406 via processing circuit 404 and includes computer code for executing (e.g., by processing circuit 404 and/or processor 406) one or more processes described herein.

[0084] In some embodiments, BMS controller 366 is implemented within a single computer (e.g., one server, one housing, etc.). In various other embodiments BMS controller 366 can be distributed across multiple servers or computers (e.g., that can exist in distributed locations). Further, while FIG. 4 shows applications 422 and 426 as existing outside of BMS controller 366, in some embodiments, applications 422 and 426 can be hosted within BMS controller 366 (e.g., within memory 408).

[0085] Still referring to FIG. 4, memory 408 is shown to include an enterprise integration layer 410, an automated measurement and validation (AM&V) layer 412, a demand response (DR) layer 414, a fault detection and diagnostics (FDD) layer 416, an integrated control layer 418, and a building subsystem integration later 420. Layers 410-420 can be configured to receive inputs from building subsystems 428 and other data sources, determine optimal control actions for building subsystems 428 based on the inputs, generate control signals based on the optimal control actions, and provide the generated control signals to building subsystems 428. The following paragraphs describe some of the general functions performed by each of layers 410-420 in BMS 400.

[0086] Enterprise integration layer 410 can be configured to serve clients or local applications with information and services to support a variety of enterprise-level applications. For example, enterprise control applications 426 can be configured to provide subsystem-spanning control to a graphical user interface (GUI) or to any number of enterprise-level business applications (e.g., accounting systems, user identification systems, etc.). Enterprise control applications 426 may also or alternatively be configured to provide configuration GUIs for configuring BMS controller 366. In yet other embodiments, enterprise control applications 426 can work with layers 410-420 to optimize building performance (e.g., efficiency, energy use, comfort, or safety) based on inputs received at interface 407 and/or BMS interface 409.

[0087] Building subsystem integration layer 420 can be configured to manage

communications between BMS controller 366 and building subsystems 428. For example, building subsystem integration layer 420 may receive sensor data and input signals from building subsystems 428 and provide output data and control signals to building subsystems 428. Building subsystem integration layer 420 may also be configured to manage communications between building subsystems 428. Building subsystem integration layer 420 translate communications (e.g., sensor data, input signals, output signals, etc.) across a plurality of multi-vendor/multi-protocol systems.

[0088] Demand response layer 414 can be configured to optimize resource usage (e.g., electricity use, natural gas use, water use, etc.) and/or the monetary cost of such resource usage in response to satisfy the demand of building 10. The optimization can be based on time-of-use prices, curtailment signals, energy availability, or other data received from utility providers, distributed energy generation systems 424, from energy storage 427 (e.g., hot TES 242, cold TES 244, etc.), or from other sources. Demand response layer 414 may receive inputs from other layers of BMS controller 366 (e.g., building subsystem integration layer 420, integrated control layer 418, etc.). The inputs received from other layers can include environmental or sensor inputs such as temperature, carbon dioxide levels, relative humidity levels, air quality sensor outputs, occupancy sensor outputs, room schedules, and the like. The inputs may also include inputs such as electrical use (e.g., expressed in kWh), thermal load measurements, pricing information, projected pricing, smoothed pricing, curtailment signals from utilities, and the like.

[0089] According to some embodiments, demand response layer 414 includes control logic for responding to the data and signals it receives. These responses can include communicating with the control algorithms in integrated control layer 418, changing control strategies, changing setpoints, or activating/deactivating building equipment or subsystems in a controlled manner. Demand response layer 414 may also include control logic configured to determine when to utilize stored energy. For example, demand response layer 414 may determine to begin using energy from energy storage 427 just prior to the beginning of a peak use hour.

[0090] In some embodiments, demand response layer 414 includes a control module configured to actively initiate control actions (e.g., automatically changing setpoints) which minimize energy costs based on one or more inputs representative of or based on demand (e.g., price, a curtailment signal, a demand level, etc.). In some embodiments, demand response layer 414 uses equipment models to determine an optimal set of control actions. The equipment models can include, for example, thermodynamic models describing the inputs, outputs, and/or functions performed by various sets of building equipment.

Equipment models may represent collections of building equipment (e.g., subplants, chiller arrays, etc.) or individual devices (e.g., individual chillers, heaters, pumps, etc.).

[0091] Demand response layer 414 may further include or draw upon one or more demand response policy definitions (e.g., databases, XML files, etc.). The policy definitions can be edited or adjusted by a user (e.g., via a graphical user interface) so that the control actions initiated in response to demand inputs can be tailored for the user’s application, desired comfort level, particular building equipment, or based on other concerns. For example, the demand response policy definitions can specify which equipment can be turned on or off in response to particular demand inputs, how long a system or piece of equipment should be turned off, what setpoints can be changed, what the allowable set point adjustment range is, how long to hold a high demand setpoint before returning to a normally scheduled setpoint, how close to approach capacity limits, which equipment modes to utilize, the energy transfer rates (e.g., the maximum rate, an alarm rate, other rate boundary information, etc.) into and out of energy storage devices (e.g., thermal storage tanks, battery banks, etc.), and when to dispatch on-site generation of energy (e.g., via fuel cells, a motor generator set, etc.).

[0092] Integrated control layer 418 can be configured to use the data input or output of building subsystem integration layer 420 and/or demand response later 414 to make control decisions. Due to the subsystem integration provided by building subsystem integration layer 420, integrated control layer 418 can integrate control activities of the subsystems 428 such that the subsystems 428 behave as a single integrated supersystem. In some embodiments, integrated control layer 418 includes control logic that uses inputs and outputs from a plurality of building subsystems to provide greater comfort and energy savings relative to the comfort and energy savings that separate subsystems could provide alone. For example, integrated control layer 418 can be configured to use an input from a first subsystem to make an energy-saving control decision for a second subsystem. Results of these decisions can be communicated back to building subsystem integration layer 420.

[0093] Integrated control layer 418 is shown to be logically below demand response layer 414. Integrated control layer 418 can be configured to enhance the effectiveness of demand response layer 414 by enabling building subsystems 428 and their respective control loops to be controlled in coordination with demand response layer 414. This configuration may advantageously reduce disruptive demand response behavior relative to conventional systems. For example, integrated control layer 418 can be configured to assure that a demand response-driven upward adjustment to the setpoint for chilled water temperature (or another component that directly or indirectly affects temperature) does not result in an increase in fan energy (or other energy used to cool a space) that would result in greater total building energy use than was saved at the chiller.

[0094] Integrated control layer 418 can be configured to provide feedback to demand response layer 414 so that demand response layer 414 checks that constraints (e.g., temperature, lighting levels, etc.) are properly maintained even while demanded load shedding is in progress. The constraints may also include setpoint or sensed boundaries relating to safety, equipment operating limits and performance, comfort, fire codes, electrical codes, energy codes, and the like. Integrated control layer 418 is also logically below fault detection and diagnostics layer 416 and automated measurement and validation layer 412. Integrated control layer 418 can be configured to provide calculated inputs (e.g., aggregations) to these higher levels based on outputs from more than one building subsystem. [0095] Automated measurement and validation (AM&V) layer 412 can be configured to verify that control strategies commanded by integrated control layer 418 or demand response layer 414 are working properly (e.g., using data aggregated by AM&V layer 412, integrated control layer 418, building subsystem integration layer 420, FDD layer 416, or otherwise). The calculations made by AM&V layer 412 can be based on building system energy models and/or equipment models for individual BMS devices or subsystems. For example, AM&V layer 412 may compare a model-predicted output with an actual output from building subsystems 428 to determine an accuracy of the model.

[0096] Fault detection and diagnostics (FDD) layer 416 can be configured to provide on going fault detection for building subsystems 428, building subsystem devices (i.e., building equipment), and control algorithms used by demand response layer 414 and integrated control layer 418. FDD layer 416 may receive data inputs from integrated control layer 418, directly from one or more building subsystems or devices, or from another data source. FDD layer 416 may automatically diagnose and respond to detected faults. The responses to detected or diagnosed faults can include providing an alert message to a user, a maintenance scheduling system, or a control algorithm configured to attempt to repair the fault or to work-around the fault.

[0097] FDD layer 416 can be configured to output a specific identification of the faulty component or cause of the fault (e.g., loose damper linkage) using detailed subsystem inputs available at building subsystem integration layer 420. In other exemplary embodiments, FDD layer 416 is configured to provide“fault” events to integrated control layer 418 which executes control strategies and policies in response to the received fault events. According to some embodiments, FDD layer 416 (or a policy executed by an integrated control engine or business rules engine) may shut-down systems or direct control activities around faulty devices or systems to reduce energy waste, extend equipment life, or assure proper control response.

[0098] FDD layer 416 can be configured to store or access a variety of different system data stores (or data points for live data). FDD layer 416 may use some content of the data stores to identify faults at the equipment level (e.g., specific chiller, specific AHU, specific terminal unit, etc.) and other content to identify faults at component or subsystem levels.

For example, building subsystems 428 may generate temporal (i.e., time-series) data indicating the performance of BMS 400 and the various components thereof. The data generated by building subsystems 428 can include measured or calculated values that exhibit statistical characteristics and provide information about how the corresponding system or process (e.g., a temperature control process, a flow control process, etc.) is performing in terms of error from its setpoint. These processes can be examined by FDD layer 416 to expose when the system begins to degrade in performance and alert a user to repair the fault before it becomes more severe.

[0099] Referring now to FIG. 5, a block diagram of another building management system (BMS) 500 is shown, according to some embodiments. BMS 500 can be used to monitor and control the devices of HVAC system 100, waterside system 200, airside system 300, building subsystems 428, as well as other types of BMS devices (e.g., lighting equipment, security equipment, etc.) and/or HVAC equipment.

[0100] BMS 500 provides a system architecture that facilitates automatic equipment discovery and equipment model distribution. Equipment discovery can occur on multiple levels of BMS 500 across multiple different communications busses (e.g., a system bus 554, zone buses 556-560 and 564, sensor/actuator bus 566, etc.) and across multiple different communications protocols. In some embodiments, equipment discovery is accomplished using active node tables, which provide status information for devices connected to each communications bus. For example, each communications bus can be monitored for new devices by monitoring the corresponding active node table for new nodes. When a new device is detected, BMS 500 can begin interacting with the new device (e.g., sending control signals, using data from the device) without user interaction.

[0101] Some devices in BMS 500 present themselves to the network using equipment models. An equipment model defines equipment object attributes, view definitions, schedules, trends, and the associated BACnet value objects (e.g., analog value, binary value, multistate value, etc.) that are used for integration with other systems. Some devices in BMS 500 store their own equipment models. Other devices in BMS 500 have equipment models stored externally (e.g., within other devices). For example, a zone coordinator 508 can store the equipment model for a bypass damper 528. In some embodiments, zone coordinator 508 automatically creates the equipment model for bypass damper 528 or other devices on zone bus 558. Other zone coordinators can also create equipment models for devices connected to their zone busses. The equipment model for a device can be created automatically based on the types of data points exposed by the device on the zone bus, device type, and/or other device attributes. Several examples of automatic equipment discovery and equipment model distribution are discussed in greater detail below. [0102] Still referring to FIG. 5, BMS 500 is shown to include a system manager 502; several zone coordinators 506, 508, 510 and 518; and several zone controllers 524, 530,

532, 536, 548, and 550. System manager 502 can monitor data points in BMS 500 and report monitored variables to various monitoring and/or control applications. System manager 502 can communicate with client devices 504 (e.g., user devices, desktop computers, laptop computers, mobile devices, etc.) via a data communications link 574 (e.g., BACnet IP, Ethernet, wired or wireless communications, etc.). System manager 502 can provide a user interface to client devices 504 via data communications link 574. The user interface may allow users to monitor and/or control BMS 500 via client devices 504.

[0103] In some embodiments, system manager 502 is connected with zone coordinators 506-510 and 518 via a system bus 554. System manager 502 can be configured to communicate with zone coordinators 506-510 and 518 via system bus 554 using a master- slave token passing (MSTP) protocol or any other communications protocol. System bus 554 can also connect system manager 502 with other devices such as a constant volume (CV) rooftop unit (RTU) 512, an input/output module (IOM) 514, a thermostat controller 516 (e.g., a TEC5000 series thermostat controller), and a network automation engine (NAE) or third-party controller 520. RTU 512 can be configured to communicate directly with system manager 502 and can be connected directly to system bus 554. Other RTUs can communicate with system manager 502 via an intermediate device. For example, a wired input 562 can connect a third-party RTU 542 to thermostat controller 516, which connects to system bus 554.

[0104] System manager 502 can provide a user interface for any device containing an equipment model. Devices such as zone coordinators 506-510 and 518 and thermostat controller 516 can provide their equipment models to system manager 502 via system bus 554. In some embodiments, system manager 502 automatically creates equipment models for connected devices that do not contain an equipment model (e.g., IOM 514, third party controller 520, etc.). For example, system manager 502 can create an equipment model for any device that responds to a device tree request. The equipment models created by system manager 502 can be stored within system manager 502. System manager 502 can then provide a user interface for devices that do not contain their own equipment models using the equipment models created by system manager 502. In some embodiments, system manager 502 stores a view definition for each type of equipment connected via system bus 554 and uses the stored view definition to generate a user interface for the equipment. [0105] Each zone coordinator 506-510 and 518 can be connected with one or more of zone controllers 524, 530-532, 536, and 548-550 via zone buses 556, 558, 560, and 564. Zone coordinators 506-510 and 518 can communicate with zone controllers 524, 530-532, 536, and 548-550 via zone busses 556-560 and 564 using a MSTP protocol or any other communications protocol. Zone busses 556-560 and 564 can also connect zone

coordinators 506-510 and 518 with other types of devices such as variable air volume (VAV) RTUs 522 and 540, changeover bypass (COBP) RTUs 526 and 552, bypass dampers 528 and 546, and PEAK controllers 534 and 544.

[0106] Zone coordinators 506-510 and 518 can be configured to monitor and command various zoning systems. In some embodiments, each zone coordinator 506-510 and 518 monitors and commands a separate zoning system and is connected to the zoning system via a separate zone bus. For example, zone coordinator 506 can be connected to VAV RTU 522 and zone controller 524 via zone bus 556. Zone coordinator 508 can be connected to COBP RTU 526, bypass damper 528, COBP zone controller 530, and VAV zone controller 532 via zone bus 558. Zone coordinator 510 can be connected to PEAK controller 534 and VAV zone controller 536 via zone bus 560. Zone coordinator 518 can be connected to PEAK controller 544, bypass damper 546, COBP zone controller 548, and VAV zone controller 550 via zone bus 564.

[0107] A single model of zone coordinator 506-510 and 518 can be configured to handle multiple different types of zoning systems (e.g., a VAV zoning system, a COBP zoning system, etc.). Each zoning system can include a RTU, one or more zone controllers, and/or a bypass damper. For example, zone coordinators 506 and 510 are shown as Verasys VAV engines (VVEs) connected to VAV RTUs 522 and 540, respectively. Zone coordinator 506 is connected directly to VAV RTU 522 via zone bus 556, whereas zone coordinator 510 is connected to a third-party VAV RTU 540 via a wired input 568 provided to PEAK controller 534. Zone coordinators 508 and 518 are shown as Verasys COBP engines (VCEs) connected to COBP RTUs 526 and 552, respectively. Zone coordinator 508 is connected directly to COBP RTU 526 via zone bus 558, whereas zone coordinator 518 is connected to a third-party COBP RTU 552 via a wired input 570 provided to PEAK controller 544.

[0108] Zone controllers 524, 530-532, 536, and 548-550 can communicate with individual BMS devices (e.g., sensors, actuators, etc.) via sensor/actuator (SA) busses. For example, VAV zone controller 536 is shown connected to networked sensors 538 via SA bus 566. Zone controller 536 can communicate with networked sensors 538 using a MSTP protocol or any other communications protocol. Although only one SA bus 566 is shown in FIG. 5, it should be understood that each zone controller 524, 530-532, 536, and 548-550 can be connected to a different SA bus. Each SA bus can connect a zone controller with various sensors (e.g., temperature sensors, humidity sensors, pressure sensors, light sensors, occupancy sensors, etc.), actuators (e.g., damper actuators, valve actuators, etc.) and/or other types of controllable equipment (e.g., chillers, heaters, fans, pumps, etc.).

[0109] Each zone controller 524, 530-532, 536, and 548-550 can be configured to monitor and control a different building zone. Zone controllers 524, 530-532, 536, and 548-550 can use the inputs and outputs provided via their SA busses to monitor and control various building zones. For example, a zone controller 536 can use a temperature input received from networked sensors 538 via SA bus 566 (e.g., a measured temperature of a building zone) as feedback in a temperature control algorithm. Zone controllers 524, 530-532, 536, and 548-550 can use various types of 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 a variable state or condition (e.g., temperature, humidity, airflow, lighting, etc.) in or around building 10.

Model Predictive Maintenance System

[0110] Referring now to FIG. 6, a block diagram of a building system 600 is shown, according to an exemplary embodiment. System 600 may include many of the same components as BMS 400 and BMS 500 as described with reference to FIGS. 4-5. For example, system 600 is shown to include building 10, network 446, and client devices 448. Building 10 is shown to include connected equipment 610, which can include any type of equipment used to monitor and/or control building 10. Connected equipment 610 can include connected chillers 612, connected AHUs 614, connected boilers 616, connected batteries 618, or any other type of equipment in a building system (e.g., heaters,

economizers, valves, actuators, dampers, cooling towers, fans, pumps, etc.) or building management system (e.g., lighting equipment, security equipment, refrigeration equipment, etc.). Connected equipment 610 can include any of the equipment of HVAC system 100, waterside system 200, airside system 300, BMS 400, and/or BMS 500, as described with reference to FIGS. 1-5. [0111] Connected equipment 610 can be outfitted with sensors to monitor various conditions of the connected equipment 610 (e.g., power consumption, on/off states, operating efficiency, etc.). For example, chillers 612 can include sensors configured to monitor chiller variables such as chilled water temperature, condensing water temperature, and refrigerant properties (e.g., refrigerant pressure, refrigerant temperature, etc.) at various locations in the refrigeration circuit. An example of a chiller 700 which can be used as one of chillers 612 is shown in FIG. 7. Chiller 700 is shown to include a refrigeration circuit having a condenser 702, an expansion valve 704, an evaporator 706, a compressor 708, and a control panel 710. In some embodiments, chiller 700 includes sensors that measure a set of monitored variables at various locations along the refrigeration circuit. Similarly, AHUs 614 can be outfitted with sensors to monitor AHU variables such as supply air temperature and humidity, outside air temperature and humidity, return air temperature and humidity, chilled fluid temperature, heated fluid temperature, damper position, etc. In general, connected equipment 610 can monitor and report variables that characterize the

performance of the connected equipment 610. Each monitored variable can be forwarded to building management system 606 as a data point including a point ID and a point value.

[0112] Monitored variables can include any measured or calculated values indicating the performance of connected equipment 610 and/or the components thereof. For example, monitored variables can include one or more measured or calculated temperatures (e.g., refrigerant temperatures, cold water supply temperatures, hot water supply temperatures, supply air temperatures, zone temperatures, etc.), pressures (e.g., evaporator pressure, condenser pressure, supply air pressure, etc.), flow rates (e.g., cold water flow rates, hot water flow rates, refrigerant flow rates, supply air flow rates, etc.), valve positions, resource consumptions (e.g., power consumption, water consumption, electricity consumption, etc.), control setpoints, model parameters (e.g., regression model coefficients), or any other time- series values that provide information about how the corresponding system, device, or process is performing. Monitored variables can be received from connected equipment 610 and/or from various components thereof. For example, monitored variables can be received from one or more controllers (e.g., BMS controllers, subsystem controllers, HVAC controllers, subplant controllers, AHU controllers, device controllers, etc.), BMS devices (e.g.., chillers, cooling towers, pumps, heating elements, etc.), or collections of BMS devices. [0113] Connected equipment 610 can also report equipment status information.

Equipment status information can include, for example, the operational status of the equipment, an operating mode (e.g., low load, medium load, high load, etc.), an indication of whether the equipment is running under normal or abnormal conditions, the hours during which the equipment is running, a safety fault code, or any other information that indicates the current status of connected equipment 610. In some embodiments, each device of connected equipment 610 includes a control panel (e.g., control panel 710 shown in FIG. 7). Control panel 710 can be configured to collect monitored variables and equipment status information from connected equipment 610 and provide the collected data to BMS 606. For example, control panel 710 can compare the sensor data (or a value derived from the sensor data) to predetermined thresholds. If the sensor data or calculated value crosses a safety threshold, control panel 710 can shut down the device. Control panel 710 can generate a data point when a safety shut down occurs. The data point can include a safety fault code which indicates the reason or condition that triggered the shutdown.

[0114] Connected equipment 610 can provide monitored variables and equipment status information to BMS 606. BMS 606 can include a building controller (e.g., BMS controller 366), a system manager (e.g., system manager 503), a network automation engine (e.g., NAE 520), or any other system or device of building 10 configured to communicate with connected equipment 610. BMS 606 may include some or all of the components of BMS 400 or BMS 500, as described with reference to FIGS. 4-5. In some embodiments, the monitored variables and the equipment status information are provided to BMS 606 as data points. Each data point can include a point ID and a point value. The point ID can identify the type of data point or a variable measured by the data point (e.g., condenser pressure, refrigerant temperature, power consumption, etc.). Monitored variables can be identified by name or by an alphanumeric code (e.g., Chilled Water Temp, 7694, etc.). The point value can include an alphanumeric value indicating the current value of the data point.

[0115] BMS 606 can broadcast the monitored variables and the equipment status information to a model predictive maintenance system 602. In some embodiments, model predictive maintenance system 602 is a component of BMS 606. For example, model predictive maintenance system 602 can be implemented as part of a METASYS® brand building automation system, as sold by Johnson Controls Inc. In other embodiments, model predictive maintenance system 602 can be a component of a remote computing system or cloud-based computing system configured to receive and process data from one or more building management systems via network 446. For example, model predictive

maintenance system 602 can be implemented as part of a PANOPTIX® brand building efficiency platform, as sold by Johnson Controls Inc. In other embodiments, model predictive maintenance system 602 can be a component of a subsystem level controller (e.g., a HVAC controller), a subplant controller, a device controller (e.g., AHU controller 330, a chiller controller, etc.), a field controller, a computer workstation, a client device, or any other system or device that receives and processes monitored variables from connected equipment 610.

[0116] Model predictive maintenance (MPM) system 602 may use the monitored variables and/or the equipment status information to identify a current operating state of connected equipment 610. The current operating state can be examined by MPM system 602 to expose when connected equipment 610 begins to degrade in performance and/or to predict when faults will occur. In some embodiments, MPM system 602 uses the information collected from connected equipment 610 to estimate the reliability of connected equipment 610. For example, MPM system 602 can estimate a likelihood of various types of failures that could potentially occur based on the current operating conditions of connected equipment 610 and an amount of time that has elapsed since connected equipment 610 has been installed and/or since maintenance was last performed. In some embodiments, MPM system 602 estimates an amount of time until each failure is predicted to occur and identifies a financial cost associated with each failure (e.g., maintenance cost, increased operating cost, replacement cost, etc.). MPM system 602 can use the reliability information and the likelihood of potential failures to predict when maintenance will be needed and to estimate the cost of performing such maintenance over a predetermined time period.

[0117] MPM system 602 can be configured to determine an optimal maintenance strategy for connected equipment 610. In some embodiments, the optimal maintenance strategy is a set of decisions which optimizes the total cost associated with purchasing, maintaining, and operating connected equipment 610 over the duration of an optimization period (e.g., 30 weeks, 52 weeks, 10 years, 30 years, etc.). The decisions can include, for example, equipment purchase decisions, equipment maintenance decisions, and equipment operating decisions. MPM system 602 can use a model predictive control technique to formulate an objective function which expresses the total cost as a function of these decisions, which can be included as decision variables in the objective function. MPM system 602 can optimize (i.e., minimize) the objective function using any of a variety of optimization techniques to identify the optimal values for each of the decision variables.

[0118] One example of an objective function which can be optimized by MPM system 602 is shown in the following equation:

where C_op,i is the cost per unit of energy (e.g., $/kWh) consumed by connected equipment 610 at time step i of the optimization period, P_op,i is the power consumption (e.g., kW) of connected equipment 610 at time step i, Dt is the duration of each time step i, C_main,i is the cost of maintenance performed on connected equipment 610 at time step i , B_main,i is a binary variable that indicates whether the maintenance is performed, C_cap,i is the capital cost of purchasing a new device of connected equipment 610 at time step i , B_cap,i is a binary variable that indicates whether the new device is purchased, and h is the duration of the horizon or optimization period over which the optimization is performed.

[0119] The first term in the objective function j represents the operating cost of connected equipment 610 over the duration of the optimization period. In some embodiments, the cost per unit of energy C_op,i is received from a utility 608 as energy pricing data. The cost C_op,i may be a time-varying cost that depends on the time of day, the day of the week (e.g., weekday vs. weekend), the current season (e.g., summer vs. winter), or other time-based factors. For example, the cost C_op,i may be higher during peak energy consumption periods and lower during off-peak or partial-peak energy consumption periods.

[0120] In some embodiments, the power consumption P_op,i is based on the heating or cooling load of building 10. The heating or cooling load can be predicted by MPM system 602 as a function of building occupancy, the time of day, the day of the week, the current season, or other factors that can affect the heating or cooling load. In some embodiments, MPM system 602 uses weather forecasts from a weather service 604 to predict the heating or cooling load. The power consumption P_op,i may also depend on the efficiency hi of connected equipment 610. For example, connected equipment 610 that operate at a high efficiency may consume less power P_op,i to satisfy the same heating or cooling load relative to connected equipment 610 that operate at a low efficiency. In general, the power consumption P_op,i of a particular device of connected equipment 610 can be modeled using the following equations:

where Load_i is the heating or cooling load on the device at time step i (e.g., tons cooling, kW heating, etc.), P_ideal,_i is the value of the equipment performance curve (e.g., tons cooling, kW heating, etc.) for the device at the corresponding load point Load_i , and hi is the operating efficiency of the device at time step i (e.g., 0 £ hi £ 1). The function f (Load_i) may be defined by the equipment performance curve for the device or set of devices represented by the performance curve.

[0121] In some embodiments, the equipment performance curve is based on manufacturer specifications for the device under ideal operating conditions. For example, the equipment performance curve may define the relationship between power consumption and

heating/cooling load for each device of connected equipment 610. However, the actual performance of the device may vary as a function of the actual operating conditions. MPM system 602 can analyze the equipment performance information provided by connected equipment 610 to determine the operating efficiency hi for each device of connected equipment 610. In some embodiments, MPM system 602 uses the equipment performance information from connected equipment 610 to determine the actual operating efficiency hi for each device of connected equipment 610. MPM system 602 can use the operating efficiency hi as an input to the objective function j and/or to calculate the corresponding value of P_{op,i ·}

[0122] Advantageously, MPM system 602 can model the efficiency hi of connected equipment 610 at each time step i as a function of the maintenance decisions B_main,i and the equipment purchase decisions B_cap,i. For example, the efficiency hi for a particular device may start at an initial value h₀ when the device is purchased and may degrade over time such that the efficiency hi decreases with each successive time step i. Performing maintenance on a device may reset the efficiency hi to a higher value immediately after the maintenance is performed. Similarly, purchasing a new device to replace an existing device may reset the efficiency hi to a higher value immediately after the new device is purchased. After being reset, the efficiency may continue to degrade over time until the next time at which maintenance is performed or a new device is purchased.

[0123] Performing maintenance or purchasing a new device may result in a relatively lower power consumption P_op,i during operation and therefore a lower operating cost at each time step i after the maintenance is performed or the new device is purchased. In other words, performing maintenance or purchasing a new device may decrease the operating cost represented by the first term of the objective function j. However, performing maintenance may increase the second term of the objective function j and purchasing a new device may increase the third term of the objective function j. The objective function j captures each of these costs and can be optimized by MPM system 602 to determine the optimal set of maintenance and equipment purchase decisions (i.e., optimal values for the binary decision variables B_main,i and B_cap,i ) over the duration of the optimization period.

[0124] In some embodiments, MPM system 602 uses the equipment performance information from connected equipment 610 to estimate the reliability of connected equipment 610. The reliability may be a statistical measure of the likelihood that connected equipment 610 will continue operating without fault under its current operating conditions. Operating under more strenuous conditions (e.g., high load, high temperatures, etc.) may result in a lower reliability, whereas operating under less strenuous conditions (e.g., low load, moderate temperatures, etc.) may result in a higher reliability. In some embodiments, the reliability is based on an amount of time that has elapsed since connected equipment 610 last received maintenance.

[0125] MPM system 602 may receive operating data from a plurality of devices of connected equipment 610 distributed across multiple buildings and can use the set of operating data (e.g., operating conditions, fault indications, failure times, etc.) to develop a reliability model for each type of equipment. The reliability models can be used by MPM system 602 to estimate the reliability of any given device of connected equipment 610 as a function of its current operating conditions and/or other extraneous factors (e.g., time since maintenance was last performed, geographic location, water quality, etc.). In some embodiments, MPM system 602 uses the estimated reliability of each device of connected equipment 610 to determine the probability that the device will require maintenance and/or replacement at each time step of the optimization period. MPM system 602 can use these probabilities to determine the optimal set of maintenance and equipment purchase decisions (i.e., optimal values for the binary decision variables B_main,i and B_cap,i) over the duration of the optimization period.

[0126] In some embodiments, MPM system 602 generates and provides equipment purchase and maintenance recommendations. The equipment purchase and maintenance recommendations may be based on the optimal values for the binary decision variables B_main,i and B_cap,i determined by optimizing the objective function j. For example, a value of B_main,25 = 1 for a particular device of connected equipment 610 may indicate that maintenance should be performed on that device at the 25^th time step of the optimization period, whereas a value of B_main,25 = 0 may indicate that the maintenance should not be performed at that time step. Similarly, a value of B_cap,25 = 1 may indicate that a new device of connected equipment 610 should be purchased at the 25^th time step of the optimization period, whereas a value of B_cap,25 = 0 may indicate that the new device should not be purchased at that time step.

[0127] Advantageously, the equipment purchase and maintenance recommendations generated by MPM system 602 are predictive recommendations based on the actual operating conditions and actual performance of connected equipment 610. The

optimization performed by MPM system 602 weighs the cost of performing maintenance and the cost of purchasing new equipment against the decrease in operating cost resulting from such maintenance or purchase decisions in order to determine the optimal maintenance strategy that minimizes the total combined cost /. In this way, the equipment purchase and maintenance recommendations generated by MPM system 602 may be specific to each group of connected equipment 610 in order to achieve the optimal cost / for that specific group of connected equipment 610. The equipment-specific recommendations may result in a lower overall cost / relative to generic preventative maintenance recommendations provided by an equipment manufacturer (e.g., service equipment every year) which may be sub-optimal for some groups of connected equipment 610 and/or some operating conditions.

[0128] In some embodiments, the equipment purchase and maintenance recommendations are provided to building 10 (e.g., to BMS 606) and/or to client devices 448. An operator or building owner can use the equipment purchase and maintenance recommendations to assess the costs and benefits of performing maintenance and purchasing new devices. In some embodiments, the equipment purchase and maintenance recommendations are provided to service technicians 620. Service technicians 620 can use the equipment purchase and maintenance recommendations to determine when customers should be contacted to perform service or replace equipment.

[0129] In some embodiments, MPM system 602 includes a data analytics and

visualization platform. MPM system 602 may provide a web interface which can be accessed by service technicians 620, client devices 448, and other systems or devices. The web interface can be used to access the equipment performance information, view the results of the optimization, identify which equipment is in need of maintenance, and otherwise interact with MPM system 602. Service technicians 620 can access the web interface to view a list of equipment for which maintenance is recommended by MPM system 602. Service technicians 620 can use the equipment purchase and maintenance recommendations to proactively repair or replace connected equipment 610 in order to achieve the optimal cost predicted by the objective function j. These and other features of MPM system 602 are described in greater detail below.

[0130] Referring now to FIG. 8, a block diagram illustrating MPM system 602 in greater detail is shown, according to an exemplary embodiment. MPM system 602 is shown providing optimization results to a building management system (BMS) 606. BMS 606 can include some or all of the features of BMS 400 and/or BMS 500, as described with reference to FIGS. 4-5. The optimization results provided to BMS 606 may include the optimal values of the decision variables in the objective function j for each time step i in the optimization period. In some embodiments, the optimization results include equipment purchase and maintenance recommendations for each device of connected equipment 610.

[0131] BMS 606 may be configured to monitor the operation and performance of connected equipment 610. BMS 606 may receive monitored variables from connected equipment 610. Monitored variables can include any measured or calculated values indicating the performance of connected equipment 610 and/or the components thereof. For example, monitored variables can include one or more measured or calculated temperatures, pressures, flow rates, valve positions, resource consumptions (e.g., power consumption, water consumption, electricity consumption, etc.), control setpoints, model parameters (e.g., equipment model coefficients), or any other variables that provide information about how the corresponding system, device, or process is performing.

[0132] In some embodiments, the monitored variables indicate the operating efficiency of each device of connected equipment 610 or can be used to calculate the operating efficiency For example, the temperature and flow rate of chilled water output by a chiller can be used to calculate the cooling load (e.g., tons cooling) served by the chiller.

The cooling load can be used in combination with the power consumption of the chiller to calculate the operating efficiency (e.g., tons cooling per kW of electricity consumed). BMS 606 may report the monitored variables to MPM system 602 for use in calculating the operating efficiency of each device of connected equipment 610.

[0133] In some embodiments, BMS 606 monitors the run hours of connected equipment 610. The run hours may indicate the number of hours within a given time period during which each device of connected equipment 610 is active. For example, the run hours for a chiller may indicate that the chiller is active for approximately eight hours per day. The run hours can be used in combination with the average power consumption of the chiller when active to estimate the total power consumption P_op,i of connected equipment 610 at each time step i.

[0134] In some embodiments, BMS 606 monitors the equipment failures and fault indications reported by connected equipment 610. BMS 606 can record the times at which each failure or fault occurs and the operating conditions of connected equipment 610 under which the fault or failure occurred. The operating data collected from connected equipment 610 can be used by BMS 606 and/or MPM system 602 to develop a reliability model for each device of connected equipment 610. BMS 606 may provide the monitored variables, the equipment run hours, the operating conditions, and the equipment failures and fault indications to MPM system 602 as equipment performance information.

[0135] BMS 606 may be configured to monitor conditions within a controlled building or building zone. For example, BMS 606 may receive input from various sensors (e.g., temperature sensors, humidity sensors, airflow sensors, voltage sensors, etc.) distributed throughout the building and may report building conditions to MPM system 602. Building conditions may include, for example, a temperature of the building or a zone of the building, a power consumption (e.g., electric load) of the building, a state of one or more actuators configured to affect a controlled state within the building, or other types of information relating to the controlled building. BMS 606 may operate connected equipment 610 to affect the monitored conditions within the building and to serve the thermal energy loads of the building. [0136] BMS 606 may provide control signals to connected equipment 610 specifying on/off states, charge/discharge rates, and/or setpoints for connected equipment 610. BMS 606 may control the equipment (e.g., via actuators, power relays, etc.) in accordance with the control signals to achieve setpoints for various building zones and/or devices of connected equipment 610. In various embodiments, BMS 606 may be combined with MPM system 602 or may be part of a separate building management system. According to an exemplary embodiment, BMS 606 is a METASYS® brand building management system, as sold by Johnson Controls, Inc.

[0137] MPM system 602 may monitor the performance of connected equipment 610 using information received from BMS 606. MPM system 602 may be configured to predict the thermal energy loads (e.g., heating loads, cooling loads, etc.) of the building for plurality of time steps in the optimization period (e.g., using weather forecasts from a weather service 604). MPM system 602 may also predict the cost of electricity or other resources (e.g., water, natural gas, etc.) using pricing data received from utilities 608. MPM system 602 may generate optimization results that optimize the economic value of operating, maintaining, and purchasing connected equipment 610 over the duration of the optimization period subject to constraints on the optimization process (e.g., load constraints, decision variable constraints, etc.). The optimization process performed by MPM system 602 is described in greater detail below.

[0138] According to an exemplary embodiment, MPM system 602 can be integrated within a single computer (e.g., one server, one housing, etc.). In various other exemplary embodiments, MPM system 602 can be distributed across multiple servers or computers (e.g., that can exist in distributed locations). In another exemplary embodiment, MPM system 602 may integrated with a smart building manager that manages multiple building systems and/or combined with BMS 606.

[0139] MPM system 602 is shown to include a communications interface 804 and a processing circuit 806. Communications interface 804 may include wired or wireless interfaces (e.g., jacks, antennas, transmitters, receivers, transceivers, wire terminals, etc.) for conducting data communications with various systems, devices, or networks. For example, communications interface 804 may include an Ethernet card and port for sending and receiving data via an Ethernet-based communications network and/or a WiFi transceiver for communicating via a wireless communications network. Communications interface 804 may be configured to communicate via local area networks or wide area networks (e.g., the Internet, a building WAN, etc.) and may use a variety of communications protocols (e.g., BACnet, IP, LON, etc ).

[0140] Communications interface 804 may be a network interface configured to facilitate electronic data communications between MPM system 602 and various external systems or devices (e.g., BMS 606, connected equipment 610, utilities 510, etc.). For example, MPM system 602 may receive information from BMS 606 indicating one or more measured states of the controlled building (e.g., temperature, humidity, electric loads, etc.) and equipment performance information for connected equipment 610 (e.g., run hours, power consumption, operating efficiency, etc.). Communications interface 804 may receive inputs from BMS 606 and/or connected equipment 610 and may provide optimization results to BMS 606 and/or other external systems or devices. The optimization results may cause BMS 606 to activate, deactivate, or adjust a setpoint for connected equipment 610 in order to achieve the optimal values of the decision variables specified in the optimization results.

[0141] Still referring to FIG. 8, processing circuit 806 is shown to include a processor 808 and memory 810. Processor 808 may 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 808 may be configured to execute computer code or instructions stored in memory 810 or received from other computer readable media (e.g., CDROM, network storage, a remote server, etc.).

[0142] Memory 810 may 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 810 may 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 810 may 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 810 may be communicably connected to processor 808 via processing circuit 806 and may include computer code for executing (e.g., by processor 808) one or more processes described herein. [0143] MPM system 602 is shown to include an equipment performance monitor 824. Equipment performance monitor 824 can receive equipment performance information from BMS 606 and/or connected equipment 610. The equipment performance information can include samples of monitored variables (e.g., measured temperature, measured pressure, measured flow rate, power consumption, etc.), current operating conditions (e.g., heating or cooling load, current operating state, etc.), fault indications, or other types of information that characterize the performance of connected equipment 610. In some embodiments, equipment performance monitor 824 uses the equipment performance information to calculate the current efficiency hi and reliability of each device of connected equipment 610. Equipment performance monitor 824 can provide the efficiency hi and reliability values to model predictive optimizer 830 for use in optimizing the objective function j.

[0144] Still referring to FIG. 8, MPM system 602 is shown to include a load/rate predictor 822. Load/rate predictor 822 may be configured to predict the energy loads ( Load_i ) (e.g., heating load, cooling load, electric load, etc.) of the building or campus for each time step i of the optimization period. Load/rate predictor 822 is shown receiving weather forecasts from a weather service 604. In some embodiments, load/rate predictor 822 predicts the energy loads Load_i as a function of the weather forecasts. In some embodiments, load/rate predictor 822 uses feedback from BMS 606 to predict loads Load_i. Feedback from BMS 606 may include various types of sensory inputs (e.g., temperature, flow, humidity, enthalpy, etc.) or other data relating to the controlled building (e.g., inputs from a HVAC system, a lighting control system, a security system, a water system, etc.).

[0145] In some embodiments, load/rate predictor 822 receives a measured electric load and/or previous measured load data from BMS 606 (e.g., via equipment performance monitor 824). Load/rate predictor 822 may predict loads Load_i as a function of a given weather forecast

, a day type (day), the time of day (t), and previous measured load data (Y_i-1). Such a relationship is expressed in the following equation:

[0146] In some embodiments, load/rate predictor 822 uses a deterministic plus stochastic model trained from historical load data to predict loads Load_i. Load/rate predictor 822 may use any of a variety of prediction methods to predict loads Load_i (e.g., linear regression for the deterministic portion and an AR model for the stochastic portion). Load/rate predictor 822 may predict one or more different types of loads for the building or campus. For example, load/rate predictor 822 may predict a hot water load Load_Hot,i, a cold water load Load_Cold,i , and an electric load Load_Elec,i for each time step i within the optimization period. The predicted load values Load_i can include some or all of these types of loads. In some embodiments, load/rate predictor 822 makes load/rate predictions using the techniques described in U.S. Patent Application No. 14/717,593 filed May 20, 2015, the entire disclosure of which is incorporated by reference herein.

[0147] Load/rate predictor 822 is shown receiving utility rates from utilities 608. Utility rates may indicate a cost or price per unit of a resource (e.g., electricity, natural gas, water, etc.) provided by utilities 608 at each time step i in the optimization period. In some embodiments, the utility rates are time-variable rates. For example, the price of electricity may be higher at certain times of day or days of the week (e.g., during high demand periods) and lower at other times of day or days of the week (e.g., during low demand periods). The utility rates may define various time periods and a cost per unit of a resource during each time period. Utility rates may be actual rates received from utilities 608 or predicted utility rates estimated by load/rate predictor 822.

[0148] In some embodiments, the utility rates include demand charges for one or more resources provided by utilities 608. A demand charge may define a separate cost imposed by utilities 608 based on the maximum usage of a particular resource (e.g., maximum energy consumption) during a demand charge period. The utility rates may define various demand charge periods and one or more demand charges associated with each demand charge period. In some instances, demand charge periods may overlap partially or completely with each other and/or with the prediction window. Model predictive optimizer 830 may be configured to account for demand charges in the high level optimization process performed by high level optimizer 832. Utilities 608 may be defined by time- variable (e.g., hourly) prices, a maximum service level (e.g., a maximum rate of

consumption allowed by the physical infrastructure or by contract) and, in the case of electricity, a demand charge or a charge for the peak rate of consumption within a certain period. Load/rate predictor 822 may store the predicted loads Load_i and the utility rates in memory 810 and/or provide the predicted loads Load_i and the utility rates to model predictive optimizer 830.

[0149] Still referring to FIG. 8, MPM system 602 is shown to include a model predictive optimizer 830. Model predictive optimizer 830 can be configured to perform a multi-level optimization process to optimize the total cost associated with purchasing, maintaining, and operating connected equipment 610. In some embodiments, model predictive optimizer 830 includes a high level optimizer 832 and a low level optimizer 834. High level optimizer 832 may optimize the objective function j for an entire set of connected equipment 610 (e.g., all of the devices within a building) or for a subset of connected equipment 610 (e.g., a single device, all of the devices of a subplant or building subsystem, etc.) to determine the optimal values for each of the decision variables (e.g., P_op,i, B_main,i and B_cap,i ) in the objective function j. The optimization performed by high level optimizer 832 is described in greater detail with reference to FIG. 9.

[0150] In some embodiments, low level optimizer 834 receives the optimization results from high level optimizer 832. The optimization results may include optimal power consumption values P_op,i and/or load values Load_i for each device or set of devices of connected equipment at each time step i in the optimization period. Low level optimizer 834 may determine how to best run each device or set of devices at the load values determined by high level optimizer 832. For example, low level optimizer 834 may determine on/off states and/or operating setpoints for various devices of connected equipment 610 in order to optimize (e.g., minimize) the power consumption of connected equipment 610 meeting the corresponding load value Load_i.

[0151] Low level optimizer 834 may be configured to generate equipment performance curves for each device or set of devices of connected equipment 610. Each performance curve may indicate an amount of resource consumption (e.g., electricity use measured in kW, water use measured in L/s, etc.) by a particular device or set of devices of connected equipment 610 as a function of the load on the device or set of devices. In some embodiments, low level optimizer 834 generates the performance curves by performing a low level optimization process at various combinations of load points (e.g., various values of Load_i) and weather conditions to generate multiple data points. The low level optimization may be used to determine the minimum amount of resource consumption required to satisfy the corresponding heating or cooling load. An example of a low level optimization process which can be performed by low level optimizer 834 is described in detail in U.S. Patent Application No. 14/634,615 titled“Low Level Central Plant

Optimization” and filed February 27, 2015, the entire disclosure of which is incorporated by reference herein. Low level optimizer 834 may fit a curve to the data points to generate the performance curves. [0152] In some embodiments, low level optimizer 834 generates equipment performance curves for a set of connected equipment 610 (e.g., a chiller subplant, a heater subplant, etc.) by combining efficiency curves for individual devices of connected equipment 610. A device efficiency curve may indicate the amount of resource consumption by the device as a function of load. The device efficiency curves may be provided by a device manufacturer or generated using experimental data. In some embodiments, the device efficiency curves are based on an initial efficiency curve provided by a device manufacturer and updated using experimental data. The device efficiency curves may be stored in equipment models 818. For some devices, the device efficiency curves may indicate that resource

consumption is a U-shaped function of load. Accordingly, when multiple device efficiency curves are combined into a performance curve for multiple devices, the resultant performance curve may be a wavy curve. The waves are caused by a single device loading up before it is more efficient to turn on another device to satisfy the subplant load. Low level optimizer 834 may provide the equipment performance curves to high level optimizer 832 for use in the high level optimization process.

[0153] Still referring to FIG. 8, MPM system 602 is shown to include an equipment controller 828. Equipment controller 828 can be configured to control connected equipment 610 to affect a variable state or condition in building 10 (e.g., temperature, humidity, etc.).

In some embodiments, equipment controller 828 controls connected equipment 610 based on the results of the optimization performed by model predictive optimizer 830. In some embodiments, equipment controller 828 generates control signals which can be provided to connected equipment 610 via communications interface 804 and/or BMS 606. The control signals may be based on the optimal values of the decision variables in the objective function j. For example, equipment controller 828 may generate control signals which cause connected equipment 610 to achieve the optimal power consumption values P_op,i for each time step i in the optimization period.

[0154] Data and processing results from model predictive optimizer 830, equipment controller 828, or other modules of MPM system 602 may be accessed by (or pushed to) monitoring and reporting applications 826. Monitoring and reporting applications 826 may be configured to generate real time“system health” dashboards that can be viewed and navigated by a user (e.g., a system engineer). For example, monitoring and reporting applications 826 may include a web-based monitoring application with several graphical user interface (GUI) elements (e.g., widgets, dashboard controls, windows, etc.) for displaying key performance indicators (KPI) or other information to users of a GUI. In addition, the GUI elements may summarize relative energy use and intensity across building management systems in different buildings (real or modeled), different campuses, or the like. Other GUI elements or reports may be generated and shown based on available data that allow users to assess performance across one or more energy storage systems from one screen. The user interface or report (or underlying data engine) may be configured to aggregate and categorize operating conditions by building, building type, equipment type, and the like. The GUI elements may include charts or histograms that allow the user to visually analyze the operating parameters and power consumption for the devices of the building system.

[0155] Still referring to FIG. 8, MPM system 602 may include one or more GUI servers, web services 812, or GUI engines 814 to support monitoring and reporting applications 826. In various embodiments, applications 826, web services 812, and GUI engine 814 may be provided as separate components outside of MPM system 602 (e.g., as part of a smart building manager). MPM system 602 may be configured to maintain detailed historical databases (e.g., relational databases, XML databases, etc.) of relevant data and includes computer code modules that continuously, frequently, or infrequently query, aggregate, transform, search, or otherwise process the data maintained in the detailed databases. MPM system 602 may be configured to provide the results of any such processing to other databases, tables, XML files, or other data structures for further querying, calculation, or access by, for example, external monitoring and reporting applications.

[0156] MPM system 602 is shown to include configuration tools 816. Configuration tools 816 can allow a user to define (e.g., via graphical user interfaces, via prompt-driven “wizards,” etc.) how MPM system 602 should react to changing conditions in BMS 606 and/or connected equipment 610. In an exemplary embodiment, configuration tools 816 allow a user to build and store condition-response scenarios that can cross multiple devices of connected equipment 610, multiple building systems, and multiple enterprise control applications (e.g., work order management system applications, entity resource planning applications, etc.). For example, configuration tools 816 can provide the user with the ability to combine data (e.g., from subsystems, from event histories) using a variety of conditional logic. In varying exemplary embodiments, the conditional logic can range from simple logical operators between conditions (e.g., AND, OR, XOR, etc.) to pseudo-code constructs or complex programming language functions (allowing for more complex interactions, conditional statements, loops, etc.). Configuration tools 816 can present user interfaces for building such conditional logic. The user interfaces may allow users to define policies and responses graphically. In some embodiments, the user interfaces may allow a user to select a pre-stored or pre-constructed policy and adapt it or enable it for use with their system.

High Level Optimizer

[0157] Referring now to FIG. 9, a block diagram illustrating high level optimizer 832 in greater detail is shown, according to an exemplary embodiment. High level optimizer 832 can be configured to determine an optimal maintenance strategy for connected equipment 610. In some embodiments, the optimal maintenance strategy is a set of decisions which optimizes the total cost associated with purchasing, maintaining, and operating connected equipment 610 over the duration of an optimization period (e.g., 30 weeks, 52 weeks, 10 years, 30 years, etc.). The decisions can include, for example, equipment purchase decisions, equipment maintenance decisions, and equipment operating decisions.

[0158] High level optimizer 832 is shown to include an operational cost predictor 910, a maintenance cost predictor 920, a capital cost predictor 930, an objective function generator 935, and an objective function optimizer 940. Cost predictors 910, 920, and 930 can use a model predictive control technique to formulate an objective function which expresses the total cost as a function of several decision variables (e.g., maintenance decisions, equipment purchase decisions, etc.) and input parameters (e.g., energy cost, device efficiency, device reliability). Operational cost predictor 910 can be configured to formulate an operational cost term in the objective function. Similarly, maintenance cost predictor 920 can be configured to formulate a maintenance cost term in the objective function and capital cost predictor 930 can be configured to formulate a capital cost term in the objective function. Objective function optimizer 940 can optimize (i.e., minimize) the objective function using any of a variety of optimization techniques to identify the optimal values for each of the decision variables.

[0159] One example of an objective function which can be generated by high level optimizer 832 is shown in the following equation:

where C_op,i is the cost per unit of energy (e.g., $/kWh) consumed by connected equipment 610 at time step i of the optimization period, P_op,i is the power consumption (e.g., kW) of connected equipment 610 at time step i, Dt is the duration of each time step i, C_main,i is the cost of maintenance performed on connected equipment 610 at time step i, B_main,i is a binary variable that indicates whether the maintenance is performed, C_cap,i is the capital cost of purchasing a new device of connected equipment 610 at time step i, B_cap,i is a binary variable that indicates whether the new device is purchased, and h is the duration of the horizon or optimization period over which the optimization is performed.

Operational Cost Predictor

[0160] Operational cost predictor 910 can be configured to formulate the first term in the objective function j. The first term in the objective function j represents the operating cost of connected equipment 610 over the duration of the optimization period and is shown to include three variables or parameters (i.e., C_op,i, P_op,i and Dt). In some embodiments, the cost per unit of energy C_op,i is determined by energy costs module 915. Energy costs module 915 can receive a set of energy prices from utility 608 as energy pricing data. In some embodiments, the energy prices are time-varying cost that depend on the time of day, the day of the week (e.g., weekday vs. weekend), the current season (e.g., summer vs.

winter), or other time-based factors. For example, the cost of electricity may be higher during peak energy consumption periods and lower during off-peak or partial-peak energy consumption periods.

[0161] Energy costs module 915 can use the energy costs to define the value of C_op,i for each time step i of the optimization period. In some embodiments, energy costs module 915 stores the energy costs as an array C_op including a cost element for each of the h time steps in the optimization period. For example, energy costs module 915 can generate the following array:

where the array C_op has a size of 1 x h and each element of the array C_op includes an energy cost value C_op,i for a particular time step i = 1 ... h of the optimization period.

[0162] Still referring to FIG. 9, operational cost predictor 910 is shown to include an ideal performance calculator 912. Ideal performance calculator 912 may receive load predictions Load_i from load/rate predictor 822 and may receive performance curves from low level optimizer 834. As discussed above, the performance curves may define the ideal power consumption P_ideal of a device or set of devices of connected equipment 610 as a function of the heating or cooling load on the device or set of devices. For example, the performance curve one or more devices of connected equipment 610 can be defined by the following equation:

where P_{ideal, i} is the ideal power consumption (e.g., kW) of connected equipment 610 at time step i and Load_i is the load (e.g., tons cooling, kW heating, etc.) on connected equipment 610 at time step i. The ideal power consumption P_{ideal, i} may represent the power consumption of the one or more devices of connected equipment 610 assuming they operate at perfect efficiency.

[0163] Ideal performance calculator 912 can use the performance curve for a device or set of devices of connected equipment 610 to identify the value of P_{ideal, i} that corresponds to the load point Load_i for the device or set of devices at each time step of the optimization period. In some embodiments, ideal performance calculator 912 stores the ideal load values as an array P_ideal including an element for each of the h time steps in the optimization period. For example, ideal performance calculator 912 can generate the following array:

where the array P_ideal has a size of h x 1 and each element of the array P_ideal includes an ideal power consumption value P_{ideal, i} for a particular time step i = 1 ... h of the optimization period.

[0164] Still referring to FIG. 9, operational cost predictor 910 is shown to include an efficiency updater 911 and an efficiency degrader 913. Efficiency updater 911 can be configured to determine the efficiency h of connected equipment 610 under actual operating conditions. In some embodiments, the efficiency hi represents the ratio of the ideal power consumption P_ideal of connected equipment to the actual power consumption P_actual of connected equipment 610, as shown in the following equation:

where P_ideal is the ideal power consumption of connected equipment 610 as defined by the performance curve for connected equipment 610 and P _actual is the actual power

consumption of connected equipment 610 In some embodiments, efficiency updater 91 1 uses the equipment performance information collected from connected equipment 610 to identify the actual power consumption value P _actual. Efficiency updater 911 can use the actual power consumption P _actual in combination with the ideal power consumption P_ideal to calculate the efficiency h.

[0165] Efficiency updater 911 can be configured to periodically update the efficiency h to reflect the current operating efficiency of connected equipment 610 For example, efficiency updater 911 can calculate the efficiency h of connected equipment 610 once per day, once per week, once per year, or at any other interval as may be suitable to capture changes in the efficiency h over time. Each value of the efficiency h may be based on corresponding values of P_ideal and P _actual at the time the efficiency h is calculated. In some embodiments, efficiency updater 911 updates the efficiency h each time the high level optimization process is performed (i.e., each time the objective function j is optimized).

The efficiency value calculated by efficiency updater 911 may be stored in memory 810 as an initial efficiency value h₀ , where the subscript 0 denotes the value of the efficiency h at or before the beginning of the optimization period (e.g., at time step 0).

[0166] In some embodiments, efficiency updater 911 updates the efficiency for one or more time steps during the optimization period to account for increases in the efficiency h of connected equipment 610 that will result from performing maintenance on connected equipment 610 or purchasing new equipment to replace or supplement one or more devices of connected equipment 610. The time steps i at which the efficiency hi is updated may correspond to the predicted time steps at which the maintenance will be performed or the equipment will replaced. The predicted time steps at which maintenance will be performed on connected equipment 610 may be defined by the values of the binary decision variables B_main,i in the objective function j. Similarly, the predicted time steps at which the equipment will be replaced may be defined by the values of the binary decision variables B_cap,i in the objective function j.

[0167] Efficiency updater 911 can be configured to reset the efficiency for a given time step i if the binary decision variables B_main,i and B_cap,i indicate that maintenance will be performed at that time step and/or new equipment will be purchased at that time step (i.e., B_main,i = 1 and/or B_cap,i = 1). For example, if B_main,i = 1, efficiency updater 911 can be configured to reset the value of to h_main , where h_main is the efficiency value that is expected to result from the maintenance performed at time step i. Similarly, if B_cap,i = 1, efficiency updater 911 can be configured to reset the value of to h_cap, where h_cap is the efficiency value that is expected to result from purchasing a new device to supplement or replace one or more devices of connected equipment 610 performed at time step i.

Efficiency updater 911 can dynamically reset the efficienc hi for one or more time steps while the optimization is being performed (e.g., with each iteration of the optimization) based on the values of binary decision variables B_main,i and B_cap,i.

[0168] Efficiency degrader 913 can be configured to predict the efficienc hi of connected equipment 610 at each time step i of the optimization period. The initial efficiency h₀ at the beginning of the optimization period may degrade over time as connected equipment 610 degrade in performance. For example, the efficiency of a chiller may degrade over time as a result of the chilled water tubes becoming dirty and reducing the heat transfer coefficient of the chiller. Similarly, the efficiency of a battery may decrease over time as a result of degradation in the physical or chemical components of the battery. Efficiency degrader 913 can be configured to account for such degradation by incrementally reducing the efficiency h i over the duration of the optimization period.

[0169] In some embodiments, the initial efficiency value h₀ is updated at the beginning of each optimization period. However, the efficiency h may degrade during the optimization period such that the initial efficiency value h₀ becomes increasingly inaccurate over the duration of the optimization period. To account for efficiency degradation during the optimization period, efficiency degrader 913 can decrease the efficiency h by a

predetermined amount with each successive time step. For example, efficiency degrader 913 can define the efficiency at each time step i = 1 ... h as follows:

where is the efficiency at time step i, is the efficiency at time step i— 1, and Dh is the degradation in efficiency between consecutive time steps. In some embodiments, this definition o hi is applied to each time step for which B_main,i = 0 and B_cap,i = 0. However, if either B_main,i = 1 or B_cap,i = 1, the value of hi may be reset to either h _main or h_cap as previously described. [0170] In some embodiments, the value of Ah is based on a time series of efficiency values calculated by efficiency updater 911. For example, efficiency degrader 913 may record a time series of the initial efficiency values h₀ calculated by efficiency updater 911, where each of the initial efficiency values h₀ represents the empirically-calculated efficiency of connected equipment 610 at a particular time. Efficiency degrader 913 can examine the time series of initial efficiency values h₀ to determine the rate at which the efficiency degrades. For example, if the initial efficiency h₀ at time t_t is h_0,1 and the initial efficiency at time t₂ is h_0.2, efficiency degrader 913 can calculate the rate of efficiency degradation as follows:

where is the rate of efficiency degradation. Efficiency degrader 913 can multiply by

the duration of each time step Dt to calculate the value of .

[0171] In some embodiments, efficiency degrader 913 stores the efficiency values over the duration of the optimization period in an array h including an element for each of the h time steps in the optimization period. For example, efficiency degrader 913 can generate the following array:

where the array h has a size of 1 x h and each element of the array h includes an efficiency value hi for a particular time step i = 1 ... h of the optimization period. Each element i of the array h may be calculated based on the value of the previous element and the value of Ah (e.g., if B_main,i = 0 and B_cap,i = 0) or may be dynamically reset to either h_main or h_cap (e.g., if B_main,i— 1 or B_cap,i— 1.

[0172] The logic characterizing the efficiency updating and resetting operations performed by efficiency updater 911 and efficiency degrader 913 can be summarized in the following equations:

which can be applied as constraints on the high level optimization performed by objective function optimizer 940.

[0173] Advantageously, efficiency updater 911 and efficiency degrader 913 can model the efficiency of connected equipment 610 at each time step i as a function of the

maintenance decisions B_main,i and the equipment purchase decisions B_cap,i. For example, the efficienc hi for a particular device may start at an initial value h₀ at the beginning of the optimization period and may degrade over time such that the efficiency decreases with each successive time step i. Performing maintenance on a device may reset the efficiency to a higher value immediately after the maintenance is performed. Similarly, purchasing a new device to replace an existing device may reset the efficiency to a higher value immediately after the new device is purchased. After being reset, the efficiency may continue to degrade over time until the next time at which maintenance is performed or a new device is purchased.

[0174] Still referring to FIG. 9, operational cost predictor 910 is shown to include a power consumption estimator 914 and an operational cost calculator 916. Power consumption estimator 914 can be configured to estimate the power consumption P_op,i of connected equipment 610 at each time step i of the optimization period. In some embodiments, power consumption estimator 914 estimates the power consumption P_op,i as a function of the ideal power consumption P_{ideal, i} calculated by ideal performance calculator 912 and the efficiency determined by efficiency degrader 913 and/or efficiency updater 911. For example, power consumption estimator 914 can calculate the power consumption P_op,i using the following equation:

where P_{ideal, i} is the power consumption calculated by ideal performance calculator 912 based on the equipment performance curve for the device at the corresponding load point Load_i and hi is the operating efficiency of the device at time step i.

[0175] In some embodiments, power consumption estimator 914 stores the power consumption values as an array P_op including an element for each of the h time steps in the optimization period. For example, power consumption estimator 914 can generate the following array:

where the array P_op has a size of h x 1 and each element of the array P_op includes a power consumption value P_op,i for a particular time step i = 1 ... h of the optimization period.

[0176] Operational cost calculator 916 can be configured to estimate the operational cost of connected equipment 610 over the duration of the optimization period. In some embodiments, operational cost calculator 916 calculates the operational cost during each time step i using the following equation:

where P_op,i is the predicted power consumption at time step i determined by power consumption estimator 914, C_op,i is the cost per unit of energy at time step i determined by energy costs module 915, and Dt is the duration of each time step. Operational cost calculator 916 can sum the operational costs over the duration of the optimization period as follows:

where Cost_op is the operational cost term of the objective function j.

[0177] In other embodiments, operational cost calculator 916 estimates the operational cost Cost_op by multiplying the cost array C_op by the power consumption array P_op and the duration of each time step Dt as shown in the following equations:

Maintenance Cost Predictor

[0178] Maintenance cost predictor 920 can be configured to formulate the second term in the objective function j. The second term in the objective function j represents the cost of performing maintenance on connected equipment 610 over the duration of the optimization period and is shown to include two variables or parameters (i.e., C_main,i and B_main,i). Maintenance cost predictor 920 is shown to include a maintenance estimator 922, a reliability estimator 924, a maintenance cost calculator 926, and a maintenance costs module 928. [0179] Reliability estimator 924 can be configured to estimate the reliability of connected equipment 610 based on the equipment performance information received from connected equipment 610. The reliability may be a statistical measure of the likelihood that connected equipment 610 will continue operating without fault under its current operating conditions. Operating under more strenuous conditions (e.g., high load, high temperatures, etc.) may result in a lower reliability, whereas operating under less strenuous conditions (e.g., low load, moderate temperatures, etc.) may result in a higher reliability. In some embodiments, the reliability is based on an amount of time that has elapsed since connected equipment 610 last received maintenance and/or an amount of time that has elapsed since connected equipment 610 was purchased or installed.

[0180] In some embodiments, reliability estimator 924 uses the equipment performance information to identify a current operating state of connected equipment 610. The current operating state can be examined by reliability estimator 924 to expose when connected equipment 610 begins to degrade in performance and/or to predict when faults will occur.

In some embodiments, reliability estimator 924 estimates a likelihood of various types of failures that could potentially occur in connected equipment 610. The likelihood of each failure may be based on the current operating conditions of connected equipment 610, an amount of time that has elapsed since connected equipment 610 has been installed, and/or an amount of time that has elapsed since maintenance was last performed. In some embodiments, reliability estimator 924 identifies operating states and predicts the likelihood of various failures using the systems and methods described in U.S. Patent Application No. 15/188,824 titled“Building Management System With Predictive Diagnostics” and filed June 21, 2016, the entire disclosure of which is incorporated by reference herein.

[0181] In some embodiments, reliability estimator 924 receives operating data from a plurality of devices of connected equipment 610 distributed across multiple buildings. The operating data can include, for example, current operating conditions, fault indications, failure times, or other data that characterize the operation and performance of connected equipment 610. Reliability estimator 924 can use the set of operating data to develop a reliability model for each type of equipment. The reliability models can be used by reliability estimator 924 to estimate the reliability of any given device of connected equipment 610 as a function of its current operating conditions and/or other extraneous factors (e.g., time since maintenance was last performed, time since installation or purchase, geographic location, water quality, etc.). [0182] One example of a reliability model which can be used by reliability estimator 924 is shown in the following equation:

where Reliability _i is the reliability of connected equipment 610 at time step i, OpCond_i are the operating conditions at time step i , Dt_main,i is the amount of time that has elapsed between the time at which maintenance was last performed and time step i , and Dt_cap,i is the amount of time that has elapsed between the time at which connected equipment 610 was purchased or installed and time step i. Reliability estimator 924 can be configured to identify the current operating conditions OpCond_i based on the equipment performance information received as a feedback from connected equipment 610. Operating under more strenuous conditions (e.g., high load, extreme temperatures, etc.) may result in a lower reliability, whereas operating under less strenuous conditions (e.g., low load, moderate temperatures, etc.) may result in a higher reliability.

[0183] Reliability estimator 924 may determine the amount of time Dt_main,i that has elapsed since maintenance was last performed on connected equipment 610 based on the values of the binary decision variables B_main,i. For each time step i , reliability estimator 924 can examine the corresponding values of B_main at time step i and each previous time step (e.g., time steps i— 1, i— 2, ... , 1). Reliability estimator 924 can calculate the value of Dt_main,i by subtracting the time at which maintenance was last performed (i.e., the most recent time at which B_main,i = 1) from the time associated with time step i. A long amount of time Dt_main,i since maintenance was last performed may result in a lower reliability, whereas a short amount of time since maintenance was last performed may result in a higher reliability.

[0184] Similarly, reliability estimator 924 may determine the amount of time Dt_cap,i that has elapsed since connected equipment 610 was purchased or installed based on the values of the binary decision variables B_cap,i. For each time step i , reliability estimator 924 can examine the corresponding values of B_cap at time step i and each previous time step (e.g., time steps i— 1, i— 2, ... , 1). Reliability estimator 924 can calculate the value of Dt_cap,i by subtracting the time at which connected equipment 610 was purchased or installed (i.e., the most recent time at which B_cap,i = 1) from the time associated with time step i. A long amount of time Dt_cap,i since connected equipment 610 was purchased or installed may result in a lower reliability, whereas a short amount of time since connected equipment 610 was purchased or installed may result in a higher reliability.

[0185] Reliability estimator 924 can be configured to reset the reliability for a given time step i if the binary decision variables B_main,i and B_cap,i indicate that maintenance will be performed at that time step and/or new equipment will be purchased at that time step (i.e., B_main,i = 1 and/or B_cap,i = 1). For example, if B_main,i = 1, reliability estimator 924 can be configured to reset the value of Reliability_i to Reliability _main, where Reliability _main is the reliability value that is expected to result from the maintenance performed at time step i. Similarly, if B_cap,i = 1, reliability estimator 924 can be configured to reset the value of Reliability_i to Reliability _cap, where Reliability_cap is the reliability value that is expected to result from purchasing a new device to supplement or replace one or more devices of connected equipment 610 performed at time step i. Reliability estimator 924 can dynamically reset the reliability for one or more time steps while the optimization is being performed (e.g., with each iteration of the optimization) based on the values of binary decision variables B_main,i and B_cap,i.

[0186] Maintenance estimator 922 can be configured to use the estimated reliability of connected equipment 610 over the duration of the optimization period to determine the probability that connected equipment 610 will require maintenance and/or replacement at each time step of the optimization period. In some embodiments, maintenance estimator 922 is configured to compare the probability that connected equipment 610 will require maintenance at a given time step to a critical value. Maintenance estimator 922 can be configured to set the value of B_main,i = 1 in response to a determination that the probability that connected equipment 610 will require maintenance at time step i exceeds the critical value. Similarly, maintenance estimator 922 can be configured to compare the probability that connected equipment 610 will require replacement at a given time step to a critical value. Maintenance estimator 922 can be configured to set the value of B_cap,i = 1 in response to a determination that the probability that connected equipment 610 will require replacement at time step i exceeds the critical value.

[0187] In some embodiments, a reciprocal relationship exists between the reliability of connected equipment 610 and the values of the binary decision variables B_main,i and B_cap,i. In other words, the reliability of connected equipment 610 can affect the values of the binary decision variables B_main,i and B_cap,i selected in the optimization, and the values of the binary decision variables B_main,i and B_cap,i can affect the reliability of connected equipment 610. Advantageously, the optimization performed by objective function optimizer 940 can identify the optimal values of the binary decision variables B_main,i and B_cap,i while accounting for the reciprocal relationship between the binary decision variables Bmain, i and B_cap,i and the reliability of connected equipment 610.

[0188] In some embodiments, maintenance estimator 922 generates a matrix B_main of the binary maintenance decision variables. The matrix B_main may include a binary decision variable for each of the different maintenance activities that can be performed at each time step of the optimization period. For example, maintenance estimator 922 can generate the following matrix:

where the matrix B_main has a size of m x h and each element of the matrix B_main includes a binary decision variable for a particular maintenance activity at a particular time step of the optimization period. For example, the value of the binary decision variable B_main,j,i indicates whether the j th maintenance activity will be performed during the tth time step of the optimization period.

[0189] Still referring to FIG. 9, maintenance cost predictor 920 is shown to include a maintenance costs module 928 and a maintenance costs calculator 926. Maintenance costs module 928 can be configured to determine costs C_main,i associated with performing various types of maintenance on connected equipment 610. Maintenance costs module 928 can receive a set of maintenance costs from an external system or device (e.g., a database, a user device, etc.). In some embodiments, the maintenance costs define the economic cost (e.g., $) of performing various types of maintenance. Each type of maintenance activity may have a different economic cost associated therewith. For example, the maintenance activity of changing the oil in a chiller compressor may incur a relatively small economic cost, whereas the maintenance activity of completely disassembling the chiller and cleaning all of the chilled water tubes may incur a significantly larger economic cost.

[0190] Maintenance costs module 928 can use the maintenance costs to define the values of C_main,i in objective function j. In some embodiments, maintenance costs module 928 stores the maintenance costs as an array C_main including a cost element for each of the maintenance activities that can be performed. For example, maintenance costs module 928 can generate the following array:

where the array C_main has a size of 1 x m and each element of the array C_main includes a maintenance cost value C_main,j for a particular maintenance activity j = 1 ... m.

[0191] Some maintenance activities may be more expensive than other. However, different types of maintenance activities may result in different levels of improvement to the efficiency h and/or the reliability of connected equipment 610. For example, merely changing the oil in a chiller may result in a minor improvement in efficiency h and/or a minor improvement in reliability, whereas completely disassembling the chiller and cleaning all of the chilled water tubes may result in a significantly greater improvement to the efficiency h and/or the reliability of connected equipment 610. Accordingly, multiple different levels of post-maintenance efficiency (i.e., h_main) and post-maintenance reliability (i.e., Reliability _main) may exist. Each level of h_main and Reliability _main may

correspond to a different type of maintenance activity.

[0192] In some embodiments, maintenance estimator 922 stores each of the different levels of h _main and Reliability_main in a corresponding array. For example, the parameter h_main can be defined as an array h_main with an element for each of the m different types of maintenance activities. Similarly, the parameter Reliability_main can be defined as an array Reliability_main with an element for each of the m different types of maintenance activities. Examples of these arrays are shown in the following equations:

where the array h_main has a size of 1 x m and each element of the array h_main includes a post-maintenance efficiency value h_{main, j} for ^a particular maintenance activity. Similarly, the array Reliability_main has a size of 1 x m and each element of the array

Reliability_main includes a post-maintenance reliability value Reliability_main,j for a particular maintenance activity.

[0193] In some embodiments, efficiency updater 911 identifies the maintenance activity associated with each binary decision variable B_main,j,i and resets the efficiency h to the corresponding post-maintenance efficiency level h_{main, j} if B_main,j,i = 1 Similarly, reliability estimator 924 can identify the maintenance activity associated with each binary decision variable B_main,j,i and can reset the reliability to the corresponding post maintenance reliability level Reliability_{main, j} if B_main,j,i = 1

[0194] Maintenance cost calculator 926 can be configured to estimate the maintenance cost of connected equipment 610 over the duration of the optimization period. In some embodiments, maintenance cost calculator 926 calculates the maintenance cost during each time step i using the following equation:

where C_main,i is an array of maintenance costs including an element for each of the m different types of maintenance activities that can be performed at time step i and B_main,i is an array of binary decision variables indicating whether each of the m maintenance activities will be performed at time step i. Maintenance cost calculator 926 can sum the maintenance costs over the duration of the optimization period as follows:

where Cost_main is the maintenance cost term of the objective function j.

[0195] In other embodiments, maintenance cost calculator 926 estimates the maintenance cost Cost_main by multiplying the maintenance cost array C_main by the matrix of binary decision variables B_main as shown in the following equations:

Capital Cost Predictor

[0196] Capital cost predictor 930 can be configured to formulate the third term in the objective function j. The third term in the objective function j represents the cost of purchasing new devices of connected equipment 610 over the duration of the optimization period and is shown to include two variables or parameters (i.e., C_cap,i and B_cap,i). Capital cost predictor 930 is shown to include a purchase estimator 932, a reliability estimator 934, a capital cost calculator 936, and a capital costs module 938.

[0197] Reliability estimator 934 can include some or all of the features of reliability estimator 924, as described with reference to maintenance cost predictor 920. For example, reliability estimator 934 can be configured to estimate the reliability of connected equipment 610 based on the equipment performance information received from connected equipment 610. The reliability may be a statistical measure of the likelihood that connected equipment 610 will continue operating without fault under its current operating conditions. Operating under more strenuous conditions (e.g., high load, high temperatures, etc.) may result in a lower reliability, whereas operating under less strenuous conditions (e.g., low load, moderate temperatures, etc.) may result in a higher reliability. In some embodiments, the reliability is based on an amount of time that has elapsed since connected equipment 610 last received maintenance and/or an amount of time that has elapsed since connected equipment 610 was purchased or installed. Reliability estimator 934 can include some or all of the features and/or functionality of reliability estimator 924, as previously described.

[0198] Purchase estimator 932 can be configured to use the estimated reliability of connected equipment 610 over the duration of the optimization period to determine the probability that new devices of connected equipment 610 will be purchased at each time step of the optimization period. In some embodiments, purchase estimator 932 is configured to compare the probability that new devices of connected equipment 610 will be purchased at a given time step to a critical value. Purchase estimator 932 can be configured to set the value of B_cap,i = 1 in response to a determination that the probability that connected equipment 610 will be purchased at time step i exceeds the critical value.

[0199] In some embodiments, purchase estimator 932 generates a matrix B_cap of the binary capital decision variables. The matrix B_cap may include a binary decision variable for each of the different capital purchases that can be made at each time step of the optimization period. For example, purchase estimator 932 can generate the following matrix:

where the matrix B_cap has a size of p x h and each element of the matrix B_cap includes a binary decision variable for a particular capital purchase at a particular time step of the optimization period. For example, the value of the binary decision variable B_cap,k,i indicates whether the kth capital purchase will be made during the ith time step of the optimization period.

[0200] Still referring to FIG. 9, capital cost predictor 930 is shown to include a capital costs module 938 and a capital cost calculator 936. Capital costs module 938 can be configured to determine costs C_cap,i associated with various capital purchases (i.e., purchasing one or more new devices of connected equipment 610). Capital costs module 938 can receive a set of capital costs from an external system or device (e.g., a database, a user device, etc.). In some embodiments, the capital costs define the economic cost (e.g., $) of making various capital purchases. Each type of capital purchase may have a different economic cost associated therewith. For example, purchasing a new temperature sensor may incur a relatively small economic cost, whereas purchasing a new chiller may incur a significantly larger economic cost.

[0201] Capital costs module 938 can use the purchase costs to define the values of C_cap,i in objective function j. In some embodiments, capital costs module 938 stores the capital costs as an array C_cap including a cost element for each of the capital purchases that can be made. For example, capital costs module 938 can generate the following array:

where the array C_cap has a size of 1 x p and each element of the array C_cap includes a cost value C_cap,k for a particular capital purchase k = 1 ... p.

[0202] Some capital purchases may be more expensive than other. However, different types of capital purchases may result in different levels of improvement to the efficiency h and/or the reliability of connected equipment 610. For example, purchasing a new sensor to replace an existing sensor may result in a minor improvement in efficiency h and/or a minor improvement in reliability, whereas purchasing a new chiller and control system may result in a significantly greater improvement to the efficiency h and/or the reliability of connected equipment 610. Accordingly, multiple different levels of post-purchase efficiency (i.e., h_cap) and post-purchase reliability (i.e., Reliability _cap) may exist. Each level of h_cap and Reliability _cap may correspond to a different type of capital purchase. [0203] In some embodiments, purchase estimator 932 stores each of the different levels of h_cap and Reliability _cap in a corresponding array. For example, the parameter h_cap can be defined as an array h_cap with an element for each of the p different types of capital purchases which can be made. Similarly, the parameter Reliability _cap can be defined as an array Reliability_cap with an element for each of the p different types of capital purchases that can be made. Examples of these arrays are shown in the following equations:

where the array h_cap has a size of 1 x p and each element of the array h_cap includes a post purchase efficiency value h_cap,k for a particular capital purchase k. Similarly, the array Reliability _cap has a size of 1 x p and each element of the array Reliability_cap includes a post-purchase reliability value Reliability_cap,k for a particular capital purchase k.

[0204] In some embodiments, efficiency updater 911 identifies the capital purchase associated with each binary decision variable B_main,k,i and resets the efficiency h to the corresponding post-purchase efficiency level h_cap,k if B_cap,k,i = 1. Similarly, reliability estimator 924 can identify the capital purchase associated with each binary decision variable B_cap,k,i and can reset the reliability to the corresponding post-purchase reliability level

.

[0205] Capital cost calculator 936 can be configured to estimate the capital cost of connected equipment 610 over the duration of the optimization period. In some

embodiments, capital cost calculator 936 calculates the capital cost during each time step i using the following equation:

where C_cap,i is an array of capital purchase costs including an element for each of the p different capital purchases that can be made at time step i and B_cap,i is an array of binary decision variables indicating whether each of the p capital purchases will be made at time step i. Capital cost calculator 936 can sum the capital costs over the duration of the optimization period as follows:

where Cost_cap is the capital cost term of the objective function j.

[0206] In other embodiments, capital cost calculator 936 estimates the capital cost Cost_cap by multiplying the capital cost array C_cap by the matrix of binary decision variables B_cap as shown in the following equations:

Objective Function Optimizer

[0207] Still referring to FIG. 9, high level optimizer 832 is shown to include an objective function generator 935 and an objective function optimizer 940. Objective function generator 935 can be configured to generate the objective function j by summing the operational cost term, the maintenance cost term, and the capital cost term formulated by cost predictors 910, 920, and 930. One example of an objective function which can be generated by objective function generator 935 is shown in the following equation:

where C_op,i is the cost per unit of energy (e.g., $/kWh) consumed by connected equipment 610 at time step i of the optimization period, P_op,i is the power consumption (e.g., kW) of connected equipment 610 at time step i , Dt is the duration of each time step i , C_main,i is the cost of maintenance performed on connected equipment 610 at time step i , B_main,i is a binary variable that indicates whether the maintenance is performed, C_cap,i is the capital cost of purchasing a new device of connected equipment 610 at time step i , B_cap,i is a binary variable that indicates whether the new device is purchased, and h is the duration of the horizon or optimization period over which the optimization is performed.

[0208] Another example of an objective function which can be generated by objective function generator 935 is shown in the following equation:

where the array C_op includes an energy cost value C_op,i for a particular time step i = 1 ... h of the optimization period, the array P_op includes a power consumption value P_op,i for a particular time step i = 1 ... h of the optimization period, each element of the array C_main includes a maintenance cost value C_main,j for a particular maintenance activity j = 1 ... m, each element of the matrix B_main includes a binary decision variable for a particular maintenance activity j = 1 ... m at a particular time step i = 1 ... h of the optimization period, each element of the array C_cap includes a capital cost value C_cap,k for a particular capital purchase k = 1 ... p, and each element of the matrix B_cap includes a binary decision variable for a particular capital purchase k = 1 ... p at a particular time step i = 1 ... h of the optimization period.

[0209] Objective function generator 935 can be configured to impose constraints on one or more variables or parameters in the objective function J. The constraints can include any of the equations or relationships described with reference to operational cost predictor 910, maintenance cost predictor 920, and capital cost predictor 930. For example, objective function generator 935 can impose a constraint which defines the power consumption values P_op,i for one or more devices of connected equipment 610 as a function of the ideal power consumption P_ideal,i and the efficiency ^ (e.g., P_op,i = P_ideal,i/hi )_· Objective function generator 935 can impose a constraint which defines the efficiency rp as a function of the binary decision variables B_main,i and B_cap,i as described with reference to efficiency updater 911 and efficiency degrader 913. Objective function generator 935 can impose a constraint which constrains the binary decision variables B_main,i and B_cap,i to a value of either zero or one and defines the binary decision variables B_main,i and B_Cap,i as a function of the reliability Reliability _i of connected equipment 610, as described with reference to maintenance estimator 922 and purchase estimator 932. Objective function generator 935 can impose a constraint which defines the reliability Reliability_i of connected equipment 610 as a function of the equipment performance information (e.g., operating conditions, run hours, etc.) as described with reference to reliability estimators 924 and 934.

[0210] Objective function optimizer 940 can optimize the objective function j to determine the optimal values of the binary decision variables B_main,i and B_cap,i over the duration of the optimization period. Objective function optimizer 940 can use any of a variety of optimization techniques to formulate and optimize the objective function j. For example, objective function optimizer 940 can use integer programming, mixed integer linear programming, stochastic optimization, convex programming, dynamic programming, or any other optimization technique to formulate the objective function j, define the constraints, and perform the optimization. These and other optimization techniques are known in the art and will not be described in detail here.

[0211] In some embodiments, objective function optimizer 940 uses mixed integer stochastic optimization to optimize the objective function j. In mixed integer stochastic optimization, some of the variables in the objective function j can be defined as functions of random variables or probabilistic variables. For example, the decision variables B_main,i and B_Cap,i can be defined as binary variables that have probabilistic values based on the reliability of connected equipment 610. Low reliability values may increase the probability that the binary decision variables B_main,i and B_cap,i will have a value of one (e.g., B_main,i = 1 and B_cap,i = 1), whereas high reliability values may increase the probability that the binary decision variables B_main,i and B_cap,i will have a value of zero (e.g., B_main,i = 0 and B_cap,i = 0). In some embodiments, maintenance estimator 922 and purchase estimator 932 use a mixed integer stochastic technique to define the values of the binary decision variables B_main,i and B_cap,i as a probabilistic function of the reliability of connected equipment 610.

[0212] As discussed above, the objective function j may represent the predicted cost of operating, maintaining, and purchasing one or more devices of connected equipment 610 over the duration of the optimization period. In some embodiments, objective function optimizer 940 is configured to project these costs back to a particular point in time (e.g., the current time) to determine the net present value (NPV) of the one or more devices of connected equipment 610 at a particular point in time. For example, objective function optimizer 940 can project each of the costs in objective function j back to the current time using the following equation:

where r is the interest rate, Cost_i is the cost incurred during time step i of the optimization period, and NP V_cost is the net present value (i.e., the present cost) of the total costs incurred over the duration of the optimization period. In some embodiments, objective function optimizer 940 optimizes the net present value NP V_cost to determine the NPV of one or more devices of connected equipment 610 at a particular point in time.

[0213] As discussed above, one or more variables or parameters in the objective function j can be updated dynamically based on closed-loop feedback from connected equipment 610. For example, the equipment performance information received from connected equipment 610 can be used to update the reliability and/or the efficiency of connected equipment 610. Objective function optimizer 940 can be configured to optimize the objective function j periodically (e.g., once per day, once per week, once per month, etc.) to dynamically update the predicted cost and/or the net present value NP V_cost based on the closed-loop feedback from connected equipment 610.

[0214] In some embodiments, objective function optimizer 940 generates optimization results. The optimization results may include the optimal values of the decision variables in the objective function j for each time step i in the optimization period. The optimization results include operating decisions, equipment maintenance decisions, and/or equipment purchase decisions for each device of connected equipment 610. In some embodiments, the optimization results optimize the economic value of operating, maintaining, and purchasing connected equipment 610 over the duration of the optimization period. In some

embodiments, the optimization results optimize the net present value of one or more devices of connected equipment 610 at a particular point in time. The optimization results may cause BMS 606 to activate, deactivate, or adjust a setpoint for connected equipment 610 in order to achieve the optimal values of the decision variables specified in the optimization results.

[0215] In some embodiments, MPM system 602 uses the optimization results to generate equipment purchase and maintenance recommendations. The equipment purchase and maintenance recommendations may be based on the optimal values for the binary decision variables B_main,i and B_cap,i determined by optimizing the objective function j. For example, a value of B_main,25 = 1 for a particular device of connected equipment 610 may indicate that maintenance should be performed on that device at the 25^th time step of the optimization period, whereas a value of B_main,25 = 0 may indicate that the maintenance should not be performed at that time step. Similarly, a value of B_cap,25 = 1 may indicate that a new device of connected equipment 610 should be purchased at the 25^th time step of the optimization period, whereas a value of B_cap,25 = 0 may indicate that the new device should not be purchased at that time step.

[0216] In some embodiments, the equipment purchase and maintenance recommendations are provided to building 10 (e.g., to BMS 606) and/or to client devices 448. An operator or building owner can use the equipment purchase and maintenance recommendations to assess the costs and benefits of performing maintenance and purchasing new devices. In some embodiments, the equipment purchase and maintenance recommendations are provided to service technicians 620. Service technicians 620 can use the equipment purchase and maintenance recommendations to determine when customers should be contacted to perform service or replace equipment.

Model Predictive Maintenance Process

[0217] Referring now to FIG. 10, a flowchart of a model predictive maintenance process 1000 is shown, according to an exemplary embodiment. Process 1000 can be performed by one or more components of building system 600. In some embodiments, process 1000 is performed by MPM system 602, as described with reference to FIGS. 6-9.

[0218] Process 1000 is shown to include operating building equipment to affect a variable state or condition of a building (step 1002) and receiving equipment performance information as feedback from the building equipment (step 1004). The building equipment can include type of equipment which can be used to monitor and/or control a building (e.g., connected equipment 610). For example, the building equipment can include chillers, AHUs, boilers, batteries, heaters, economizers, valves, actuators, dampers, cooling towers, fans, pumps, lighting equipment, security equipment, refrigeration equipment, or any other type of equipment in a building system or building management system. The building equipment can include any of the equipment of HVAC system 100, waterside system 200, airside system 300, BMS 400, and/or BMS 500, as described with reference to FIGS. 1-5. The equipment performance information can include samples of monitored variables (e.g., measured temperature, measured pressure, measured flow rate, power consumption, etc.), current operating conditions (e.g., heating or cooling load, current operating state, etc.), fault indications, or other types of information that characterize the performance of the building equipment.

[0219] Process 1000 is shown to include estimating an efficiency and reliability of the building equipment as a function of the equipment performance information (step 1006). In some embodiments, step 1006 is performed by efficiency updater 911 and reliability estimators 924, 926 as described with reference to FIG. 9. Step 1006 can include using the equipment performance information to determine the efficiency h of the building equipment under actual operating conditions. In some embodiments, the efficienc hi represents the ratio of the ideal power consumption P_ideal of the building equipment to the actual power consumption P _actual of the building equipment, as shown in the following equation:

where P_ideal is the ideal power consumption of the building equipment as defined by the performance curve for the building equipment and P _actual is the actual power consumption of the building equipment. In some embodiments, step 1006 includes using the equipment performance information collected in step 1002 to identify the actual power consumption value P _actual . Step 1006 can include using the actual power consumption P _actual in combination with the ideal power consumption P_ideal to calculate the efficiency h.

[0220] Step 1006 can include periodically updating the efficiency h to reflect the current operating efficiency of the building equipment. For example, step 1006 can include calculating the efficiency h of the building equipment once per day, once per week, once per year, or at any other interval as may be suitable to capture changes in the efficiency h over time. Each value of the efficiency h may be based on corresponding values of P_ideal and P _actual at the time the efficiency h is calculated. In some embodiments, step 1006 includes updating the efficiency h each time the high level optimization process is performed (i.e., each time the objective function j is optimized). The efficiency value calculated in step 1006 may be stored in memory 810 as an initial efficiency value h₀ , where the subscript 0 denotes the value of the efficiency h at or before the beginning of the optimization period (e.g., at time step 0).

[0221] Step 1006 can include predicting the efficienc hi of the building equipment at each time step i of the optimization period. The initial efficiency h₀ at the beginning of the optimization period may degrade over time as the building equipment degrade in performance. For example, the efficiency of a chiller may degrade over time as a result of the chilled water tubes becoming dirty and reducing the heat transfer coefficient of the chiller. Similarly, the efficiency of a battery may decrease over time as a result of degradation in the physical or chemical components of the battery. Step 1006 can account for such degradation by incrementally reducing the efficiency over the duration of the optimization period.

[0222] In some embodiments, the initial efficiency value h₀ is updated at the beginning of each optimization period. However, the efficiency h may degrade during the optimization period such that the initial efficiency value h₀ becomes increasingly inaccurate over the duration of the optimization period. To account for efficiency degradation during the optimization period, step 1006 can include decreasing the efficiency h by a predetermined amount with each successive time step. For example, step 1006 can include defining the efficiency at each time step i = 1 ... h as follows:

where is the efficiency at time step i, h _i-1 is the efficiency at time step i— 1, and Dh is the degradation in efficiency between consecutive time steps. In some embodiments, this definition of is applied to each time step for which B_main,i = 0 and B_cap,i = 0. However, if either B_main,i = 1 or B_cap,i = 1, the value of hi may be reset to either h _main or h_cap in step 1018.

[0223] In some embodiments, the value of Ah is based on a time series of efficiency values. For example, step 1006 may include recording a time series of the initial efficiency values h₀ , where each of the initial efficiency values h₀ represents the empirically- calculated efficiency of the building equipment at a particular time. Step 1006 can include examining the time series of initial efficiency values h₀ to determine the rate at which the efficiency degrades. For example, if the initial efficiency h₀ at time t₁ is h_0,1 and the initial efficiency at time t₂ is h_0.2, the rate of efficiency degradation can be calculated as follows:

where is the rate of efficiency degradation. Step 1006 can include multiplying by the

duration of each time step Dt to calculate the value of .

[0224] Step 1006 can include estimating the reliability of the building equipment based on the equipment performance information received in step 1004. The reliability may be a statistical measure of the likelihood that the building equipment will continue operating without fault under its current operating conditions. Operating under more strenuous conditions (e.g., high load, high temperatures, etc.) may result in a lower reliability, whereas operating under less strenuous conditions (e.g., low load, moderate temperatures, etc.) may result in a higher reliability. In some embodiments, the reliability is based on an amount of time that has elapsed since the building equipment last received maintenance and/or an amount of time that has elapsed since the building equipment were purchased or installed.

[0225] In some embodiments, step 1006 includes using the equipment performance information to identify a current operating state of the building equipment. The current operating state can be examined to expose when the building equipment begin to degrade in performance and/or to predict when faults will occur. In some embodiments, step 1006 includes estimating a likelihood of various types of failures that could potentially occur the building equipment. The likelihood of each failure may be based on the current operating conditions of the building equipment, an amount of time that has elapsed since the building equipment have been installed, and/or an amount of time that has elapsed since maintenance was last performed. In some embodiments, step 1006 includes identifying operating states and predicts the likelihood of various failures using the systems and methods described in U.S. Patent Application No. 15/188,824 titled“Building Management System With

Predictive Diagnostics” and filed June 21, 2016, the entire disclosure of which is incorporated by reference herein.

[0226] In some embodiments, step 1006 includes receiving operating data from building equipment distributed across multiple buildings. The operating data can include, for example, current operating conditions, fault indications, failure times, or other data that characterize the operation and performance of the building equipment. Step 1006 can include using the set of operating data to develop a reliability model for each type of equipment. The reliability models can be used in step 1006 to estimate the reliability of any given device of the building equipment as a function of its current operating conditions and/or other extraneous factors (e.g., time since maintenance was last performed, time since installation or purchase, geographic location, water quality, etc.).

[0227] One example of a reliability model which can be used in step 1006 is shown in the following equation:

where Reliability_i is the reliability of the building equipment at time step i, OpCond_i are the operating conditions at time step i , Dt_main,i is the amount of time that has elapsed between the time at which maintenance was last performed and time step i , and Dt_cap,i is the amount of time that has elapsed between the time at which the building equipment were purchased or installed and time step i. Step 1006 can include identifying the current operating conditions OpCond_i based on the equipment performance information received as a feedback from the building equipment. Operating under more strenuous conditions (e.g., high load, extreme temperatures, etc.) may result in a lower reliability, whereas operating under less strenuous conditions (e.g., low load, moderate temperatures, etc.) may result in a higher reliability.

[0228] Still referring to FIG. 10, process 1000 is shown to include predicting an energy consumption of the building equipment over an optimization period as a function of the estimated efficiency (step 1008). In some embodiments, step 1008 is performed by ideal performance calculator 912 and/or power consumption estimator, as described with reference to FIG. 9. Step 1008 can include receiving load predictions Load_i from load/rate predictor 822 and performance curves from low level optimizer 834. As discussed above, the performance curves may define the ideal power consumption P_ideal of the building equipment a function of the heating or cooling load on the device or set of devices. For example, the performance curve for the building equipment can be defined by the following equation:

where P_{ideal, i} is the ideal power consumption (e.g., kW) of the building equipment at time step i and Load_i is the load (e.g., tons cooling, kW heating, etc.) on the building equipment at time step i. The ideal power consumption P_{ideal, i} may represent the power consumption of the building equipment assuming they operate at perfect efficiency. Step 1008 can include using the performance curve for the building equipment to identify the value of P_ideal, _ί that corresponds to the load point Load_i for the building equipment at each time step of the optimization period.

[0229] In some embodiments, step 1008 includes estimating the power consumption P_op,i as a function of the ideal power consumption P_{ideal, i} and the efficiency hi of the building equipment. For example, step 1008 can include calculating the power consumption P_op,i using the following equation:

where P_{ideal, i} is the power consumption based on the equipment performance curve for the building equipment at the corresponding load point Load_i and hi is the operating efficiency of the building equipment at time step i.

[0230] Still referring to FIG. 10, process 1000 is shown to include defining a cost Cost_op of operating the building equipment over the optimization period as a function of the predicted energy consumption (step 1010). In some embodiments, step 1010 is performed by operational cost calculator 916, as described with reference to FIG. 9. Step 1010 can include calculating the operational cost during each time step i using the following equation:

where P_op,i is the predicted power consumption at time step i determined in step 1008, C_op,i is the cost per unit of energy at time step i, and Dt is the duration of each time step. Step 1010 can include summing the operational costs over the duration of the optimization period as follows:

where Cost_op is the operational cost term of the objective function j.

[0231] In other embodiments, step 1010 can include calculating the operational cost Cost_op by multiplying the cost array C_op by the power consumption array P_op and the duration of each time step Dt as shown in the following equations:

where the array C_op includes an energy cost value C_op,i for a particular time step i = 1 ... h of the optimization period, the array P_op includes a power consumption value P_op,i for a particular time step i = 1 ... h of the optimization period. [0232] Still referring to FIG. 10, process 1000 is shown to include defining a cost of performing maintenance on the building equipment over the optimization period as a function of the estimated reliability (step 1012). Step 1012 can be performed by

maintenance cost predictor 920, as described with reference to FIG. 9. Step 1012 can include using the estimated reliability of the building equipment over the duration of the optimization period to determine the probability that the building equipment will require maintenance and/or replacement at each time step of the optimization period. In some embodiments, step 1012 includes comparing the probability that the building equipment will require maintenance at a given time step to a critical value. Step 1012 can include setting the value of B_main,i = 1 in response to a determination that the probability that the building equipment will require maintenance at time step i exceeds the critical value.

Similarly, step 1012 can include comparing the probability that the building equipment will require replacement at a given time step to a critical value. Step 1012 can include setting the value of B_cap,i = 1 in response to a determination that the probability that the building equipment will require replacement at time step i exceeds the critical value.

[0233] Step 1012 can include determining the costs C_main,i associated with performing various types of maintenance on the building equipment. Step 1012 can include receiving a set of maintenance costs from an external system or device (e.g., a database, a user device, etc.). In some embodiments, the maintenance costs define the economic cost (e.g., $) of performing various types of maintenance. Each type of maintenance activity may have a different economic cost associated therewith. For example, the maintenance activity of changing the oil in a chiller compressor may incur a relatively small economic cost, whereas the maintenance activity of completely disassembling the chiller and cleaning all of the chilled water tubes may incur a significantly larger economic cost. Step 1012 can include using the maintenance costs to define the values of C_main,i in objective function j.

[0234] Step 1012 can include estimating the maintenance cost of the building equipment over the duration of the optimization period. In some embodiments, step 1012 includes calculating the maintenance cost during each time step i using the following equation:

where B_main,i is an array of maintenance costs including an element for each of the m different types of maintenance activities that can be performed at time step i and B_main,i is an array of binary decision variables indicating whether each of the m maintenance activities will be performed at time step i. Step 1012 can include summing the maintenance costs over the duration of the optimization period as follows:

where Cost_main is the maintenance cost term of the objective function j.

[0235] In other embodiments, step 1012 includes estimating the maintenance cost Cost_main by multiplying the maintenance cost array C_main by the matrix of binary decision variables B_main as shown in the following equations:

where each element of the array C_main includes a maintenance cost value C_main,j for a particular maintenance activity j = 1 ... m and each element of the matrix B_main includes a binary decision variable for a particular maintenance activity j = 1 ... m at a particular time step i = 1 ... h of the optimization period.

[0236] Still referring to FIG. 10, process 1000 is shown to include defining a cost Cost_cap of purchasing or replacing the building equipment over the optimization period as a function of the estimated reliability (step 1014). Step 1014 can be performed by capital cost predictor 930, as described with reference to FIG. 9. In some embodiments, step 1014 includes using the estimated reliability of the building equipment over the duration of the optimization period to determine the probability that new devices of the building equipment will be purchased at each time step of the optimization period. In some embodiments, step 1014 includes comparing the probability that new devices of the building equipment will be purchased at a given time step to a critical value. Step 1014 can include setting the value of B_cap,i = 1 in response to a determination that the probability that the building equipment will be purchased at time step i exceeds the critical value.

[0237] Step 1014 can include determining the costs C_cap,i associated with various capital purchases (i.e., purchasing one or more new devices of the building equipment). Step 1014 can include receiving a set of capital costs from an external system or device (e.g., a database, a user device, etc.). In some embodiments, the capital costs define the economic cost (e.g., $) of making various capital purchases. Each type of capital purchase may have a different economic cost associated therewith. For example, purchasing a new temperature sensor may incur a relatively small economic cost, whereas purchasing a new chiller may incur a significantly larger economic cost. Step 1014 can include using the purchase costs to define the values of C_cap,i in objective function j.

[0238] Some capital purchases may be more expensive than other. However, different types of capital purchases may result in different levels of improvement to the efficiency h and/or the reliability of the building equipment. For example, purchasing a new sensor to replace an existing sensor may result in a minor improvement in efficiency h and/or a minor improvement in reliability, whereas purchasing a new chiller and control system may result in a significantly greater improvement to the efficiency h and/or the reliability of the building equipment. Accordingly, multiple different levels of post-purchase efficiency (i.e., Vcap) and post-purchase reliability (i.e., Reliability _cap) may exist. Each level of h_cap and Reliability _cap may correspond to a different type of capital purchase.

[0239] Step 1014 can include estimating the capital cost of the building equipment over the duration of the optimization period. In some embodiments, step 1014 includes calculating the capital cost during each time step i using the following equation:

where C_cap,i is an array of capital purchase costs including an element for each of the p different capital purchases that can be made at time step i and B_cap,i is an array of binary decision variables indicating whether each of the p capital purchases will be made at time step i. Step 1014 can include summing the capital costs over the duration of the

optimization period as follows:

where Cost_cap is the capital cost term of the objective function j.

[0240] In other embodiments, step 1014 includes estimating the capital cost Cost_cap by multiplying the capital cost array C_cap by the matrix of binary decision variables B_cap as shown in the following equations:

where each element of the array C_cap includes a capital cost value C_cap,k for a particular capital purchase k = 1 ... p and each element of the matrix B_cap includes a binary decision variable for a particular capital purchase k = 1 ... p at a particular time step i = 1 ... h of the optimization period.

[0241] Still referring to FIG. 10, process 1000 is shown to include optimizing an objective function including the costs Cost_op , Cost_main, and Cost_cap to determine an optimal maintenance strategy for the building equipment (step 1016). Step 1016 can include generating the objective function j by summing the operational cost term, the maintenance cost term, and the capital cost term formulated in steps 1010-1014. One example of an objective function which can be generated in step 1016 is shown in the following equation:

[0242] Another example of an objective function which can be generated in step 1016 is shown in the following equation:

[0243] Step 1016 can include imposing constraints on one or more variables or parameters in the objective function J. The constraints can include any of the equations or relationships described with reference to operational cost predictor 910, maintenance cost predictor 920, and capital cost predictor 930. For example, step 1016 can include imposing a constraint which defines the power consumption values P_op,i for one or more devices of the building equipment as a function of the ideal power consumption P_{ideal, i} and the efficiency rp (e.g., P_0p,i = P_{ideal, i}/hi)_· Step 1016 can include imposing a constraint which defines the efficiency rp as a function of the binary decision variables B_main,i and B_cap,i as described with reference to efficiency updater 911 and efficiency degrader 913. Step 1016 can include imposing a constraint which constrains the binary decision variables B_main,i and B_cap,i to a value of either zero or one and defines the binary decision variables B_main,i and B_cap,i as a function of the reliability Reliability _i of connected equipment 610, as described with reference to maintenance estimator 922 and purchase estimator 932. Step 1016 can include imposing a constraint which defines the reliability Reliability _t of connected equipment 610 as a function of the equipment performance information (e.g., operating conditions, run hours, etc.) as described with reference to reliability estimators 924 and 934.

[0244] Step 1016 can include optimizing the objective function j to determine the optimal values of the binary decision variables B_main,i and B_cap,i over the duration of the optimization period. Step 1016 can include using any of a variety of optimization techniques to formulate and optimize the objective function j. For example, step 1016 can include using integer programming, mixed integer linear programming, stochastic optimization, convex programming, dynamic programming, or any other optimization technique to formulate the objective function j, define the constraints, and perform the optimization. These and other optimization techniques are known in the art and will not be described in detail here.

[0245] In some embodiments, step 1016 includes using mixed integer stochastic optimization to optimize the objective function j. In mixed integer stochastic optimization, some of the variables in the objective function j can be defined as functions of random variables or probabilistic variables. For example, the decision variables B_main,i and B_cap,i can be defined as binary variables that have probabilistic values based on the reliability of the building equipment. Low reliability values may increase the probability that the binary decision variables B_main,i and B_cap,i will have a value of one (e.g., B_main,i = 1 and B_cap,i = 1), whereas high reliability values may increase the probability that the binary decision variables B_main,i and B_cap,i will have a value of zero (e.g., B_main,i = 0 and B_cap,i = 0). In some embodiments, step 1016 includes using a mixed integer stochastic technique to define the values of the binary decision variables B_main,i and B_cap,i as a probabilistic function of the reliability of the building equipment.

[0246] As discussed above, the objective function j may represent the predicted cost of operating, maintaining, and purchasing one or more devices of the building equipment over the duration of the optimization period. In some embodiments, step 1016 includes projecting these costs back to a particular point in time (e.g., the current time) to determine the net present value (NPV) of the one or more devices of the building equipment at a particular point in time. For example, step 1016 can include projecting each of the costs in objective function j back to the current time using the following equation:

where r is the interest rate, Cost_i is the cost incurred during time step i of the optimization period, and NP V_cost is the net present value (i.e., the present cost) of the total costs incurred over the duration of the optimization period. In some embodiments, step 1016 includes optimizing the net present value NP V_cost to determine the NPV of the building equipment at a particular point in time.

[0247] As discussed above, one or more variables or parameters in the objective function / can be updated dynamically based on closed-loop feedback from the building equipment. For example, the equipment performance information received from the building equipment can be used to update the reliability and/or the efficiency of the building equipment. Step 1016 can include optimizing the objective function j periodically (e.g., once per day, once per week, once per month, etc.) to dynamically update the predicted cost and/or the net present value NP V_cost based on the closed-loop feedback from the building equipment.

[0248] In some embodiments, step 1016 include generating optimization results. The optimization results may include the optimal values of the decision variables in the objective function j for each time step i in the optimization period. The optimization results include operating decisions, equipment maintenance decisions, and/or equipment purchase decisions for each device of the building equipment. In some embodiments, the

optimization results optimize the economic value of operating, maintaining, and purchasing the building equipment over the duration of the optimization period. In some embodiments, the optimization results optimize the net present value of one or more devices of the building equipment at a particular point in time. The optimization results may cause BMS 606 to activate, deactivate, or adjust a setpoint for the building equipment in order to achieve the optimal values of the decision variables specified in the optimization results.

[0249] In some embodiments, process 1000 includes using the optimization results to generate equipment purchase and maintenance recommendations. The equipment purchase and maintenance recommendations may be based on the optimal values for the binary decision variables B_main,i and B_cap,i determined by optimizing the objective function j. For example, a value of B_main,25 = 1 for a particular device of the building equipment may indicate that maintenance should be performed on that device at the 25^th time step of the optimization period, whereas a value of B_main,25 = 0 may indicate that the maintenance should not be performed at that time step. Similarly, a value of B_cap,25 = 1 may indicate that a new device of the building equipment should be purchased at the 25^th time step of the optimization period, whereas a value of B_cap,25 = 0 may indicate that the new device should not be purchased at that time step.

[0250] In some embodiments, the equipment purchase and maintenance recommendations are provided to building 10 (e.g., to BMS 606) and/or to client devices 448. An operator or building owner can use the equipment purchase and maintenance recommendations to assess the costs and benefits of performing maintenance and purchasing new devices. In some embodiments, the equipment purchase and maintenance recommendations are provided to service technicians 620. Service technicians 620 can use the equipment purchase and maintenance recommendations to determine when customers should be contacted to perform service or replace equipment.

[0251] Still referring to FIG. 10, process 1000 is shown to include updating the efficiency and the reliability of the building equipment based on the optimal maintenance strategy (step 1018). In some embodiments, step 1018 includes updating the efficiency for one or more time steps during the optimization period to account for increases in the efficiency h of the building equipment that will result from performing maintenance on the building equipment or purchasing new equipment to replace or supplement one or more devices of the building equipment. The time steps i at which the efficiency hi is updated may correspond to the predicted time steps at which the maintenance will be performed or the equipment will replaced. The predicted time steps at which maintenance will be performed on the building equipment may be defined by the values of the binary decision variables B_main,i in the objective function j. Similarly, the predicted time steps at which the building equipment will be replaced may be defined by the values of the binary decision variables B_cap,i in the objective function j.

[0252] Step 1018 can include resetting the efficiency for a given time step i if the binary decision variables B_main,i and B_cap,i indicate that maintenance will be performed at that time step and/or new equipment will be purchased at that time step (i.e., B_main,i = 1 and/or B_cap,i = 1). For example, if B_main,i = 1, step 1018 can include resetting the value of hi to h_main , where h_main is the efficiency value that is expected to result from the maintenance performed at time step i. Similarly, if B_cap,i = 1, step 1018 can include resetting the value of to h_cap, where h_cap is the efficiency value that is expected to result from purchasing a new device to supplement or replace one or more devices of the building equipment performed at time step i. Step 1018 can include resetting the efficiency for one or more time steps while the optimization is being performed (e.g., with each iteration of the optimization) based on the values of binary decision variables B_main,i and B_cap,i.

[0253] Step 1018 may include determining the amount of time Dt_main,i that has elapsed since maintenance was last performed on the building equipment based on the values of the binary decision variables B_main,i. For each time step i , step 1018 can examine the corresponding values of B_main at time step i and each previous time step (e.g., time steps i— 1, i— 2, ... , 1). Step 1018 can include calculating the value of Dt_main,i by subtracting the time at which maintenance was last performed (i.e., the most recent time at which B_{main, ί} = 1) from the time associated with time step i. A long amount of time Dt_main,i since maintenance was last performed may result in a lower reliability, whereas a short amount of time since maintenance was last performed may result in a higher reliability.

[0254] Similarly, step 1018 may include determining the amount of time Dt_cap,i that has elapsed since the building equipment were purchased or installed based on the values of the binary decision variables B_cap,i. For each time step i , step 1018 can examine the corresponding values of B_cap at time step i and each previous time step (e.g., time steps i— 1, i— 2, , 1). Step 1018 can include calculating the value of Dt_cap,i by subtracting the time at which the building equipment were purchased or installed (i.e., the most recent time at which B_cap,i = 1) from the time associated with time step i. A long amount of time Dt_cap,i since the building equipment were purchased or installed may result in a lower reliability, whereas a short amount of time since the building equipment were purchased or installed may result in a higher reliability

[0255] Some maintenance activities may be more expensive than other. However, different types of maintenance activities may result in different levels of improvement to the efficiency h and/or the reliability of the building equipment. For example, merely changing the oil in a chiller may result in a minor improvement in efficiency h and/or a minor improvement in reliability, whereas completely disassembling the chiller and cleaning all of the chilled water tubes may result in a significantly greater improvement to the efficiency h and/or the reliability of the building equipment. Accordingly, multiple different levels of post-maintenance efficiency (i.e., h_main) and post-maintenance reliability (i.e., Reliability _main) may exist. Each level of h_main and Reliability_main may correspond to a different type of maintenance activity.

[0256] In some embodiments, step 1018 includes identifying the maintenance activity associated with each binary decision variable B_main,j,i and resets the efficiency h to the corresponding post-maintenance efficiency level h_{main , j} if B_main,j,i = 1 Similarly, step 1018 may include identifying the maintenance activity associated with each binary decision variable B_main,j,i and can reset the reliability to the corresponding post-maintenance reliability level Reliability_main,j i B_main,j,i = .

[0257] Some capital purchases may be more expensive than other. However, different types of capital purchases may result in different levels of improvement to the efficiency h and/or the reliability of the building equipment. For example, purchasing a new sensor to replace an existing sensor may result in a minor improvement in efficiency h and/or a minor improvement in reliability, whereas purchasing a new chiller and control system may result in a significantly greater improvement to the efficiency h and/or the reliability of the building equipment. Accordingly, multiple different levels of post-purchase efficiency (i.e., Reap) and post-purchase reliability (i.e., Reliability _cap) may exist. Each level of h_cap and Reliability _cap may correspond to a different type of capital purchase.

[0258] In some embodiments, step 1018 includes identifying the capital purchase associated with each binary decision variable B_main,k,i and resetting the efficiency h to the corresponding post-purchase efficiency level h _cap,k if B_cap,k,i = 1. Similarly, step 1018 may include identifying the capital purchase associated with each binary decision variable B_cap,k,i and can resetting the reliability to the corresponding post-purchase reliability level Reliability _cap,k if B_main,k,i— 1.

Model Predictive Maintenance with Financial Analysis Functionality

Overview

[0259] Referring generally to FIGS. 11-14, systems and methods for a model predictive maintenance (MPM) system with financial analysis functionality are shown, according to some embodiments. Integrating financial analysis into the MPM system can ensure that optimizations account for a time value of money rather than only advertised costs. As described herein, costs can refer to any literal cost at a particular time step whereas a value of money can be used to determine how much a cost is worth in terms of a baseline value of money (e.g., a value of money at a current time). The time value of money can refer to how a value of money can change over time. For example, if a 5% interest rate is estimated over a next year, $1.00 at a current time can be worth the equivalent of $1.05 at the next year due to a decrease in value of money. The value of money can increase/decrease for a variety of reasons such as, for example, changing federal interest rates, inflation/deflation, etc. As described herein, interest rates are used to refer generally to various reasons for changes in the value of money. In some embodiments, interest rates are used to refer to one or more specific reasons for changes in the value of money. In some embodiments, interest rates are used to refer to an aggregate of all changes in the value of money.

[0260] If the time value of money is not accounted for if optimizing an objective function (e.g., the objective function j), decisions made based on the optimization may be inaccurate. For example, consider a situation where a current cost of replacing a chiller unit is $1,000, a cost of replacing the chiller unit in a year is $1,030, and a current interest rate is 5%. If the interest rate (i.e., the time value of money) is not accounted for, it may be determined that replacing the chiller unit at a current time is more cost-effective than replacing the chiller unit next year as $1,000 is less than $1,030. However, by incorporating the interest rate, it can be determined that an adjusted cost of replacing the chiller unit next year is more cost- effective than replacing the chiller unit at the current time (assuming constant operational costs). In particular, an adjusted cost of replacing the chiller unit next year can be determined to be approximately $981 in terms of a current value of money. As such, accounting for the interest rate can be beneficial for determining how to optimally maintain and replace building equipment over time.

MPM System with Financial Analysis

[0261] Referring now to FIG. 11, MPM system 602 of FIG. 8 is shown in greater detail, according to some embodiments. In particular, high level optimizer 832 is shown to receive interest rates from an interest rate provider 1102. Interest rate provider 1102 can be any service, system, controller, person, etc. that can provide interest rate values to MPM system 602. For example, interest rate provider 1102 may be a banking service that estimates interest rate values. In some embodiments, interest rate provider 1102 automatically provides interest rates to MPM system 602 as the interest rates are updated or provides the interest rates on a predetermined scheduled (e.g., every day). In some embodiments, MPM system 602 requests interest rates based on a need for the interest rates. For example, MPM system 602 may send a request to interest rate provider 1102 to provide the interest rates prior to performing an optimization process. It should be appreciated that MPM system 602 can obtain values of the interest rate by other various methods depending on how interest rate provider 1102 operates. In some embodiments, interest rate provider 1102 is a component of MPM system 602.

[0262] Based on the received interest rates, high level optimizer 832 can perform an optimization process to generate optimization results that account for interest rates over time. The optimization process performed by high level optimizer 832 is described in greater detail below with reference to FIG. 12, however a brief explanation is provided here for clarity. As interest rates evolve over time, a value of money (or another type of cost) can change. Particularly, assuming a positive interest rate, the value of money may decrease over time (i.e., a value of an amount money at a current time is higher than the value of the same amount of money at a future time). Due to changes in the value of money, decisions included in the optimization results can be determined based on current year dollars (i.e., the current value of money) such that future values of money are adjusted to be reflective of the current year dollars.

[0263] In some embodiments, high level optimizer 832 uses a constant interest rate for each time step of a time period (e.g., an optimization period). Using the constant interest rate can simplify calculations, thereby resulting in processing savings. In some

embodiments, high level optimizer 832 uses time-varying interest rates such that each time step of the time period is associated with a specific interest rate. By using time-varying interest rates, results based on the optimization performed by high level optimizer 832 can be determined more accurately as changes in interest rates over time can be accounted for.

[0264] If interest rates are positive, high level optimizer 832 can multiply all future costs by a factor between zero and one based on a value of the interest rate. In some

embodiments, as described above, the interest rate utilized by high level optimizer 832 is a constant rate over the optimization period. In some embodiments, the interest rate varies over time such that an interest rate at a first time step of the optimization period may be different than an interest rate at a second time step. In any case, a factor including the interest rate can be calculated for each time step of an optimization period and multiplied by a total cost of maintenance, replacement, operations, and/or any other costs for each time step. Advantageously, the interest rate can be incorporated into the optimization performed by high level optimizer 832 independent of an optimization method used to perform the optimization.

[0265] By incorporating the interest rate, high level optimizer 832 can generate operational, maintenance, and replacement decisions for building equipment that account for a time value of money. In this way, overall costs can be further optimized (e.g., reduced) for a user (e.g., a building owner) as maintenance/replacement activities can be more accurately determined by accounting for a current value of costs at different time steps of the optimization period.

[0266] Referring now to FIG. 12, a block diagram further illustrating high level optimizer 832 of FIG. 9 is shown, according to some embodiments. As shown in FIG. 12, high level optimizer 832 can incorporate interest rates in the objective function j and optimize the objective function j based on the interest rates.

[0267] High level optimizer 832 is shown to include an interest rate predictor 1202 that can estimate interest rates and provide the estimated interest rates to objective function generator 935. Interest rate predictor 1202 is shown to receive interest rate information. In some embodiments, the interest rate information is included in information provided by interest rate provider 1102 as described with reference to FIG. 11. The interest rate information can include various information that interest rate predictor 1202 can use to estimate interest rates over an optimization period. For example, the interest rate information may include future interest rates. If the interest rate information includes future interest rates, interest rate predictor 1202 can directly generate and provide an interest rate term, discussed in greater detail below, to objective function generator 935. As another example, the interest rate information may include values of past interest rates indicating what the interest rates were at prior time steps. Based on the past interest rates, interest rate predictor 1202 can estimate future interest rates. For example, if interest rates for a past three time steps were 0.02, 0.03, and 0.04 respectively, interest rate predictor 1202 may calculate an average of the past interest rates (i.e., 0.03) to include in the interest rate term provided to objective function generator 935 for upcoming time steps of the optimization period. In general, interest rate predictor 1202 can determine the interest rates using a variety of estimation techniques. [0268] The interest rate term provided by interest rate predictor 1202 can be determined based on estimated interest rates for future time steps of the optimization period. In some embodiments, the interest rate term has the following form:

where a_k is the interest rate term for a time step k and r is a constant interest rate for all time steps of the optimization period. a_k as shown above is calculated based on a constant value of r over the optimization period. However, a time-varying interest rate can be used to calculate a_{k .} Specifically, a_k with time-varying interest rates can be given by the following:

where r_i is an interest rate at a time step i such that i £ k. In this case, a_k can be provided for each time step during the optimization period based on interest rates from a first time step through time step k.

[0269] High level optimizer 832 is also shown to include a failure risk predictor 1204. Failure risk predictor 1204 can generate a risk cost term and provide the risk cost term to objective function generator 935. As building equipment degrades over time, a probability of the building equipment failing may increase. Specifically, the probability that the building equipment may fail at a future time step may be greater than or equal to the probability that the building equipment may fail at a current time step if no

maintenance/replacement of the building equipment is performed. Failure of building equipment may require BMS 606 to incur costs related to maintenance and/or replacement of the building equipment along with various opportunity costs such as unmet loads or missed production. For example, if an indoor unit (IDU) of a variable refrigerant flow (VRF) system fails and the failure results in a safety hazard for occupants of a room, costs related to performing maintenance/replacement of the IDU and costs related to closing the room (e.g., renting a new room for the occupants, cancelling meetings in the room, missed production, etc.) may be incurred.

[0270] The risk cost term generated by failure risk predictor 1204 can incorporate a probability of failure of tracked building equipment for time steps of an optimization period along with a cost of failure of the tracked building equipment. As described, the tracked building equipment can include any building equipment for which a degradation state and/or other performance information is observed.

[0271] Based on the risk cost term provided by failure risk predictor 1204, objective function generator 935 can generate an objective function (e.g., the objective function j) incorporating the risk cost term along with the cost terms provided by predictors 910-930. For example, the objective function generated by objective function generator 935 may have the following form:

where c_op,k (d_k ) is an operational cost dependent on a state of degradation <d_k, c_main,k is a cost of maintenance at time step k of an optimization period, c_{replace k} is a cost of replacement at time step k, m_k is a binary vector representing which maintenance actions are taken at time step k, P_fail,k(d_k) is a vector of probabilities of failure for each component of the tracked building equipment (e.g., each tracked component of BMS 606) dependent on the state of degradation d_k, C_fail,k is a cost of failure of the tracked building equipment, and k is a total number of time steps of the optimization period. In the above objective function, the T superscript indicates a transpose of the associated matrix. Values of C_fail,k can include a cost to repair/replace the tracked building equipment and/or any opportunity costs related to failure of the tracked building equipment. It should be appreciated that the first block of the maintenance vector includes maintenance options while the second block of the maintenance vector includes replacement options. The first and second blocks are split apart to illustrate how maintenance and replacement of building equipment are both considered. In some embodiments, the first and second blocks indicating maintenance and replacement options respectively are combined into a single block. Further, it should be appreciated that C_fail,k ^T _fail,k(d_k) illustrates the risk cost term of the objective function.

[0272] In some embodiments, the objective function generated by objective function generator 935 incorporating the risk cost term has the following form:

where c_fail,i is a cost of failure of building equipment at a time step i of an optimization period, P_fail,i(d_i) is a probability of failure at time step i based on a state of degradation at time step i , and all other variables are as described above. Failure risk of building equipment is described in greater detail in U.S. Patent Application No. 16/457,314 filed June 28, 2019, and in U.S. Patent Application No. 15/426,962 filed February 7, 2017, the entire disclosures of which are incorporated by reference herein.

[0273] Based on the objective function generated incorporating the risk cost term, the operational cost term, the maintenance cost term, and the capital cost term, objective function generator 935 can incorporate the interest rate term provided by interest rate predictor 1202. For example, the objective function j incorporating the interest rate term can be shown by the following equation:

where a_k is given by the following equation:

assuming a constant interest rate r. As described above, r can be time-varying such that a_k is given by the following equation:

Another example of the objective function j generated by objective function generator 935 can be shown by the following equation:

[0274] By incorporating the interest rate term in the objective function j, a total cost of operating, replacing, and maintaining the building equipment can be adjusted based on an interest rate at each time step k of the optimization period. As such, the optimization can be performed such that costs at future steps are adjusted to a value of money at a present time step. In some embodiments, a time step other than the present time step is used as a baseline for a value of money to which costs for other time steps are adjusted to.

[0275] Based on the objective function including the risk cost term and the interest rate term, objective function optimizer 940 can determine optimal values of decision variables such that an overall cost is optimized (e.g., minimized). Due to the risk cost term, certain maintenance and/or replacement may occur at an earlier/later time step than if the risk cost term were not included in the objective function. Particularly, the risk cost term can be managed by objective function optimizer 940 such that a probability of failure for any building device of building equipment is kept sufficiently low such that costs are optimized. The probability of failure of the building equipment can be estimated over a time period based on degradation models of the building equipment. The degradation models can define how the building equipment is expected to degrade based on how the building equipment is operated. For example, a building device that is operating at a maximum load and in a high temperature space may degrade quicker than a building device operated at a low load and cooler temperatures. In some embodiments, degradation models of building equipment are provided during installation of the building equipment. In some

embodiments, degradation models of the building equipment are generated by MPM system 602 based on measured performance variables of the building equipment over time.

[0276] In some embodiments, the risk cost term requires objective function optimizer 940 to ensure building devices of building equipment have maintenance/replacement performed more frequently than if the risk cost term were not included in the objective function such that degradation states of the building devices do not reach critical levels where the building devices are likely to fail.

[0277] In some embodiments, failure of building equipment is considered to occur if a value of d_i exceeds a randomly distributed threshold value. In some embodiments, the threshold values of failure for each building device of building equipment differ depending on the specific building device. For example, if degradation is measured as a percentage of reliability as compared to reliability at installation, a specific IDU may be considered to have failed if the specific IDU falls below 30% of installation reliability, whereas a fan of an HVAC system may be considered to have failed if the fan falls below 20% of installation reliability. In some embodiments, the threshold value of failure for each building device of building equipment is the same. For example, if degradation is measured based on a percentage of installation reliability, if any building device falls below 15% of installation reliability, the building device may be considered to have failed. In some embodiments, failure of building equipment is considered to occur if, for example, the building equipment cannot start, the building equipment is producing outputs that are dangerous for occupants (e.g., smoke, harmful gasses, etc.). Other metrics of failure can also be used to determine if the building equipment has failed. As such, if optimizing the objective function, objective function optimizer 940 can determine values of decisions variables that decrease a probability of building devices failing.

[0278] In some embodiments, objective function optimizer 940 allows some building devices of building equipment to have a high probability of failure (e.g., >50%, >60%, etc.) in order to prioritize maintenance/replacement of other building devices. For example, to optimize costs, objective function optimizer 940 may determine values of decisions variables that result in a fan having a high probability of failure in order perform

maintenance/replacement of a ventilation shaft at an earlier time step. The decision to temporarily allow the fan to have the high probability of failure may a smaller impact on cost (e.g., due to additional maintenance and/or opportunity costs) in comparison to if the ventilation shaft were to fail. As such, maintenance/replacement of the ventilation shaft may be prioritized over maintenance/replacement of the fan in order to further optimize (e.g., reduce) overall costs.

[0279] In some embodiments, the optimization performed by objective function optimizer 940 is constrained by a risk aversion value. A risk aversion value can be set by a user and/or the system to indicate a maximum allowable probability of failure for certain building devices. For example, a user may set a risk aversion value of 45% for building devices with a failure cost greater than $500. Due to the risk aversion value, the optimization can determine an optimal maintenance and replacement schedule such that any building device with an estimated failure cost greater than $500 has a probability of failure of less than 45% throughout an optimization period. Effectively, a risk aversion value can place a constraint on the optimization such that decision variables related to maintenance and/or replacement of building equipment ensure probability of failure of certain building devices is kept below a particular value. In some embodiments, if objective function optimizer 940 cannot determine a solution that maintains a probability of failure of a particular building device below a risk aversion value, an alert is provided to a user indicating the probability of failure of the particular building device may exceed the risk aversion value. [0280] In some embodiments, a probability of failure at any week into the future is found by integrating a density function from the beginning of a week to the end of the week. The probability of failure can be multiplied by a cost of failure and added to the cost function (e.g., the objective function j). In some embodiments, the cost of failure is a random variable rather than a fixed variable. In some embodiments, the probability of failure is displayed on a device (e.g., a mobile device, a computer, etc.). For example, a cumulative distribution function (CDF) of the probability of failure can be indicated on the device as a gradient indicating a probability of failure. The gradient may, for example, transition from green to yellow to red such that green indicates a probability of failure is low, yellow indicates failure is likely approaching, and red indicates failure is likely to happen in the near future.

[0281] Due to the interest rate term, decision variables set by objective function optimizer 940 can be determined such that costs are adjusted for each time step into the future. As a result, some maintenance/replacement activities may be determined to be optimal at different time steps due to the value of money changing over time. For example, consider a situation where a cost of performing maintenance on an outdoor unit (ODU) of a VRF system is constant throughout an optimization period by a maintenance provider (i.e., the maintenance provider does not change a cost of the maintenance throughout the

optimization period). If a positive interest rate exists, the value of money may decrease over time from a current time step. As such, in terms of a present value of money, performing the maintenance of the ODU at a future time step may be less expensive than performing the maintenance at the current time step due to the value of money decreasing while the cost of the maintenance is constant. Alternatively, as another example, if the maintenance provider does adjust the cost of maintenance in accordance with interest rates, a value of the maintenance may be the same at both the current time step and the future time step. Without accounting for the interest rates, the cost increase can appear to increase a value of the maintenance, even though in reality the value is constant when adjusted to a present value of money. As should be evident, the interest rate can impact decisions of the optimization performed by objective function optimizer 940.

[0282] Referring now to FIG. 13, a graph 1300 illustrating differences in a total predicted cost of performing a maintenance activity on building equipment due to an interest rate is shown, according to some embodiments. While graph 1300 is shown specific to a maintenance activity, it should be appreciated that interest rates for other activities (e.g., operational activities, replacement activities, etc.) can be approached similar to and/or the same as discussed below. As shown by graph 1300, a first time step can represent a current time step for which a value of money in future time steps can be calculated based on if accounting for an interest rate. At the first time step, an adjusted cost 1302 and a non- adjusted cost 1304 are shown to be equivalent. Adjusted cost 1302 can represent a cost of performing the maintenance activity that is adjusted based on an interest rate over time whereas non-adjusted cost 1304 can represent a cost of performing the maintenance that is not adjusted based on the interest rate. Adjusted cost 1302 and a non-adjusted cost 1304 may be equivalent at the first time step as an interest rate at the current time step may be 0. In other words, adjusted cost 1302 and non-adjusted cost 1304 can be equivalent at the first time step as a value of the cost of the maintenance activity in terms of a current value of money is equivalent due to the interest rate equaling 0.

[0283] As shown by graph 1300, adjusted cost 1302 and non-adjusted cost 1304 begin to diverge starting at a second time step. At the second time step (and throughout all future time steps shown in graph 1300), non-adjusted cost 1304 maintains a constant cost value. Non-adjusted cost 1304 can maintain the constant cost value as a cost of the maintenance may not change over time. For example, the maintenance activity may cost $1,000 at every step during the optimization period. However, adjusted cost 1302 can begin to decrease starting at the second time step by accounting for an interest rate over time. Specifically, graph 1300 can represent a positive interest rate at all time steps such that the value of money decreases over time. By accounting for the interest rate, adjusted cost 1302 can decrease as based on the value of money at the first time step. In other words, values of non-adjusted cost 1304 can reflect a literal cost of the maintenance activity at each time step whereas adjusted cost 1302 can reflect a cost of the maintenance activity based on the value of money at the first time step. As such, adjusted cost 1302 can indicate actual values of the maintenance activity that should be used if performing an optimization of an objective function (e.g., the objective function j). It should be appreciated that graph 1300 may not be drawn to scale depending on values of the interest rate over time.

MPM Process with Financial Analysis

[0284] Referring now to FIG. 14, a process 1400 for generating an optimal maintenance and replacement strategy for building equipment that accounts for interest rates is shown, according to some embodiments. In some embodiments, certain steps of process 1400 are similar to and/or the same as certain steps of process 1000 as described with reference to FIG. 10. By accounting for the interest rates, decisions that further optimize (e.g., minimize) costs over an optimization can be obtained. Accounting for the interest rates can ensure any decisions generated as a result of performing the optimization account for a time value of money. In this way, changes in the value of money can be accounted for such that all costs are calculated reflective of a current value of money regardless of what time step during an optimization period said costs may occur during. In some embodiments, a different baseline value of money other than the current value of money is used to calculate costs based on. In some embodiments, some and/or all steps of process 1400 are performed by MPM system 602.

[0285] Process 1400 is shown to include operating building equipment to affect a variable state or condition in a building (step 1402). In some embodiments, steps 1402-1414 are similar to and/or the same as steps 1002-1014 of process 1000 as described with reference to FIG. 10. In some embodiments, steps 1402-1414 are performed by MPM system 602.

[0286] Process 1400 is shown to defining a cost Cost_risk associated with a failure risk of the building equipment over the optimization period as a function of the estimated reliability (step 1416). Cost_risk can be defined by a total of all risk costs C_risk,k for each time step k of an optimization period. In some embodiments, step 1416 includes using the estimated reliability of the building equipment over the optimization period to determine a probability of failure of devices of the building equipment at each time step of the optimization period. The probability of failure can be determined based on a degradation model of the building equipment. The degradation model can define the building equipment may degrade over time based on operating conditions of the building equipment (e.g., a load of the building equipment, temperature in a space where the building equipment operates, etc.). Based on the probability of failure of devices, an impact of failure on total costs over the optimization can be estimated. To estimate the impact of failure on total costs, costs related to equipment failure can be determined. In particular, a cost to perform maintenance/replacement of building devices and/or opportunity costs related to failure of the building devices can be determined. Opportunity costs can include any costs beyond maintenance/replacement costs that are incurred due to failure of a building device. For example, if a heater of an HVAC system fails, a space where the heater is located may need to be temporarily closed down (e.g., for occupant safety). Closing the space may result in costs related to occupants renting other spaces, cancellation of valuable meetings, etc., all of which can result in additional costs and/or lost opportunities that can affect total costs of a building system over an optimization period.

[0287] Step 1416 can include determining the costs C_risk,k associated with various risk costs (e.g., a total of maintenance/replacement costs and opportunity costs) at a time step k. Based on the equipment performance information and/or the estimated efficiency and reliability of building equipment determined/estimated in steps 1404 and 1406 respectively, a state of degradation can be estimated. As the estimated state of degradation increases, a probability of failure of building devices may also increase.

[0288] To estimate a state of degradation of all building devices, step 1416 can include, for example, comparing a current estimated reliability of each building device and an optimal reliability based on when each building device was originally installed. To determine a value of C_risk,k, step 1416 can also include estimating a failure cost associated with each building device at each time step k. In some embodiments, failure cost of a building device is estimated by users. In some embodiments, failure cost of a building device is estimated by a system (e.g., MPM system 602) based on various information such as, for example, a location of the building device, how the building device affects conditions of a space, etc.

[0289] Based on the probability of failure and a failure cost of each building device for a time step k, C_risk,k can be determined by the following equation:

where P_fail,k(d_k is a vector of probabilities of failure for each building device of the tracked building equipment on the state of degradation d_k , C_fail,k matrix defining a cost of failure of each building devices. Further, a value of Cost_risk (i.e., a total risk cost over an optimization period) can be determined by the following equation:

where h is a total number of time steps in the optimization period. In some embodiments, step 1416 is performed by failure risk predictor 1204.

[0290] Process 1400 is also shown to include estimating an interest rate at each time step of the optimization period to define an interest rate term a_k (step 1418). The interest rate at each time step can be estimated based on available interest rate information. The available interest rate information can include information such as estimated future interest rates, historical interest rates, economic predictions, etc. Based on the available interest rate information, the interest rates can be estimated for each time step. In some embodiments, a single interest rate r is estimated and applied to each time step. In some embodiments, the interest rate is time-varying such during the optimization period is associated with a specific interest rate value.

[0291] Based on the interest rate(s) determined, a_k can be determined for each time step k. If the single interest rate r is used, a_k may have the following form:

Alternatively, if the time-varying interest rate is determined for each time step k , a_k may have the following form:

In this way, a_k can define a factor to apply to costs related maintenance, replacement, operational, and failure risk as to ensure each cost is calculated in terms of a current value of money. In some embodiments, a different value of money rather than the current value of money is used as a baseline to calculate adjusted costs.

[0292] Process 1400 is also shown to include optimizing an objective function including the costs Cost_op , Cost_main, Cost_risk , Cost_cap, and a_k to determine an optimal maintenance and replacement strategy for the building equipment (step 1420). In some embodiments, step 1420 is similar to and/or the same as step 1016 of process 1000 as described with reference to FIG. 10. The optimal maintenance and replacement strategy can indicate optimal decisions related to maintaining and/or replacing the building equipment over the optimization. By incorporating Cost_risk into the objective function, certain building devices of the building equipment may be prioritized for maintenance/replacement to ensure a probability of failure is kept low. To optimize (e.g., reduce) results of the objective function, building devices with a high opportunity cost associated with failure may be determined by the objective function to receive additional and/or more frequent

maintenance/replacement to ensure a probability of failure of the building devices with the high opportunity cost is kept low (e.g., 1%, 5%, etc.). [0293] In some embodiments, the optimization is constrained by a risk aversion value. A risk aversion value can be set by a user and/or the system to indicate a maximum allowable probability of failure for certain building devices. For example, a user may set a risk aversion value of 20% for building devices with a failure cost equal to or greater than $1,000. Due to the risk aversion value, the optimization can determine an optimal maintenance and replacement schedule such that any building device with an estimated failure cost equal to or greater than $1,000 has a probability of failure of less than 20% throughout an optimization period. Effectively, a risk aversion value can place a constraint on the optimization such that decision variables related to maintenance and/or replacement of building equipment ensure probability of failure of certain building devices is kept below a particular value.

[0294] Further, by accounting for the interest rate over the optimization period, costs at each time step can be adjusted to reflect a value of money at a first time step of the optimization period. In this way, changes in the value of money should not affect decisions of the optimization. In some embodiments, the objective function optimized in step 1420 has the following form:

where all variables are as defined above with reference to FIG. 12. In this case, c_op,k (d_k) over each time step k can define Cost_op , m_k over eac time step k can define a

combined Cost_main and Cost_cap, and c_fail,k ^Tp_fail,k(d_k ) over each time step k can define Cost_{risk .} As shown in the above objective function, a_k can be applied to each cost for each time step k of the optimization period. In this way, all costs are adjusted to be reflective of a value of money at the first time step (i.e., time step k = 1). In some embodiments, step 1420 is performed by objective function optimizer 940.

[0295] Process 1400 is shown to include updating the efficiency and reliability of the building equipment based on the optimal maintenance and replacement strategy (step 1422). In some embodiments, step 1422 is similar to and/or the same as step 1018 of process 1000 as described with reference to FIG. 10. In some embodiments, step 1422 is performed by MPM system 602. Configuration of Exemplary Embodiments

[0296] 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 can be reversed or otherwise varied and the nature or number of discrete elements or positions can 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 can be varied or re-sequenced according to alternative embodiments. Other substitutions, modifications, changes, and omissions can be made in the design, operating conditions and arrangement of the exemplary embodiments without departing from the scope of the present disclosure.

[0297] The present disclosure contemplates methods, systems and program products on any machine-readable media for accomplishing various operations. The embodiments of the present disclosure can 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. 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. [0298] 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 can 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.

Claims

WHAT IS CLAIMED IS:

1. A model predictive maintenance system for building equipment, the system comprising:

one or more processing circuits comprising one or more processors and memory storing instructions that, when executed by the one or more processors, cause the one or more processors to perform operations comprising:

performing an optimization of an objective function that defines a present value of a total cost of operating the building equipment and performing maintenance on the building equipment as a function of operating decisions and maintenance decisions for the building equipment for a plurality of time steps within a time period, the total cost comprising one or more costs incurred during one or more future time steps of the time period; and

operating the building equipment and performing maintenance on the building equipment in accordance with decisions defined by a result of the optimization.

2. The system of Claim 1, wherein the objective function defines the present value as a function of a constant interest rate for the plurality of time steps within the time period.

3. The system of Claim 1, wherein the objective function defines the present value as a function of an interest rate that varies over the time period.

4. The system of Claim 1, wherein the objective function further defines a second present value of a total cost of replacing the building equipment as a function of

replacement decisions for the building equipment for the plurality of time steps within the time period, the total cost of replacing the building equipment comprising a cost of replacing the building equipment incurred during a future time step of the time period.

5. The system of Claim 1, wherein the objective function further defines a risk cost associated with a failure risk of the building equipment at the plurality of time steps of the time period, the risk cost determined based on a degradation model of the building equipment.

6. The system of Claim 1, wherein:

the present value is a net present value of operating and maintaining the building equipment over the time period;

the optimization is performed to minimize the net present value.

7. The system of Claim 1, the operations further comprising updating the present value based on closed-loop feedback of the building equipment, the closed-loop feedback of the building equipment used to update at least one of:

an efficiency of the building equipment; or

a reliability of the building equipment;

wherein the optimization is performed based on the efficiency of the building equipment and the reliability of the building equipment.

8. A method for performing model predictive maintenance of building equipment, the method comprising:

9. The method of Claim 8, wherein the objective function defines the present value as a function of a constant interest rate for the plurality of time steps within the time period.

10. The method of Claim 8, wherein the objective function defines the present value as a function of an interest rate that varies over the time period.

11. The method of Claim 8, wherein the objective function further defines a second present value of a total cost of replacing the building equipment as a function of

12. The method of Claim 8, wherein the objective function further defines a risk cost associated with a failure risk of the building equipment at the plurality of time steps of the time period, the risk cost determined based on a degradation model of the building equipment.

13. The method of Claim 8, wherein:

the optimization is performed to minimize the net present value.

14. The method of Claim 8, further comprising updating the present value based on closed-loop feedback of the building equipment, the closed-loop feedback of the building equipment used to update at least one of:

an efficiency of the building equipment; or

a reliability of the building equipment;

15. A controller for performing model predictive maintenance of building equipment, the controller comprising:

one or more processors; and

one or more non-transitory computer-readable media storing instructions that, when executed by the one or more processors, cause the one or more processors to perform operations comprising:

16. The controller of Claim 15, wherein the objective function defines the present value as a function of a constant interest rate for the plurality of time steps within the time period.

17. The controller of Claim 15, wherein the objective function defines the present value as a function of an interest rate that varies over the time period.

18. The controller of Claim 15, wherein the objective function further defines a second present value of a total cost of replacing the building equipment as a function of

19. The controller of Claim 15, wherein the objective function further defines a risk cost associated with a failure risk of the building equipment at the plurality of time steps of the time period, the risk cost determined based on a degradation model of the building equipment.

20. The controller of Claim 15, wherein:

the optimization is performed to minimize the net present value.