BUILDING HVAC SYSTEM WITH MODEL CALIBRATION

Abstract

A controller for HVAC equipment uses a predictive model for the HVAC equipment to calculate a plurality of values of a model-predicted heating or cooling load of the HVAC equipment at a plurality of time steps within a time period, obtains a plurality of values of an actual heating or cooling load of the HVAC equipment at the plurality of time steps within the time period, generates a calibration model that relates the model-predicted heating or cooling load to the actual heating or cooling load using the plurality of values of the model-predicted heating or cooling load and the plurality of values of the actual heating or cooling load, uses the calibration model to calculate calibrated values of the model-predicted heating or cooling load of the HVAC equipment, and operates the HVAC equipment using the calibrated values of the model-predicted heating or cooling load.

Description

BACKGROUND

The present disclosure relates generally to heating, ventilation, or air conditioning (HVAC) systems for buildings, and more particularly to system identification for developing and using a predictive model to control building HVAC equipment.

System identification refers to the process of generating of a predictive model that describes a real system. For example, in the context of a building HVAC system, system identification can be performed to develop a thermal model of a building or building space which can be used for predictive control (e.g., model predictive control). Because the physical phenomena that govern such systems are often complex, nonlinear, and poorly understood, system identification requires the determination of model parameters based on measured and recorded data from the real system in order to generate an accurate predictive model.

SUMMARY

One implementation of the present disclosure is a controller for HVAC equipment including one or more processors and one or more non-transitory computer-readable media storing instructions. When executed by the one or more processors, the instructions cause the one or more processors to perform operations including using a predictive model for the HVAC equipment to calculate a plurality of values of a model-predicted heating or cooling load of the HVAC equipment at a plurality of time steps within a time period, obtaining a plurality of values of an actual heating or cooling load of the HVAC equipment at the plurality of time steps within the time period, generating a calibration model that relates the model-predicted heating or cooling load to the actual heating or cooling load using the plurality of values of the model-predicted heating or cooling load and the plurality of values of the actual heating or cooling load, using the calibration model to calculate calibrated values of the model-predicted heating or cooling load of the HVAC equipment, and operating the HVAC equipment using the calibrated values of the model-predicted heating or cooling load.

In some embodiments, using the calibration model to calculate the calibrated values of the model-predicted heating or cooling load comprises performing an equation-based calibration process includes providing the plurality of values of the model-predicted heating or cooling load as inputs to the calibration model and calculating the adjusted values of the model-predicted heating or cooling load as outputs of the calibration model.

In some embodiments, using the calibration model to calculate the calibrated values of the model-predicted heating or cooling load comprises performing a model-based calibration process includes obtaining adjusted model parameters by modifying parameters of the predictive model based on parameters of the calibration model, replacing the parameters of the predictive model with the adjusted model parameters to generate a calibrated predictive model, and using the calibrated predictive model to directly output the calibrated values of the model-predicted heating or cooling load.

In some embodiments, generating the calibration model includes performing a regression process using the plurality of values of the model-predicted heating or cooling load at the plurality of time steps and the plurality of values of the actual heating or cooling load at the plurality of time steps to generate values of parameters of the calibration model.

In some embodiments, generating the calibration model comprises further includes determining whether the parameters of the calibration model are practical in representing physics of building thermal dynamics and adjusting the values of the parameters of the calibration model in response to determining that the values of the parameters of the calibration model are not practical in representing the physics of the building thermal dynamics.

In some embodiments, operations further include obtaining initial states of the predictive model by running the predictive model for a previous time period prior to the time period comprising the plurality of time steps.

In some embodiments, using the predictive model to calculate the plurality of values of the model-predicted heating or cooling load includes determining whether the HVAC equipment are on or off at each time step of the time period, setting a value of the model-predicted heating or cooling load to zero for each time step during which the HVAC equipment are off during the time period, using the predictive model to calculate a value of the model-predicted heating or cooling load for each time step during which the HVAC equipment are on during the time period.

In some embodiments, operating the HVAC equipment using the calibrated values of the model-predicted heating or cooling load includes using the calibrated values of the model-predicted heating or cooling load to plan a sequence of control actions for the HVAC equipment over a future time period and operating the HVAC equipment over a future time period using the sequence of control actions.

In some embodiments, operating the HVAC equipment using the calibrated values of the model-predicted heating or cooling load includes performing an optimization-based control process using the calibrated values of the model-predicted heating or cooling load to generate control actions for the HVAC equipment over a future time period.

In some embodiments, operating the HVAC equipment using the calibrated values of the model-predicted heating or cooling load includes estimating a cost savings resulting from operating the HVAC equipment in accordance with the calibrated values of the model-predicted heating or cooling load and using the cost savings to perform a measurement and verification process for the HVAC equipment.

Another implementation of the present disclosure is a method for operating HVAC equipment including using a predictive model for the HVAC equipment to calculate a plurality of values of a model-predicted heating or cooling load of the HVAC equipment at a plurality of time steps within a time period, obtaining a plurality of values of an actual heating or cooling load of the HVAC equipment at the plurality of time steps within the time period, generating a calibration model that relates the model-predicted heating or cooling load to the actual heating or cooling load using the plurality of values of the model-predicted heating or cooling load and the plurality of values of the actual heating or cooling load, using the calibration model to calculate calibrated values of the model-predicted heating or cooling load of the HVAC equipment, and operating the HVAC equipment using the calibrated values of the model-predicted heating or cooling load.

In some embodiments, using the calibration model to calculate the calibrated values of the model-predicted heating or cooling load comprises performing an equation-based calibration process includes providing the plurality of values of the model-predicted heating or cooling load as inputs to the calibration model and calculating the adjusted values of the model-predicted heating or cooling load as outputs of the calibration model.

In some embodiments, using the calibration model to calculate the calibrated values of the model-predicted heating or cooling load comprises performing a model-based calibration process includes obtaining adjusted model parameters by modifying parameters of the predictive model based on parameters of the calibration model, replacing the parameters of the predictive model with the adjusted model parameters to generate a calibrated predictive model, and using the calibrated predictive model to directly output the calibrated values of the model-predicted heating or cooling load.

In some embodiments, generating the calibration model includes performing a regression process using the plurality of values of the model-predicted heating or cooling load at the plurality of time steps and the plurality of values of the actual heating or cooling load at the plurality of time steps to generate values of parameters of the calibration model.

In some embodiments, generating the calibration model comprises further includes determining whether the parameters of the calibration model are practical in representing physics of building thermal dynamics and adjusting the values of the parameters of the calibration model in response to determining that the values of the parameters of the calibration model are not practical in representing the physics of the building thermal dynamics.

In some embodiments, method further includes obtaining initial states of the predictive model by running the predictive model for a previous time period prior to the time period comprising the plurality of time steps.

In some embodiments, using the predictive model to calculate the plurality of values of the model-predicted heating or cooling load includes determining whether the HVAC equipment are on or off at each time step of the time period, setting a value of the model-predicted heating or cooling load to zero for each time step during which the HVAC equipment are off during the time period, using the predictive model to calculate a value of the model-predicted heating or cooling load for each time step during which the HVAC equipment are on during the time period.

In some embodiments, operating the HVAC equipment using the calibrated values of the model-predicted heating or cooling load includes using the calibrated values of the model-predicted heating or cooling load to plan a sequence of control actions for the HVAC equipment over a future time period and operating the HVAC equipment over a future time period using the sequence of control actions.

In some embodiments, operating the HVAC equipment using the calibrated values of the model-predicted heating or cooling load includes performing an optimization-based control process using the calibrated values of the model-predicted heating or cooling load to generate control actions for the HVAC equipment over a future time period.

In some embodiments, operating the HVAC equipment using the calibrated values of the model-predicted heating or cooling load includes estimating a cost savings resulting from operating the HVAC equipment in accordance with the calibrated values of the model-predicted heating or cooling load and using the cost savings to perform a measurement and verification process for the HVAC equipment.

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 FIGURES

Various objects, aspects, features, and advantages of the disclosure will become more apparent and better understood by referring to the detailed description taken in conjunction with the accompanying drawings, in which like reference characters identify corresponding elements throughout. In the drawings, like reference numbers generally indicate identical, functionally similar, and/or structurally similar elements.

FIG. 1 is a drawing of a building equipped with a HVAC system, according to an exemplary embodiment.

FIG. 2 is a block diagram of the building and HVAC system of FIG. 1, according to an exemplary embodiment.

FIG. 3 is a circuit-style diagram of a model of the building and HVAC system of FIG. 1, according to an exemplary embodiment.

FIG. 4 is a block diagram of a controller for use with the HVAC system of FIG. 1, according to an exemplary embodiment.

FIG. 5 is a detailed block diagram of a model identifier of the controller of FIG. 4, according to an exemplary embodiment.

FIG. 6 is flowchart of a process for calibrating and using a predictive model to operate HVAC equipment which can be performed by the HVAC system of FIG. 1, according to an exemplary embodiment.

FIG. 7 is flowchart of another process for calibrating and using a predictive model to operate HVAC equipment which can be performed by the HVAC system of FIG. 1, according to an exemplary embodiment.

DETAILED DESCRIPTION OF THE FIGURES

Overview

Referring generally to the FIGURES, systems and methods for calibrating and using a predictive model to operate HVAC equipment are shown, according to an exemplary embodiment. The systems and methods described herein can be used to adapt a model that predicts a heating or cooling load for HVAC equipment to ensure that the model-predicted heating or cooling load values accurately reflect the actual heating or cooling load values. Various model calibration techniques are disclosed including an equation-based calibration in which the model-predicted heating or cooling load values are adjusted after being generated by the model and a model-based calibration in which the parameters of the model are adjusted such that the model-predicted heating or cooling load values are accurate and do not require further adjustment. The systems and methods described herein can be used to generate and adapt predictive models for HVAC equipment, perform a measurement and verification (M&V) process, and enable various other use cases as described in detail below.

Building HVAC Systems

Referring to FIG. 1, a perspective view of a building 10 is shown. Building 10 is served by a building management system (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

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.

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.

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.

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.

HVAC system 100 thereby provides heating and cooling to the building 10. The building 10 also includes other sources of heat transfer that the indoor air temperature in the building 10. The building mass (e.g., walls, floors, furniture) influences the indoor air temperature in building 10 by storing or transferring heat (e.g., if the indoor air temperature is less than the temperature of the building mass, heat transfers from the building mass to the indoor air). People, electronic devices, other appliances, etc. (“heat load”) also contribute heat to the building 10 through body heat, electrical resistance, etc. Additionally, the outside air temperature impacts the temperature in the building 10 by providing heat to or drawing heat from the building 10.

HVAC System and Model

Referring now to FIG. 2, a block diagram of the HVAC system 100 with building 10 is shown, according to an exemplary embodiment. More particularly, FIG. 2 illustrates the variety of heat transfers that affect the indoor air temperature T_ia of the indoor air 201 in zone 200 of building 10. Zone 200 is a room, floor, area, etc. of building 10. In general, the primary goal of the HVAC system 100 is to maintain the indoor air temperature T_ia in the zone 200 at or around a desired temperature to facilitate the comfort of occupants of the zone 200 or to meet other needs of the zone 200.

As shown in FIG. 2, the indoor air temperature T_ia of the zone 200 has a thermal capacitance C_ia. The indoor air temperature T_ia is affected by a variety of heat transfers {dot over (Q)} into the zone 200, as described in detail below. It should be understood that although all heat transfers {dot over (Q)} are shown in FIG. 2 as directed into the zone 200, the value of one or more of the heat transfers {dot over (Q)} may be negative, such that heat flows out of the zone 200.

The heat load 202 contributes other heat transfer {dot over (Q)}_other to the zone 200. The heat load 202 includes the heat added to the zone by occupants (e.g., people, animals) that give off body heat in the zone 200. The heat load 202 also includes computers, lighting, and other electronic devices in the zone 200 that generate heat through electrical resistance, as well as solar irradiance.

The building mass 204 contributes building mass heat transfer {dot over (Q)}_m to the zone 200. The building mass 204 includes the physical structures in the building, such as walls, floors, ceilings, furniture, etc., all of which can absorb or give off heat. The building mass 204 has a temperature T_m and a lumped mass thermal capacitance C_m. The resistance of the building mass 204 to exchange heat with the indoor air 201 (e.g., due to insulation, thickness/layers of materials, etc.) may be characterized as mass thermal resistance R_mi.

The outdoor air 206 contributes outside air heat transfer {dot over (Q)}_oa to the zone 200. The outdoor air 206 is the air outside of the building 10 with outdoor air temperature T_oa. The outdoor air temperature T_oa fluctuates with the weather and climate. Barriers between the outdoor air 206 and the indoor air 201 (e.g., walls, closed windows, insulation) create an outdoor-indoor thermal resistance R_oi to heat exchange between the outdoor air 206 and the indoor air 201.

The HVAC system 100 also contributes heat to the zone 200, denoted as {dot over (Q)}_HVAC. The HVAC system 100 includes HVAC equipment 210, controller 212, an indoor air temperature sensor 214 and an outdoor air temperature sensor 216. The HVAC equipment 210 may include the waterside system 120 and airside system 130 of FIG. 1, or other suitable equipment for controllably supplying heating and/or cooling to the zone 200. In general, HVAC equipment 210 is controlled by a controller 212 to provide heating (e.g., positive value of {dot over (Q)}_HVAC) or cooling (e.g., a negative value of {dot over (Q)}_HVAC) to the zone 200.

The indoor air temperature sensor 214 is located in the zone 200, measures the indoor air temperature T_ia, and provides the measurement of T_ia to the controller 212. The outdoor air temperature sensor 216 is located outside of the building 10, measures the outdoor air temperature T_oa, and provides the measurement of T_oa to the controller 212.

The controller 212 receives the temperature measurements T_oa and T_ia, generates a control signal for the HVAC equipment 210, and transmits the control signal to the HVAC equipment 210. The operation of the controller 212 is discussed in detail below. In general, the controller 212 considers the effects of the heat load 202, building mass 204, and outdoor air 206 on the indoor air 201 in controlling the HVAC equipment 210 to provide a suitable level of {dot over (Q)}_HVAC. A model of this system for use by the controller 212 is described with reference to FIG. 3.

In the embodiments described herein, the control signal provide to the HVAC equipment 210 by the controller 110 indicates a temperature setpoint T_sp for the zone 200. To determine the temperature setpoint T_sp, the controller 212 assumes that the relationship between the indoor air temperature T_ia and the temperature setpoint T_sp follows a proportional-integral control law with saturation, represented as:

$\begin{array}{cc}{\dot{Q}}_{\mathrm{HVAC},j}=K_{p,j}{\epsilon }_{sp}+K_{I,j}{\int }_0^t{\epsilon }_{sp}\left(s\right)\mathrm{ds}& \left(\mathrm{Eq}.A\right)\end{array}$ $\begin{array}{cc}{\epsilon }_{sp}=T_{\mathrm{sp},j}-T_{ia}& \left(\mathrm{Eq}.B\right)\end{array}$

where j∈{clg, hlg} is the index that is used to denote either heating or cooling mode. Different parameters K_p,j and K_l,j are needed for the heating and cooling mode. Moreover, the heating and cooling load is constrained to the following set: {dot over (Q)}_HVAC,j∈[0, {dot over (Q)}_clg,max] for cooling mode (j=clg) and {dot over (Q)}_HVAC,j∈[−{dot over (Q)}_htg,max, 0] for heating mode (j=htg). As discussed in detail below with reference to FIG. 4, the controller 212 uses this model in generating a control signal for the HVAC equipment 210.

Referring now to FIG. 3, a circuit-style diagram 300 (i.e., a thermal circuit model) corresponding to the zone 200 and the various heat transfers {dot over (Q)} of FIG. 2 is shown, according to an exemplary embodiment. In general, the diagram 300 models the zone 200 as a two thermal resistance, two thermal capacitance, control-oriented thermal mass system. This model can be characterized by the following system of linear differential equations, described with reference to FIG. 3 below:

$\begin{array}{cc}{C}_{ia}{\dot{T}}_{ia}=\frac{1}{R_{mi}}\left(T_m-T_{ia}\right)+\frac{1}{R_{oi}}\left(T_{oa}-T_{ia}\right)-{\dot{Q}}_{HVAC}+{\dot{Q}}_{other}& \left(\mathrm{Eq}.C\right)\end{array}$ $\begin{array}{cc}{C}_m{\dot{T}}_m=\frac{1}{R_{mi}}\left(T_{ia}-T_m\right)& \left(\mathrm{Eq}.D\right)\end{array}$

where the first line (Eq. C) focuses on the indoor air temperature T_ia, and each term in Eq. C corresponds to a branch of diagram 300 as explained below.

Indoor air node 302 corresponds to the indoor air temperature T_ia. From indoor air node 302, the model branches in several directions, including down to a ground 304 via a capacitor 306 with a capacitance C_ia. The capacitor 306 models the ability of the indoor air to absorb or release heat and is associated with the rate of change of the indoor heat transfer {dot over (T)}_ia. Accordingly, the capacitor 306 enters Eq. C on the left side of the equation as C_ia{dot over (T)}_ia.

From indoor air node 302, the diagram 300 also branches left to building mass node 310, which corresponds to the thermal mass temperature T_m. A resistor 312 with mass thermal resistance R_mi separates the indoor air node 302 and the building mass node 310, modeling the heat transfer {dot over (Q)}_m from the building mass 204 to the indoor air 201 as

$\frac{1}{R_{mi}}\left(T_m-T_{ia}\right).$

This term is included on the right side of Eq. C above as contributing to the rate of change of the indoor air temperature {dot over (T)}_ia.

The diagram 300 also branches up from indoor air node 302 to outdoor air node 314. A resistor 316 with outdoor-indoor thermal resistance R_oi separates the indoor air node 302 and the outdoor air node 314, modeling the flow heat from the outdoor air 206 to the indoor air 201 as

$\frac{1}{R_{oi}}\left(T_{oa}-T_{ia}\right).$

This term is also included on the right side of Eq. C above as contributing to the rate of change of the indoor air temperature {dot over (T)}_ia.

Also from indoor air node 302, the diagram 300 branches right to two {dot over (Q)} sources, namely {dot over (Q)}_HVAC and {dot over (Q)}_other. As mentioned above, {dot over (Q)}_other corresponds to heat load 202 and to a variety of sources of energy that contribute to the changes in the indoor air temperature T_ia. {dot over (Q)}_other is not measured or controlled by the HVAC system 100, yet contributes to the rate of change of the indoor air temperature {dot over (T)}_ia. {dot over (Q)}_HVAC is generated and controlled by the HVAC system 100 to manage the indoor air temperature T_ia. Accordingly, {dot over (Q)}_HVAC and {dot over (Q)}_other are included on the right side of Eq. C above.

The second nonlinear differential equation (Eq. D) above focuses on the rate of change {dot over (T)}_m in the building mass temperature T. The capacity of the building mass to receive or give off heat is modelled by capacitor 318. Capacitor 318 has lumped mass thermal capacitance C_m and is positioned between a ground 304 and the building mass node 310 and regulates the rate of change in the building mass temperature T_m. Accordingly, the capacitance C_m is included on left side of Eq. D. Also branching from the building mass node 310 is resistor 312 leading to indoor air node 302. As mentioned above, this branch accounts for heat transfer {dot over (Q)}_m between the building mass 204 and the indoor air 201. Accordingly, the term

$\frac{1}{R_{mi}}\left(T_{ia}-T_m\right)$

is included on the right side of Eq. D.

As described in detail below, the model represented by diagram 300 is used by the controller 212 in generating a control signal for the HVAC equipment 210. More particularly, the controller 212 uses a state-space representation of the model shown in diagram 300. The state-space representation used by the controller 212 can be derived by incorporating Eq. A and B with Eq. C and D, and writing the resulting system of equations as a linear system of differential equations to get:

$\begin{array}{cc}\left[\begin{array}{c}{\stackrel{.}{T}}_{\mathrm{ia}}\\ {\stackrel{.}{T}}_m\\ \stackrel{.}{I}\end{array}\right]=\left[\begin{array}{ccc}\frac{1}{C_{\mathrm{ia}}}\left(K_{p,j}-\frac{1}{R_{mi}}-\frac{1}{R_{\mathrm{oi}}}\right)& \frac{1}{C_{\mathrm{ia}}{R}_{mi}}& \frac{K_{I,j}}{C_{\mathrm{ia}}}\\ \frac{1}{C_m{R}_{mi}}& -\frac{1}{C_m{R}_{mi}}& 0\\ -1& 0& 0\end{array}\right]\left[\begin{array}{c}{T}_{\mathrm{ia}}\\ T_m\\ I\end{array}\right]+\left[\begin{array}{cc}-\frac{K_{p,j}}{C_{\mathrm{ia}}}& \frac{1}{C_{\mathrm{ia}}{R}_{\mathrm{oi}}}\\ 0& 0\\ 1& 0\end{array}\right]\left[\begin{array}{c}{T}_{\mathrm{spj}}\\ T_{\mathrm{oa}}\end{array}\right]+\left[\begin{array}{c}\frac{1}{C_{\mathrm{ia}}}\\ 0\\ 0\end{array}\right]{\stackrel{.}{Q}}_{\mathrm{other}};& \left(\mathrm{Eq}.E\right)\end{array}$ $\begin{array}{cc}\left[\begin{array}{c}{T}_{\mathrm{ia}}\\ {\stackrel{.}{Q}}_{\mathrm{HVAC},j}\end{array}\right]=\left[\begin{array}{ccc}1& 0& 0\\ -K_{p,j}& 0& K_{I,j}\end{array}\right]\left[\begin{array}{c}{T}_{\mathrm{ia}}\\ T_m\\ I\end{array}\right]+\left[\begin{array}{cc}0& 0\\ K_{p,j}& 0\end{array}\right]\left[\begin{array}{c}{T}_{\mathrm{sp},j}\\ T_{\mathrm{oa}}\end{array}\right];& \left(\mathrm{Eq}.F\right)\end{array}$

where I represents the integral term ∫₀^tε_sp(s)ds from Eq. A. The resulting linear system has three states (T_ia, T_m, I), two inputs (T_sp,j, T_oa), two outputs (T_ia, {dot over (Q)}_HVAC), and one disturbance {dot over (Q)}_other. Because {dot over (Q)}_other is not measured or controlled, the controller 212 models the disturbance {dot over (Q)}_other using an input disturbance model that adds a fourth state d to the state space representation. In a more compact form, this linear system of differential equations can be written as:

$\begin{array}{cc}\dot{x}\left(t\right)=A_c\left(\theta \right)x\left(t\right)+B_c\left(\theta \right)u\left(t\right);& \left(\mathrm{Eq}.G\right)\end{array}$ $\begin{array}{cc}y\left(t\right)=C_c\left(\theta \right)x\left(t\right)+D_c\left(\theta \right)u\left(t\right);& \left(\mathrm{Eq}.H\right)\end{array}$ $\mathrm{where}$ $A_c\left(\theta \right)=\left[\begin{array}{ccc}-\left({\theta }_1+{\theta }_2+{\theta }_4{\theta }_5\right)& {\theta }_2& {\theta }_4{\theta }_5{\theta }_6\\ {\theta }_3& -{\theta }_3& 0\\ -1& 0& 0\end{array}\right],B_c\left(\theta \right)=\left[\begin{array}{cc}{\theta }_4{\theta }_5& {\theta }_1\\ 0& 0\\ 1& 0\end{array}\right],$ $C_c\left(\theta \right)=\left[\begin{array}{ccc}1& 0& 0\\ -{\theta }_5& 0& {\theta }_5{\theta }_6\end{array}\right],D_c\left(\theta \right)=\left[\begin{array}{cc}0& 0\\ {\theta }_5& 0\end{array}\right];$ ${\theta }_1=\frac{1}{C_{ia}{R}_{oi}};{\theta }_2=\frac{1}{C_{ia}{R}_{mi}};{\theta }_3=\frac{1}{C_m{R}_{mi}};{\theta }_4=\frac{1}{C_{ia}};{\theta }_5=K_p;\mathrm{and}{\theta }_6=\frac{1}{\tau }$ $\dot{x}\left(t\right)=\left[\begin{array}{c}{\stackrel{.}{T}}_{ia}\\ {\dot{T}}_m\\ \stackrel{.}{I}\end{array}\right];x\left(t\right)=\left[\begin{array}{c}{T}_{ia}\\ T_m\\ I\end{array}\right];u\left(t\right)=\left[\begin{array}{c}{T}_{\mathrm{spj}}\\ T_{\mathrm{oa}}\end{array}\right].$

As described in detail below, the controller 212 uses a two-step process to parameterize the system. In the first step, the controller 212 identifies the system parameters θ={θ₁, θ₂, θ₃, θ₄, θ₅, θ₆} (i.e., the values of C_ia, C_m, R_mi, R_oi, K_p,j, K_i,j). The disturbance state d is then introduced into the model and an Kalman estimator gain is added, such that in the second step the controller 212 identifies the Kalman gain parameters K.

As used herein, the term “variable” refers to an item/quantity capable of varying in value over time or with respect to change in some other variable. A “value” as used herein is an instance of that variable at a particular time. A value may be measured or predicted. For example, the temperature setpoint T_sp is a variable that changes over time, while T_sp(3) is a value that denotes the setpoint at time step 3 (e.g., 68 degrees Fahrenheit). The term “predicted value” as used herein describes a quantity for a particular time step that may vary as a function of one or more parameters.

Controller for HVAC Equipment with System Identification

Referring now to FIG. 4, a detailed diagram of the controller 212 is shown, according to an exemplary embodiment. The controller 212 includes a processing circuit 400 and a communication interface 402. The communication interface 402 is structured to facilitate the exchange of communications (e.g., data, control signals) between the processing circuit 400 and other components of HVAC system 100. As shown in FIG. 4, the communication interface 402 facilitates communication between the processing circuit 400 and the outdoor air temperature sensor 216 and the indoor air temperature sensor 214 to all temperature measurements T_oa and T_ia to be received by the processing circuit 400. The communication interface 402 also facilitates communication between the processing circuit 400 and the HVAC equipment 210 that allows a control signal (indicated as temperature setpoint T_sp) to be transmitted from the processing circuit 400 to the HVAC equipment 210.

The processing circuit 400 is structured to carry out the functions of the controller described herein. The processing circuit 400 includes a processor 404 and a memory 406. The processor 404 may be implemented as a general-purpose processor, an application-specific integrated circuit, one or more field programmable gate arrays, a digital signal processor, a group of processing components, or other suitable electronic processing components. The memory 406, described in detail below, includes one or more memory devices (e.g., RAM, ROM, NVRAM, Flash Memory, hard disk storage) that store data and/or computer code for facilitating at least some of the processes described herein. For example, the memory 406 stores programming logic that, when executed by the processor 404, controls the operation of the controller 212. More particularly, the memory 406 includes a training data generator 408, a training data database 410, a model identifier 412, a model predictive controller 414, and an equipment controller 416. The various generators, databases, identifiers, controllers, etc. of memory 406 may be implemented as any combination of hardware components and machine-readable media included with memory 406.

The equipment controller 416 is configured to generate a temperature setpoint T_sp that serves as a control signal for the HVAC equipment 210. The equipment controller receives inputs of the indoor air temperature T_ia from the indoor air temperature sensor 214 via the communication interface 402 and {dot over (Q)}_HVAC from the model predictive controller 414 (during normal operation) and the training data generator 408 (during a training data generation phase described in detail below). The equipment controller 416 uses T_ia and {dot over (Q)}_HVAC to generate T_sp by solving Eq. A and Eq. B above for T_sp. The equipment controller 416 then provides the control signal T_sp to the HVAC equipment 210 via the communication interface 402.

The model predictive controller 414 determines {dot over (Q)}_HVAC based on an identified model and the temperature measurements T_ia, T_oa, and provides {dot over (Q)}_HVAC to the equipment controller 416. The model predictive controller 414 follows a model predictive control (MPC) approach. The MPC approach involves predicting future system states based on a model of the system, and using those predictions to determine the controllable input to the system (here, {dot over (Q)}_HVAC) that bests achieves a control goal (e.g., to maintain the indoor air temperature near a desired temperature). A more accurate model allows the MPC to provide better control based on more accurate predictions. Because the physical phenomena that define the behavior of the system (i.e., of the indoor air 201 in the building 10) are complex, nonlinear, and/or poorly understood, a perfect model derived from first-principles is generally unachievable or unworkable. Thus, the model predictive controller 414 uses a model identified through a system identification process facilitated by the training data generator 408, the training data database 410, and the model identifier 412, described in detail below.

System identification, as facilitated by the training data generator 408, the training data database 410, and the model identifier 412, is a process of constructing mathematical models of dynamic systems. System identification provides a suitable alternative to first-principles-derived model when first principles models are unavailable or too complex for on-line MPC computations. System identification captures the important and relevant system dynamics based on actual input/output data (training data) of the system, in particular by determining model parameters particular to a building or zone to tune the model to the behavior of the building/zone. As described in detail below, the training data generator 408, the training data database 410, and the model identifier 412 each contribute to system identification by the controller 212.

The training data generator 408 is configured to generate training data by providing an excitation signal to the system. That is, the training data generator provides various {dot over (Q)}_HVAC values to the equipment controller 416 for a number N of time steps k, and receives the measured output response of the indoor air temperature T_ia at each time step k from the air temperature sensor 214. The various {dot over (Q)}_HVAC values may be chosen by the training data generator 408 to explore the system dynamics as much as possible (e.g., across a full range of possible {dot over (Q)}_HVAC values, different patterns of {dot over (Q)}_HVAC values, etc.).

The equipment controller 416 receives the various {dot over (Q)}_HVAC values and generates various control inputs T_sp in response. The temperature setpoint T_sp for each time step k is provided to the HVAC equipment 210, which operates accordingly to heat or cool the zone 200 (i.e., to influence T_ia). The temperature setpoints T_sp may also be provided to the training data generator 408 to be included in the training data. The training data generator 408 receives an updated measurement of the indoor air temperature T_ia for each time step k and may also receive the outdoor air temperature T_oa for each time step k. The training data generator 408 thereby causes the states, inputs, and outputs of the system to vary across the time steps k and generates data corresponding to the inputs and outputs.

The inputs and outputs generated by the training data generator 408 are provided to the training data database 410. More particularly, in the nomenclature of the model of Eq. E and Eq. F above, the training data generator 408 provides inputs T_sp and T_oa and outputs {dot over (Q)}_HVAC and T_ia for each time step k to the training data database 410.

The training data database 410 stores the inputs and outputs for each time step k provided by the training data generator 408. Each input and output are tagged with a time step identifier, so that data for the same time step can be associated together. The training data database 410 thereby collects and stores input and output data for each time step k, k=0, . . . , N, or, more specifically, T_sp(k), T_oa(k), T_ia(k), and {dot over (Q)}_HVAC(k), for k, k=0, . . . , N. This data is grouped together in the training data database 410 in a set of training data Z^N. In the notation of Eq. G and Eq. H, Z^N=[y(1), u(1), y(2), u(2), . . . , y(N), u(N)].

In some embodiments, the training data is refined using a saturation detection and removal process. System and methods for saturation detection and removal suitable for use to refine the training data Z^N are described in U.S. patent application Ser. No. 15/900,459, filed Feb. 20, 2018, incorporated by reference herein in its entirety. For example, as described in detail therein, the training data may be filtered by determining whether the operating capacity is in a non-transient region for a threshold amount of a time period upon determining that an error for the building zone exists for the time period, and in response to a determination that the operating capacity is in the non-transient region for at least the threshold amount of the time period, indicating the time period as a saturation period. Data from the saturation period can then be removed from the training data.

The model identifier 412 accesses the training data database 410 to retrieve the training data Z^N and uses the training data Z^N to identify a model of the system. The model identifier 412 includes a system parameter identifier 418 and a gain parameter identifier 420. As shown in detail in FIG. 5 and discussed in detail with reference thereto, the system parameter identifier 418 carries out a first step of system identification, namely identifying the model parameters, while the gain parameter identifier 420 carries out the second step, namely determining a Kalman gain estimator. The model parameters and the Kalman gain estimator are included in an identified model of the system, and that model is provided to the model predictive controller 414. The model predictive controller can thus facilitate the control of the HVAC equipment 210 as described above.

Referring now to FIG. 5, a detailed view of the model identifier 412 is shown, according to an exemplary embodiment. As mentioned above, the model identifier 412 includes the system parameter identifier 418 and the gain parameter identifier 420. The system parameter identifier 418 is structured to identify the matrices A, B, C, D of Eqs. G and H, i.e., the values of θ={θ₁, θ₂, θ₃, θ₄, θ₅, θ₆}. In the embodiment described herein, this corresponds to finding the values of C_ia, C_m, R_mi, R_oi, K_p,j, and K_i,j.

The system parameter identifier 418 includes a model framework identifier 422, a prediction error function generator 424, and an optimizer 426. The model framework identifier 422 identifies that the model of the system, denoted as (θ), corresponds to the form described above in Eqs. G and H, i.e.,

$\begin{array}{cc}\dot{x}\left(t\right)=A_c\left(\theta \right)x\left(t\right)+B_c\left(\theta \right)u\left(t\right);& \left(\mathrm{Eq}.G\right)\end{array}$ $\begin{array}{cc}y\left(t\right)=C_c\left(\theta \right)x\left(t\right)+D_c\left(\theta \right)u\left(t\right).& \left(\mathrm{Eq}.H\right)\end{array}$

The model framework identifier 422 thereby determines that the system parameter identifier 418 has the goal of determining a parameter vector {circumflex over (θ)}_N from the set of θ∈⊂^d, where is the set of admissible model parameter values. The resulting possible models are given by the set: M={(θ), θ∈}. The goal of the system parameter identifier 418 is to select a parameter vector {circumflex over (θ)}_N from among possible values of θ that best matches the model to the physical system (i.e., the vector θ is a list of variables and the vector {circumflex over (θ)}_N is a list of values), thereby defining matrices A, B, C, and D. The model framework identifier 422 also receives training data Z^N and sorts the training data (i.e., T_sp(k), T_oa(k), T_ia(k), and {dot over (Q)}_HVAC(k), for k, k=0, . . . , N) into the notation of Eq. G-H as input/output data Z^N=[y(1), u(1), y(2), u(2), . . . , y(N), u(N)].

The prediction error function generator 424 receives the model framework M={(θ), θ∈} and the training data Z^N from the model framework identifier 422. The prediction error function generator 424 applies a prediction error method to determine the optimal parameter vector {circumflex over (θ)}_N. In general, prediction error methods determine the optimal parameter vector {circumflex over (θ)}_N by minimizing some prediction performance function V_N(θ, Z^N) that is based in some way on the difference between predicted outputs and the observed/measured outputs included in the training data Z^N. That is, the parameter estimation θ_N is determined as:

{circumflex over (θ)}_N={circumflex over (θ)}_N(Z^N)=arg V_N(θ,Z^N).

The prediction error function generator 424 use one or more of several possible prediction error approaches to generate a prediction performance function V_N(θ, Z^N). In the embodiment shown, the prediction error function generator applies a simulation approach. In the simulation approach, the prediction error function generator 424 uses the model (θ), the input trajectory [u(1), u(2), . . . , u(N)], and an initial state x(0) to produce predicted outputs in terms of θ. That is, the prediction error function generator 424 predicts:

[ŷ(1|0,θ),ŷ(2|0,θ) . . . ,ŷ(k|0,θ) . . . ,ŷ(N|0,θ)],

where ŷ(k|0, θ) denotes the predicted output at time step k given the training data from time 0 and the model (θ). The prediction error function generator 424 then calculates a prediction error at each time step k is given by ε(k, θ):=y(k)−ŷ(k|0, θ). The prediction error function generator 424 then squares the two-norm of each prediction error ε(k, θ) and sums the results to determine the prediction performance function, which can be written as:

$\begin{array}{cc}{V}_N\left(\theta ,Z^N\right)={\sum }_{k=1}^N{y\left(k\right)-\hat{y}\left(k|0,\theta \right)}_2^2.& \left(\mathrm{Eq}.I\right)\end{array}$

In an alternative embodiment, the prediction error function generator 424 applies a one-step-ahead prediction error method to generate the prediction performance function V_N(θ, Z^N). In the one-step-ahead prediction error method, the prediction error function generator 424 uses past input-output data and the model (θ) the model to predict the output one step ahead in terms of θ. That is, in the one-step ahead prediction error method, the prediction error function generator 424 generates one-step ahead predictions ŷ(k|k−1, θ), which denotes the predicted output at time step k given the past input-output sequence Z^k−1 and using parameters θ. The one-step ahead prediction ŷ(k|k−1, θ) is then compared to the measured output y(k) by the prediction error function generator 424 to determine the prediction error at k, defined as ε(k, θ):=y(k)−ŷ(k|k−1, θ). The prediction error function generator 424 then squares the two-norm of the prediction errors for each k and sums the results, generating a prediction performance function that can be expressed in a condensed form as:

$\begin{array}{cc}{V}_N\left(\theta ,Z^N\right)=\frac{1}{N}{\sum }_{k=1}^N{y\left(k\right)-\hat{y}\left(k|k-1,\theta \right)}_2^2.& \left(\mathrm{Eq}.J\right)\end{array}$

In other alternative embodiments, the prediction error function generator 424 uses a multi-step ahead prediction error approach to generate the prediction performance function. An example of a multi-step ahead prediction error approach is described in detail in U.S. Pat. No. 10,718,542 granted Jul. 21, 2020, the entire disclosure of which is incorporated by reference herein. The prediction error function generator 424 then provides the performance function V_N(θ, Z^N) (i.e., from Eq. I or Eq. J in various embodiments) to the optimizer 426.

The optimizer 426 receives the prediction error function generated by the prediction error function generator 424 and optimizes the prediction error function in θ to determine {circumflex over (θ)}_N. More specifically, the optimizer 426 finds the minimum value of the prediction error function V_N(θ, Z^N) as θ is varied throughout the allowable values of θ∈. That is, the optimizer 426 determines {circumflex over (θ)}_N based on:

{circumflex over (θ)}_N={circumflex over (θ)}_N(Z^N)=V_N(θ,Z^N).

The optimizer 426 then uses {circumflex over (θ)}_N to calculate the matrices A, B, C, and D. The system parameter identifier 418 then provides the identified matrices A, B, C, D to the gain parameter identifier 420.

The gain parameter identifier 420 receives the model with the matrices A, B, C, D (i.e., the model parameters) from system parameter identifier 418, as well as the training data Z^N from the training data database 410, and uses that information to identify the gain parameters. The gain parameter identifier 420 includes an estimator creator 428, a prediction error function generator 430, and an optimizer 432.

The estimator creator 428 adds a disturbance model and introduces a Kalman estimator gain to account for thermal dynamics of the system, for example for the influence of {dot over (Q)}_other on the system. The estimator creator 428 generates an augmented model with disturbance state d, given by:

$\left[\begin{array}{c}\stackrel{.}{x}\left(t\right)\\ \stackrel{.}{d}\left(t\right)\end{array}\right]=\left[\begin{array}{cc}{A}_c& B_d\\ 0& 0\end{array}\right]\left[\begin{array}{c}x\left(t\right)\\ d\left(t\right)\end{array}\right]+\left[\begin{array}{c}{B}_c\\ 0\end{array}\right]u\left(t\right);$ $y\left(t\right)=\left[\begin{array}{cc}{C}_c& C_d\end{array}\right]\left[\begin{array}{c}x\left(t\right)\\ d\left(t\right)\end{array}\right]+D_{c}u\left(t\right)$

where the parameters A_c, B_c, C_c, and D_c are the matrices A, B, C, D received from the system parameter identifier 418 and the disturbance model is selected with

$B_d=\frac{1}{C_{ia}}$

and C_d=0.

The estimator creator 428 then converts the model to a discrete time model, for example using 5-minute sampling periods, resulting in the matrices A_dis, B_dis, C_dis, D_dis and the disturbance model discrete time matrix B_ddis. The estimator creator 428 then adds a parameterized estimator gain, resulting in the following model:

$\begin{array}{cc}\left[\begin{array}{c}\hat{x}\left(t+1❘t\right)\\ \hat{d}\left(t+1❘t\right)\end{array}\right]=\left[\begin{array}{cc}{A}_{\mathrm{dis}}& B_{d_{\mathrm{dis}}}\\ 0& I\end{array}\right]\left[\begin{array}{c}\hat{x}\left(t❘t-1\right)\\ \hat{d}\left(t❘t-1\right)\end{array}\right]+\left[\begin{array}{c}{B}_{\mathrm{dis}}\\ 0\end{array}\right]u\left(t\right)+\underset{=:K\left(\varphi \right)}{\underbrace{\left[\begin{array}{c}{K}_x\left(\varphi \right)\\ K_d\left(\varphi \right)\end{array}\right]}}\left(y\left(t\right)-\hat{y}\left(t❘t-1\right)\right);& \left(\mathrm{Eq}.K\right)\end{array}$ $\begin{array}{cc}\hat{y}\left(t❘t-1\right)=\left[\begin{array}{cc}{C}_{\mathrm{dis}}& 0\end{array}\right]\left[\begin{array}{c}\hat{x}\left(t❘t-1\right)\\ \hat{d}\left(t❘t-1\right)\end{array}\right]+D_{\mathrm{dis}}u\left(t\right).& \left(\mathrm{EQ}.L\right)\end{array}$

The matrix K(ϕ) is the estimator gain parameterized with the parameter vector ϕ where:

$K_x\left(\varphi \right)=\left[\begin{array}{cc}{\varphi }_1& {\varphi }_2\\ {\varphi }_3& {\varphi }_4\\ {\varphi }_5& {\varphi }_6\end{array}\right];$ $K_d\left(\varphi \right)=\left[\begin{array}{cc}{\varphi }_7& {\varphi }_8\end{array}\right].$

In this notation, {circumflex over (x)}(t+1|t) is an estimate of the state at time t+1 obtained using the Kalman filter and made utilizing information at sampling time t. For example, with a sampling time of five minutes, {circumflex over (x)}(t+1|t) is an estimate of the state five minutes after the collection of the data that the estimate is based on. The goal of the gain parameter identifier 420 is to identify parameters {circumflex over (ϕ)}_N (i.e., a vector of for each of ϕ₁ . . . ϕ₈) that make the model best match the physical system.

The estimator creator 428 then provides the discrete time model with estimator gain (i.e., Eqs. K-L) to the prediction error function generator 430. The prediction error function generator 430 receives the model from the estimator creator 428 as well as the training data Z^N from the training data database 410, and uses the model (with the estimator gain) and the training data Z^N to generate a prediction performance function. The prediction error function generator 430 can use any of a variety of prediction error methods including a single-step ahead prediction error method, a multi-step ahead prediction error method, or any other prediction error method (e.g., the simulation approach discussed above). Examples of a multi-step ahead prediction error method are described in detail in U.S. Pat. No. 10,718,542 granted Jul. 21, 2020.

Each multiple prediction ŷ(k+h|k−1, ϕ) is then compared to the corresponding measured output y(k) by the prediction error function generator 430 to determine the prediction error at k, defined as ε(k, θ):=y(k)−ŷ(k+h|k−1, ϕ). The prediction error function generator 430 then squares the two-norm of the prediction errors for each k and sums the results, in some embodiments using a weighting function w(h). The prediction error function generator 430 thereby generates a prediction performance function that can be expressed in a condensed form as:

$\begin{array}{cc}{V}_N\left(\varphi ,Z^N\right)=\sum _{k=1}^{N-h_{\max }+1}\sum _{h=0}^{h_{\max }}w\left(h\right){y\left(k+h\right)-\hat{y}\left(k+h|k-1,\varphi \right)}_2^2.& \left(\mathrm{Eq}.M\right)\end{array}$

The prediction error function generator 430 then provides the prediction performance function (i.e., Eq. M) to the optimizer 432. The optimizer 432 receives the prediction error function V_N(ϕ, Z^N) generated by the prediction error function generator 430 and optimizes the prediction error function in ϕ to determine {circumflex over (ϕ)}_N. More specifically, the optimizer 426 finds the minimum value of the prediction error function V_N(ϕ, Z^N) as ϕ is varied throughout the allowable values of ϕ. In some cases, all real values of ϕ are allowable. That is, the optimizer 426 determines {circumflex over (ϕ)}_N based on:

{circumflex over (ϕ)}_N={circumflex over (ϕ)}_N(Z^N)=arg min_ϕV_N(ϕ,Z^N).

The optimizer 432 then uses {circumflex over (ϕ)}_N to calculate the matrices K_x(ϕ) and K_d(ϕ), resulting in a fully identified model. The gain parameter identifier 420 provides the identified model to the model predictive controller 414.

Model Calibration

In some embodiments, the model identifier 412 is configured to calibrate the identified model (e.g., Eqs. C-H) to account for differences between the values of {dot over (Q)}_HVAC calculated from the model and the actual values of {dot over (Q)}_HVAC based on sensor data or operating data for HVAC equipment (e.g., load data for chillers, controllers, etc.). As used herein, the variable {dot over (Q)}_HVAC,actual denotes the actual {dot over (Q)}_HVAC based on sensor data or operating data for the HVAC equipment, whereas the variable {dot over (Q)}_HVAC,model denotes the {dot over (Q)}_HVAC calculated from the model. An expression for {dot over (Q)}_HVAC,model can be obtained by rearranging Eq. C above as follows:

$\begin{array}{cc}{\dot{Q}}_{\mathrm{HVAC},\mathrm{model}}=C_{\mathrm{ia}}{\dot{T}}_{\mathrm{ia}}-\frac{1}{R_{mi}}\left(T_m-T_{ia}\right)-\frac{1}{R_{oi}}\left(T_{oa}-T_{ia}\right)-\alpha {\dot{Q}}_{other}& \left(\mathrm{Eq}.N\right)\end{array}$

where α is a scaling factor applied to the heat load disturbance {dot over (Q)}_other. The model shown in Eq. N can be used to back-calculate the value of {dot over (Q)}_HVAC,model when the values for the other variables T_m, T_ia, T_oa, and {dot over (Q)}_other are known or can be estimated/calculated.

When using Eq. N to back-calculate the values of {dot over (Q)}_HVAC,model, values for some of the variables in Eq. N can be obtained from sensors. For example, values of the indoor air temperature T_ia and the outdoor air temperature T_oa can be obtained from the indoor air temperature sensor 214 and the outdoor air temperature sensor 216 respectively, as described with reference to FIGS. 2-4. Values for other variables can be estimated or calculated. For example, values of the building mass temperature T_m can be obtained from the model because T_m is one of the system states estimated/predicted by the model. Values of the heat load disturbance {dot over (Q)}_other can be obtained using the techniques described in U.S. Pat. No. 11,215,375 titled “Building Control System with Heat Disturbance Estimation and Prediction” granted Jan. 4, 2022, the entire disclosure of which is incorporated by reference herein. Values for each of these variables can be gathered/generated over time and stored in a database (e.g., as a timeseries of values). Historical values of these variables can be used to back-calculate the values of {dot over (Q)}_HVAC,model for historical time steps, whereas current or future values of these variables can be used to estimate or predict the values of {dot over (Q)}_HVAC,model for future time steps.

In some embodiments, the model identifier 412 uses a calibration model to express the actual HVAC load {dot over (Q)}_HVAC,actual as a function of the model-calculated HVAC load {dot over (Q)}_HVAC,model as follows:

$\begin{array}{cc}{\dot{Q}}_{\mathrm{HVAC},\mathrm{actual}}={\beta }_0{\dot{Q}}_{\mathrm{HVAC},\mathrm{model}}+{\beta }_1+{\beta }_{2}t+{\beta }_3{t}^2& \left(\mathrm{Eq}.O\right)\end{array}$

where t is a time factor value (e.g., hour factor values from 0 to 23, one for each hour in the day), β₁ is an offset, and β₂ and β₃ are time scale factors. The values of β₀-β₃ are model coefficients which can be obtained by performing a system identification or model training process, using the values of {dot over (Q)}_HVAC,model, {dot over (Q)}_HVAC,actual, and t as training data. During the model training process, the model identifier 412 can obtain the training data values of t and the other variables {dot over (Q)}_HVAC,model and {dot over (Q)}_HVAC,actual based on the particular time step to which Eq. O is applied. For example, the values of {dot over (Q)}_HVAC,model can be obtained by back-calculation using Eq. N as described above, using the values of T_m, T_ia, T_oa, and {dot over (Q)}_other at a particular time step t. For example, if the time step t=0 (midnight), the values of T_m, T_ia, T_oa, and {dot over (Q)}_other can be obtained for that same time step and used to back-calculate {dot over (Q)}_HVAC model at that time step. Similarly, the values of {dot over (Q)}_HVAC,actual can be obtained from actual sensor data or equipment operating data for that time step. The model identifier 412 can obtain a set of training data including values for {dot over (Q)}_HVAC,model, {dot over (Q)}_HVAC,actual, and t over a given time period (i.e., for each time step within the time period) and use the training data to perform a model fitting process to generate or determine values of the model coefficients β₁-β₃.

In some embodiments, the model identifier 412 calculates the values of {dot over (Q)}_HVAC,model using Eq N. and then plugs the calculated values of {dot over (Q)}_HVAC,model into Eq. O after the values of β₁-β₃ have been determined to calculate the values of {dot over (Q)}_HVAC,actual. This process referred to as “equation-based calibration” in the present disclosure. In other embodiments, the model identifier 412 calibrates or updates the parameters of the predictive model (e.g., Eqs. C-H) such that the values of {dot over (Q)}_HVAC predicted by the model more closely align with {dot over (Q)}_HVAC,actual. This process referred to as “model-based calibration” in the present disclosure. The steps performed by the model identifier 412 when performing model-based calibration are described below.

For the model-based calibration, the expression for {dot over (Q)}_HVAC,actual from Eq. O can be combined with the expression for {dot over (Q)}_HVAC,model from Eq. N to express {dot over (Q)}_HVAC,actual as follows:

$\begin{array}{cc}{\widehat{\stackrel{.}{Q}}}_{\mathrm{HVAC},\mathrm{actual}}={\beta }_0{\dot{Q}}_{\mathrm{HVAC},\mathrm{model}}+{\beta }_1+{\beta }_{2}t+{\beta }_3{t}^2={\beta }_0\left(C_{ia}{\dot{T}}_{ia}-\frac{1}{R_{mi}}\left(T_m-T_{ia}\right)-\frac{1}{R_{oi}}\left(T_{oa}-T_{ia}\right)-\alpha {\dot{Q}}_{other}\right)+{\beta }_1+{\beta }_{2}t+{\beta }_3{t}^2& \left(\mathrm{Eq}.P\right)\end{array}$

where the hat notation {dot over ({circumflex over (Q)})}_HVAC,actual indicates a predicted or estimated value for {dot over (Q)}_HVAC,model rather than the actual value obtained from sensor data or equipment operating data. The values of {dot over (Q)} HVAC,actual may be referred to as adjusted values of the model-predicted HVAC load {dot over (Q)}_HVAC,model, as they have been adjusted or adapted to more accurately reflect the values of {dot over (Q)}_HVAC,actual.

To have the same format as Eq. N, Eq. P can be rearranged as:

$\begin{array}{cc}{\widehat{\stackrel{.}{Q}}}_{\mathrm{HVAC},\mathrm{actual}}={\beta }_0{C}_{ia}{\dot{T}}_{\mathrm{ia}}-\frac{{\beta }_0}{R_{mi}}\left(T_m-T_{ia}\right)-\frac{{\beta }_0}{R_{oi}}\left(T_{oa}-T_{ia}\right)-{\beta }_0\alpha {\dot{Q}}_{other}+{\beta }_1+{\beta }_{2}t+{\beta }_3{t}^2={\beta }_0{C}_{ia}{\dot{T}}_{\mathrm{ia}}-\frac{{\beta }_0}{R_{mi}}\left(T_m-T_{ia}\right)-\frac{{\beta }_0}{R_{oi}}\left(T_{oa}-T_{ia}\right)-\alpha \left({\beta }_0{\dot{Q}}_{other}-\frac{{\beta }_1+{\beta }_{2}t+{\beta }_3{t}^2}{\alpha }\right)& \left(\mathrm{Eq}.Q\right)\end{array}$

Comparing Eq. Q with Eq. N, it is evident that the original parameters of the model have changed as follows when calibrating the model to predict {dot over ({circumflex over (Q)})}_HVAC,actual instead of {dot over (Q)}_HVAC,model:

$C_{ia}^{\prime }={\beta }_0{C}_{ia}$ $R_{mi}^{\prime }=\frac{R_{mi}}{{\beta }_0}$ $R_{oi}^{\prime }=\frac{R_{oi}}{{\beta }_0}$ $C_m^{\prime }={\beta }_0{C}_m$ ${\dot{Q}}_{\mathrm{other}}^{\prime }={\beta }_0{\dot{Q}}_{\mathrm{other}}-\frac{{\beta }_1+{\beta }_{2}t+{\beta }_3{t}^2}{\alpha }$

The calibrated model shown in Eq. Q can be rewritten in terms of the updated parameters as follows:

$\begin{array}{cc}{\widehat{\stackrel{.}{Q}}}_{\mathrm{HVAC},\mathrm{actual}}=C_{ia}^{\prime }{\dot{T}}_{ia}-\frac{1}{R_{mi}^{\prime }}\left(T_m-T_{ia}\right)-\frac{1}{R_{oi}^{\prime }}\left(T_{oa}-T_{ia}\right)-\alpha {\dot{Q}}_{\mathrm{other}}^{\prime }& \left(\mathrm{Eq}.R\right)\end{array}$

The state-space parameters θ₁-θ₄ used in Eqs. G-H can be rewritten in terms of the updated parameters as follows:

$\begin{array}{cc}{\theta }_1^{\prime }=\frac{1}{C_{ia}^{\prime }{R}_{\mathrm{oi}}^{\prime }}=\frac{1}{{\beta }_0{C}_{ia}\frac{R_{\mathrm{oi}}}{{\beta }_0}}=\frac{1}{C_{ia}{R}_{\mathrm{oi}}}={\theta }_1& \left(\mathrm{Eqs}.S\right)\end{array}$ ${\theta }_2^{\prime }=\frac{1}{C_{ia}^{\prime }{R}_{mi}^{\prime }}=\frac{1}{{\beta }_0{C}_{ia}\frac{R_{mi}}{{\beta }_0}}=\frac{1}{C_{ia}{R}_{mi}}={\theta }_2$ ${\theta }_3^{\prime }=\frac{1}{C_m^{\prime }{R}_{mi}^{\prime }}=\frac{1}{{\beta }_0{C}_m\frac{R_{mi}}{{\beta }_0}}=\frac{1}{C_m{R}_{mi}}={\theta }_3$ ${\theta }_4^{\prime }=\frac{1}{C_{ia}^{\prime }}=\frac{1}{{\beta }_0{C}_{ia}}=\frac{{\theta }_4}{{\beta }_0}$

It is evident from Eqs. S that only the indoor air coefficient θ₄ has been changed (i.e., scaled by a factor of 1/β₀) whereas the other state-space parameters θ₁-θ₃ remain unchanged. Additionally, the scaling parameter α applied to {dot over (Q)}_other remains unchanged, whereas the value of {dot over (Q)}_other is changed to

${\dot{Q}}_{\mathrm{other}}^{\prime }={\beta }_0{\dot{Q}}_{\mathrm{other}}-\frac{{\beta }_1+{\beta }_{2}t+{\beta }_3{t}^2}{\alpha }.$

In some embodiments, the model identifier 412 can calibrate the predictive model shown in Eqs. C-D and/or Eq. N by replacing the thermal capacitances C_ia and C_m, the thermal resistances R_mi and R_oi, and the heat load disturbance {dot over (Q)}_other with the updated values C_ia′, C_m′, R_mi′, R_oi′, and {dot over (Q)}_other′ as defined above. Similarly, the model identifier 412 can calibrate the predictive model shown in Eqs. G-H to replace the state space parameters θ₁-θ₄ and the heat load disturbance {dot over (Q)}_other with the updated values of θ₁′-θ₄′ and {dot over (Q)}_other′ as defined above. Notably, only θ₄ and {dot over (Q)}_other change in the state-space representation of the predictive model, whereas the parameters θ₁-θ₃ remain unchanged.

Advantageously, the model calibration process performed by the model identifier 412 calibrates (e.g., adapts, updates, modifies, etc.) the predictive model to more accurately predict {dot over (Q)}_HVAC,actual instead of {dot over (Q)}_HVAC,model. The predicted values of {dot over (Q)}_HVAC,actual (i.e., {dot over (Q)} HVAC,actual) can then be used by the equipment controller 416 in the same manner as {dot over (Q)}_HVAC as described with reference to FIG. 4. For example, the equipment controller 416 can use the predicted values of {dot over ({circumflex over (Q)})}_HVAC,actual to predict the energy consumption or other resource consumption (e.g., water, natural gas, electricity, etc.) of the HVAC equipment 210 required to satisfy the HVAC load {dot over ({circumflex over (Q)})}_HVAC,actual. The equipment controller 416 can be configured to convert the HVAC load {dot over ({circumflex over (Q)})}_HVAC,actual into corresponding resource consumption values using equipment curves (e.g., performance curves, subplant curves, etc.) that define the relationships between {dot over ({circumflex over (Q)})}_HVAC,actual and the corresponding resource consumption values for various types of HVAC equipment 210. Exemplary techniques for using equipment curves to predict resource consumption values are described in detail in U.S. Pat. No. 10,706,375 granted Jul. 7, 2020, the entire disclosure of which is incorporated by reference herein.

In some embodiments, the equipment controller 416 can use the HVAC load {dot over ({circumflex over (Q)})}_HVAC,actual and/or the corresponding resource consumption values to calculate the cost of satisfying the HVAC load {dot over ({circumflex over (Q)})}_HVAC,actual. For example, the equipment controller 416 can use resource prices (e.g., time-varying costs of electricity, natural gas, water, etc.) to determine the cost of consuming the required amount of resources at each time step to serve the corresponding HVAC load {dot over ({circumflex over (Q)})}_HVAC,actual. In some embodiments, the equipment controller 416 uses the resource consumption costs to perform an optimization process. For example, the equipment controller 416 may optimize an objective function that accounts for the amounts or costs of resources consumed over a given time period (e.g., a future time period). The values of {dot over (Q)}_HVAC,actual can be predicted for each time step within the time period using the techniques described above and then used to calculate corresponding amounts or costs of resource consumption, which can then be used as inputs to the objective function. In some embodiments, the equipment controller 416 adjusts the values of {dot over ({circumflex over (Q)})}_HVAC,actual or the corresponding amounts or costs of resource consumption as decision variables in the optimization process to plan an optimal trajectory of {dot over (Q)}_HVAC,actual over the time period. An exemplary optimization process of this type is described in detail in U.S. Pat. No. 10,175,681 titled “High Level Central Plant Optimization” granted Jan. 8, 2019, the entire disclosure of which is incorporated by reference herein.

In some embodiments, the equipment controller 416 and/or the model predictive controller 414 uses the HVAC load {dot over ({circumflex over (Q)})}_HVAC,actual to generate temperature setpoints or other operating decisions for the HVAC equipment 210. For example, the equipment controller 416 and/or the model predictive controller 414 may perform a predictive control process or other control process to determine the appropriate setpoints, on/off states, and/or other operating decisions for the HVAC equipment 210 that will result in the HVAC equipment 210 producing the required HVAC load {dot over ({circumflex over (Q)})}_HVAC,actual. Various techniques which can be used by the equipment controller 416 and/or the model predictive controller 414 for determining operating decisions for HVAC equipment 210 required to satisfy a given HVAC load {dot over ({circumflex over (Q)})}_HVAC,actual are described in detail in U.S. Pat. No. 10,101,731 titled “Low Level Central Plant Optimization” granted Oct. 16, 2018, the entire disclosure of which is incorporated by reference herein.

In some embodiments, the equipment controller 416 and/or the model predictive controller 414 uses the HVAC load {dot over ({circumflex over (Q)})}_HVAC,actual to perform a measurement and verification (M&V) process for the HVAC equipment 210. The M&V process may include estimating a cost savings resulting from operating the HVAC equipment 210 in accordance with setpoints generated by performing a predictive control process (e.g., MPC) as compared to baseline setpoints for the HVAC equipment 210. The values of the HVAC load {dot over ({circumflex over (Q)})}_HVAC,actual can be used to determine the estimated cost associated with the MPC process using resource prices and equipment curves as described above. The estimated cost associated with the MPC process may include the cost of operating the HVAC equipment 210 to produce the HVAC load {dot over ({circumflex over (Q)})}_HVAC,actual over a future time period. This estimated cost can be compared against the estimated cost predicted to result from operating the HVAC equipment 210 in accordance with baseline setpoints to determine the estimated cost savings.

Equipment On/Off Schedules

As discussed above, the model identifier 412 can back-calculate the values of {dot over (Q)}_HVAC,model at various times (e.g., for each time step within a given time period) using the corresponding values of the variables T_m, T_ia, T_oa, and {dot over (Q)}_other at those times using Eq. N. The back-calculated values of {dot over (Q)}_HVAC,model can then be used as an input to Eq. P to calculate the values of {dot over ({circumflex over (Q)})} HVAC,actual if the equation-based calibration is used. Alternatively, the model identifier 412 can back-calculate the values of {dot over ({circumflex over (Q)})}_HVAC,actual directly at various times using the corresponding values of the variables T_m, T_ia, T_oa, and {dot over (Q)}_other at those times using Eqs. P-S if the model-based calibration is used.

The model identifier 412 can consider the operating schedules for the HVAC equipment 210 when back-calculating the values of {dot over (Q)}_HVAC model. In some embodiments, the model identifier 412 accesses the operating schedules for the HVAC equipment 210 (e.g., from a stored schedule in the BMS) to identify time periods during which the HVAC equipment 210 were on (e.g., powered, operating, online, etc.) and time periods during which the HVAC equipment 210 were off (e.g., not powered, not operating, offline, etc.). The model identifier 412 may set the values of {dot over (Q)}_HVAC,model to zero for any time periods during which the HVAC equipment 210 were off. In other words, the model identifier 412 may force the values of {dot over (Q)}_HVAC,model to zero at any time step when the HVAC equipment 210 were off, regardless of the values of T_m, T_ia, T_oa, and {dot over (Q)}_other at those time steps.

In some embodiments, the model identifier 412 accesses historical operating schedules to determine historical time steps at which the HVAC equipment 210 were on/off. However, it is contemplated that the same analysis can be applied to future time steps using planned or predicted operating schedules for the HVAC equipment 210. For example, the model identifier 412 can obtain a schedule that defines the planned on/off states of the HVAC equipment 210 for a future time period. The model identifier 412 can use the planned on/off states for the HVAC equipment 210 over the future time period to set the values of {dot over (Q)}_HVAC,model to zero for any future time steps during which the HVAC equipment 210 are planned to be off. Regardless of whether the time step is in the past, present, or future, the same or similar analysis can be applied using either historical, present, or future schedules for the HVAC equipment 210.

Initial Model States

As discussed above, the model identifier 412 may use the indoor air temperature T_ia and the building mass temperature T_m as model states in a state-space model (e.g., Eqs. C-H). In some embodiments, the values of T_ia can be measured directly, whereas the values of T_m may not be capable of direct measurement. However, the model identifier 412 may obtain the values of T_m from the predictive model when obtaining the values of the input variables required to calculate {dot over (Q)}_HVAC,model using Eq. N and/or {dot over ({circumflex over (Q)})}_HVAC,actual using Eqs. P-S.

The model states may be part of a state vector x(t) which evolves over time as the model is run. For example, measured or actual values of the variables in the model can be observed as the model is run and used to update or correct the state estimates in the state vector x(t). However, it is expected that the initial values of the model states may be somewhat inaccurate. Accordingly, to obtain a more accurate estimate of the model states at a given time t, the model identifier 412 may run the predictive model over a time period before the given time t. For example, if the values of the model states are desired at time t=24 (e.g., the beginning of day 2), the model identifier 412 may run the predictive model beginning at time t=0 (e.g., the beginning of day 1) for an embodiment in which each time step is equal to one hour. Default or baseline values of the model states x(0) can be used to initialize the model at time t=0. As the model is run from times 0<t<24, the model states evolve (e.g., based on actual values observed during that time period) and may become more accurate over time.

Model Calibration and Use Processes

Referring now to FIG. 6, a process 600 for calibrating and using a predictive model to operate HVAC equipment is shown, according to an exemplary embodiment. Process 600 can be performed by one or more components of the HVAC system 100 including the controller 212 and/or various components thereof (e.g., the model identifier 412). Process 600 can be run to calibrate the predictive models shown in Eqs. C-H to account for differences between the values of {dot over (Q)}_HVAC calculated from the model and the actual values of {dot over (Q)}_HVAC based on sensor data or operating data for HVAC equipment (e.g., load data for chillers, controllers, etc.).

Process 600 is shown to include using an operating schedule for HVAC equipment to obtain an on/off status of the HVAC equipment at time t (step 602). Step 602 may include accessing an operating schedule for the HVAC equipment 210 (e.g., from a stored schedule in the BMS) to identify time periods during which the HVAC equipment 210 were on (e.g., powered, operating, online, etc.) and time periods during which the HVAC equipment 210 were off (e.g., not powered, not operating, offline, etc.) during a historical time period. Step 602 can also be used to determine the planned on/off states for the HVAC equipment 210 over a future time period using a schedule for the HVAC equipment 210 over the future time period.

Process 600 is shown to include determining whether the HVAC equipment 210 is on or off at time t (step 604). If the status of the HVAC equipment 210 is off at time t, process 600 proceeds to step 606 in which the value of {dot over (Q)}_HVAC,model is set to zero at time t. Alternatively, if the status of the HVAC equipment 210 is on at time t, process 600 proceeds to step 608 in which the value of {dot over (Q)}_HVAC,model is calculated using values of the input variables at time t. Step 608 can be performed using Eq. N, repeated here for convenience:

$\begin{array}{cc}{\dot{Q}}_{\mathrm{HVAC},\mathrm{model}}=C_{ia}{\dot{T}}_{ia}-\frac{1}{R_{mi}}\left(T_m-T_{ia}\right)-\frac{1}{R_{oi}}\left(T_{oa}-T_{ia}\right)-\alpha {\dot{Q}}_{\mathrm{other}}& \left(\mathrm{Eq}.N\right)\end{array}$

The values of the input variables in step 608 may include T_m, T_ia, T_oa, and {dot over (Q)}_other, whereas the thermal capacitance C_ia and the thermal resistances R_mi and R_oi are model parameters.

Values for some of the input variables in Eq. N can be obtained from sensors. For example, values of the indoor air temperature T_ia and the outdoor air temperature T_oa can be obtained from the indoor air temperature sensor 214 and the outdoor air temperature sensor 216 respectively, as described with reference to FIGS. 2-4. Values for other variables can be estimated or calculated. For example, values of the building mass temperature T_m can be obtained from the model because T_m is one of the system states estimated/predicted by the model. Values of the heat load disturbance {dot over (Q)}_other can be obtained using the techniques described in U.S. Pat. No. 11,215,375 titled “Building Control System with Heat Disturbance Estimation and Prediction” granted Jan. 4, 2022, the entire disclosure of which is incorporated by reference herein. Values for each of these variables can be gathered/generated over time and stored in a database (e.g., as a timeseries of values). Historical values of these variables can be used to back-calculate the values of {dot over (Q)}_HVAC,model for historical time steps, whereas current or future values of these variables can be used to estimate or predict the values of {dot over (Q)}_HVAC model for future time steps.

Process 600 may include repeating steps 602-608 for each time step within a time period to obtain a value of {dot over (Q)}_HVAC,model for each time step. Values of {dot over (Q)}_HVAC,actual can also be obtained for each time step (step 612). The values of {dot over (Q)}_HVAC,actual can be obtained based on actual operating data for the HVAC equipment 210 indicating the actual thermal energy load produced by the HVAC equipment. The values of {dot over (Q)}_HVAC,actual can be derived from equipment operating setpoints (e.g., using a stored relationship between setpoints and thermal energy load), equipment operating modes or states, or other data that indicates the actual thermal energy load {dot over (Q)}_HVAC,actual produced by the HVAC equipment 210 at each time step.

Process 600 is shown to include calibrating a model for {dot over ({circumflex over (Q)})}_HVAC,actual using the values of {dot over (Q)}_HVAC,actual and {dot over (Q)}_HVAC,model at each time step as training data (step 614). The type of calibration performed in step 614 may vary depending on whether the model is calibrated using an equation-based calibration or a model-based calibration. However, both types of calibration involve using the values of {dot over (Q)}_HVAC,actual and {dot over (Q)}_HVAC,model as training data to calibrate a model that relates {dot over (Q)}_HVAC,actual to {dot over (Q)}_HVAC,model, as shown in Eq. O repeated below.

$\begin{array}{cc}{\dot{Q}}_{\mathrm{HVAC},\mathrm{actual}}={\beta }_0{\dot{Q}}_{\mathrm{HVAC},\mathrm{model}}+{\beta }_1+{\beta }_{2}t+{\beta }_3{t}^2& \left(\mathrm{Eq}.O\right)\end{array}$

The calibration may include performing a model fitting or regression process to determine values of the model coefficients β₁-β₃, referred to herein as calibration parameters. In the equation-based calibration, the values of {dot over (Q)}_HVAC,model can be plugged-in to the calibrated model (Eq. P) to calculate the values of {dot over ({circumflex over (Q)})}_HVAC,actual. Conversely, in the model-based calibration, the values of the calibration parameters β₁-β₃ can be used to update the parameters in the predictive model as shown in Eqs. Q-S. Both the equation-based calibration and the model-based calibration are described in greater detail with reference to FIG. 7.

Process 600 is shown to include using the model-predicted values of {dot over ({circumflex over (Q)})}_HVAC,actual to operate the HVAC equipment (step 616). Advantageously, the model calibration process 600 calibrates (e.g., adapts, updates, modifies, etc.) the predictive model to more accurately predict {dot over (Q)}_HVAC,actual instead of {dot over (Q)}_HVAC,model. The predicted values of {dot over (Q)}_HVAC,actual (i.e., {dot over ({circumflex over (Q)})}_HVAC,actual) can then be used by the equipment controller 416 in the same manner as {dot over (Q)}_HVAC as described with reference to FIG. 4. For example, the equipment controller 416 can use the predicted values of {dot over ({circumflex over (Q)})}_HVAC,actual to predict the energy consumption or other resource consumption (e.g., water, natural gas, electricity, etc.) of the HVAC equipment 210 required to satisfy the HVAC load {dot over ({circumflex over (Q)})}_HVAC,actual· The equipment controller 416 can be configured to convert the HVAC load {dot over ({circumflex over (Q)})}_HVAC,actual into corresponding resource consumption values using equipment curves (e.g., performance curves, subplant curves, etc.) that define the relationships between {dot over ({circumflex over (Q)})}_HVAC,actual and the corresponding resource consumption values for various types of HVAC equipment 210. Exemplary techniques for using equipment curves to predict resource consumption values are described in detail in U.S. Pat. No. 10,706,375 granted Jul. 7, 2020, the entire disclosure of which is incorporated by reference herein.

In some embodiments, the equipment controller 416 can use the HVAC load {dot over ({circumflex over (Q)})}_HVAC,actual and/or the corresponding resource consumption values to calculate the cost of satisfying the HVAC load {dot over ({circumflex over (Q)})}_HVAC,actual. For example, the equipment controller 416 can use resource prices (e.g., time-varying costs of electricity, natural gas, water, etc.) to determine the cost of consuming the required amount of resources at each time step to serve the corresponding HVAC load {dot over ({circumflex over (Q)})}_HVAC,actual. In some embodiments, the equipment controller 416 uses the resource consumption costs to perform an optimization process. For example, the equipment controller 416 may optimize an objective function that accounts for the amounts or costs of resources consumed over a given time period (e.g., a future time period). The values of {dot over (Q)}_HVAC,actual can be predicted for each time step within the time period using the techniques described above and then used to calculate corresponding amounts or costs of resource consumption, which can then be used as inputs to the objective function. In some embodiments, the equipment controller 416 adjusts the values of {dot over ({circumflex over (Q)})} HVAC,actual or the corresponding amounts or costs of resource consumption as decision variables in the optimization process to plan an optimal trajectory of {dot over (Q)}_HVAC,actual over the time period. An exemplary optimization process of this type is described in detail in U.S. Pat. No. 10,175,681 titled “High Level Central Plant Optimization” granted Jan. 8, 2019, the entire disclosure of which is incorporated by reference herein.

In some embodiments, the equipment controller 416 and/or the model predictive controller 414 uses the HVAC load {dot over (Q)}_HVAC,actual to generate temperature setpoints or other operating decisions for the HVAC equipment 210. For example, the equipment controller 416 and/or the model predictive controller 414 may perform a predictive control process or other control process to determine the appropriate setpoints, on/off states, and/or other operating decisions for the HVAC equipment 210 that will result in the HVAC equipment 210 producing the required HVAC load {dot over (Q)}_HVAC,actual. Various techniques which can be used by the equipment controller 416 and/or the model predictive controller 414 for determining operating decisions for HVAC equipment 210 required to satisfy a given HVAC load {dot over (Q)}_HVAC,actual are described in detail in U.S. Pat. No. 10,101,731 titled “Low Level Central Plant Optimization” granted Oct. 16, 2018, the entire disclosure of which is incorporated by reference herein.

Referring now to FIG. 7, another process 700 for calibrating and using a predictive model to operate HVAC equipment is shown, according to an exemplary embodiment. Process 700 can be performed by one or more components of the HVAC system 100 including the controller 212 and/or various components thereof (e.g., the model identifier 412). Process 700 can be run to calibrate the predictive models shown in Eqs. C-H to account for differences between the values of {dot over (Q)}_HVAC calculated from the model and the actual values of {dot over (Q)}_HVAC based on sensor data or operating data for HVAC equipment (e.g., load data for chillers, controllers, etc.). In some embodiments, process 700 can be combined with process 600 to perform a single integrated process which includes the steps of both process 600 and process 700.

Process 700 is shown to include running the predictive model for a first time period to increase the accuracy of the state estimates (step 702). The state estimates may include, for example, the indoor air temperature T_ia and the building mass temperature T_m. The model states may be part of a state vector x(t) which evolves over time as the model is run. For example, measured or actual values of the variables in the model can be observed as the model is run and used to update or correct the state estimates in the state vector x(t). Step 702 may include running the predictive model over a first time period to increase the accuracy of the state estimates at the end of the first time period. For example, to increase the accuracy of the model states at time t=24 (e.g., the beginning of day 2), step 702 may include running the predictive model beginning at time t=0 (e.g., the beginning of day 1) for an embodiment in which each time step is equal to one hour. Default or baseline values of the model states x(0) can be used to initialize the model at time t=0. As the model is run from times 0<t<24, the model states evolve (e.g., based on actual values observed during that time period) and may become more accurate over time.

Process 700 is shown to include obtaining values for each input variable in the model for each time step in a second time period (step 704). The second time period may occur after (e.g., immediately after) the first time period. The model states at the end of the first time period may be the same as the model states at the beginning of the second time period. In step 704, values for the input variables in Eq. N. may be obtained including values for T_m, T_ia, T_oa, and {dot over (Q)}_other. In some embodiments, other input data may also be gathered in step 704. For example, step 704 may include obtaining values for sampling rate, coefficient of performance (COP), a predictive model (e.g., MPC model), energy price, setpoints of MPC (e.g., baseline setpoints, implemented setpoints, etc.), on/off schedules of MPC (e.g., baseline schedules, implemented schedules, etc.), initial conditions of MPC (e.g., baseline initial conditions, implemented initial conditions, etc.), and/or values of {dot over (Q)}_HVAC,actual. In some embodiments, values for some or all of these variables and other input data are obtained for each time step in the second time period.

Process 700 is shown to include back-calculating {dot over (Q)}_HVAC,model for each time step in the second time period (step 706). Step 706 may be the same as or similar to step 608 of process 600. For example, step 706 may include using the values of the input data gathered in step 704 as inputs to the model shown in Eq. N, repeated here for convenience:

$\begin{array}{cc}{\dot{Q}}_{\mathrm{HVAC},\mathrm{model}}=C_{\mathrm{ia}}{\dot{T}}_{\mathrm{ia}}-\frac{1}{R_{mi}}\left(T_m-T_{ia}\right)-\frac{1}{R_{oi}}\left(T_{oa}-T_{ia}\right)-\alpha {\dot{Q}}_{\mathrm{other}}& \left(\mathrm{Eq}.N\right)\end{array}$

The result of step 706 may include a value for {dot over (Q)}_HVAC,model for each time step in the second time period.

Process 700 is shown to include performing a regression process to obtain values of the calibration parameters β₁-β₃ (step 708). Step 708 may include using the values of {dot over (Q)}_HVAC,actual obtained in step 704 for each time step in the second time period and the values of {dot over (Q)}_HVAC,model obtained from the back-calculation in step 706 for each time step in the second time period as training data to calibrate a model that relates {dot over (Q)}_HVAC,actual to {dot over (Q)}_HVAC,model, as shown in Eq. O repeated below.

$\begin{array}{cc}{\dot{Q}}_{\mathrm{HVAC},\mathrm{actual}}={\beta }_0{\dot{Q}}_{\mathrm{HVAC},\mathrm{model}}+{\beta }_1+{\beta }_{2}t+{\beta }_3{t}^2& \left(\mathrm{Eq}.O\right)\end{array}$

As discussed above, t is a time factor value (e.g., hour factor values from 0 to 23, one for each hour in the day), β₁ is an offset, and β₂ and β₃ are time scale factors. The values of β₀-β₃ are model coefficients (i.e., calibration parameters) which can be obtained by performing a regression process (e.g., a system identification or model training process), using the values of {dot over (Q)}_HVAC,model, {dot over (Q)}_HVAC,actual, and t as training data. The result of step 708 may include values for the calibration parameters β₀-β₃.

In some embodiments, step 708 includes checking the feasibility of the calibration parameters β₀-β₃ and making adjustments to the calibration parameters β₀-β₃ if any of them are determined to be infeasible or unrealistic (e.g., not representative of a real physical system, not practical in representing physics of building thermal dynamics). For example, a first option may include checking whether the scale factor β₀ is less than zero. If β₀<0, step 708 may include setting β₀=1 and rerunning the regression in step 708 to determine the values of the remaining calibration parameters β₁-β₃. As a second option, step 708 may include setting β₂=0 and β₃=0, constraining β₀≥0, and rerunning the regression in step 708 to determine the values of β₀ and β₁. As a third option, step 708 may include performing the regression to determine values of all the calibration parameters β₀-β₃ and modifying β₀ to be at least 0.1. In some embodiments, step 708 includes performing all of the first option, the second option, and the third option, each of which results in a different set of values for β₀-β₃, and then checking which set of values of β₀-β₃ results in the lowest error (e.g., mean square error (MSE) of the regression process. The set of values of β₀-β₃ with the lowest error may then be selected for use in subsequent steps of process 700.

Process 700 is shown to include determining the desired calibration type (step 710). In some embodiments, the calibration types may include equation-based calibration and model-based calibration. If equation-based calibration is selected as the desired calibration type, process 700 may proceed to step 712 in which the pre-calibration model is used to calculate {dot over (Q)}_HVAC,model (step 712). The pre-calibration model used in step 712 may include the model shown in Eq. N or Eqs. C-H. This model is referred to as “pre-calibration” because it uses the original values of the thermal capacitances C_ia and C_m, the thermal resistances R_mi and R_oi, and the heat load disturbance {dot over (Q)}_other and/or the state space parameters θ₁-θ₄ before the model is updated or calibrated to replace these parameters with updated values as shown in Eqs. Q-S. The pre-calibration model can be used to calculate a value of {dot over (Q)}_HVAC,model for each time step in the second time period. In some embodiments, step 712 is unnecessary because the values of {dot over (Q)}_HVAC,model from step 706 can be reused instead of calculating them again. The values of {dot over ({circumflex over (Q)})}_HVAC,actual can then be calculated based on the values of {dot over (Q)}_HVAC,model and the calibration parameters β₁-β₃ (step 714). Step 714 may include using Eq. O or Eq. P to calculate the values of {dot over ({circumflex over (Q)})}_HVAC,actual using the values of {dot over (Q)}_HVAC model and the calibration parameters β₁-β₃ as inputs.

Conversely, if model-based calibration is selected as the desired calibration type in step 710, process 700 may proceed to step 716 in which the model parameters of the predictive model are updated based on the calibration parameters β₁-β₃ (step 716). Step 716 may include updating the model to replace the original model parameters C_ia, C_m, R_mi, R_oi, {dot over (Q)}_other and/or θ₁-θ₄ with the updated values parameters C_ia′, C_m′, R_mi′, R_oi′, {dot over (Q)}_other′ and/or θ₁′-θ₄′ as shown in Eqs. P-S. For embodiments in which the model is a state-space model including the parameters θ₁-θ₄, only the values of θ₄ and {dot over (Q)}_other may need to be updated as shown in Eqs. S above (e.g., θ₄′=θ₄/β₀ and

${\dot{Q}}_{\mathrm{other}}^{\prime }={\beta }_0{\dot{Q}}_{\mathrm{other}}-\frac{{\beta }_1+{\beta }_{2}t+{\beta }_3{t}^2}{a}).$

The values of {dot over ({circumflex over (Q)})}_HVAC,actual can then be calculated directly from the calibrated model (step 718).

Although not explicitly shown in FIG. 7, it is contemplated that the predicted values of {dot over ({circumflex over (Q)})}_HVAC,actual obtained from process 700 can be used in the same manner as described with reference to step 616 of process 600.

Configuration of Exemplary Embodiments

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, calculation steps, processing steps, comparison steps, and decision steps.

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.

As used herein, the term “circuit” may include hardware structured to execute the functions described herein. In some embodiments, each respective “circuit” may include machine-readable media for configuring the hardware to execute the functions described herein. The circuit may be embodied as one or more circuitry components including, but not limited to, processing circuitry, network interfaces, peripheral devices, input devices, output devices, sensors, etc. In some embodiments, a circuit may take the form of one or more analog circuits, electronic circuits (e.g., integrated circuits (IC), discrete circuits, system on a chip (SOCs) circuits, etc.), telecommunication circuits, hybrid circuits, and any other type of “circuit.” In this regard, the “circuit” may include any type of component for accomplishing or facilitating achievement of the operations described herein. For example, a circuit as described herein may include one or more transistors, logic gates (e.g., NAND, AND, NOR, OR, XOR, NOT, XNOR, etc.), resistors, multiplexers, registers, capacitors, inductors, diodes, wiring, and so on).

The “circuit” may also include one or more processors communicably coupled to one or more memory or memory devices. In this regard, the one or more processors may execute instructions stored in the memory or may execute instructions otherwise accessible to the one or more processors. In some embodiments, the one or more processors may be embodied in various ways. The one or more processors may be constructed in a manner sufficient to perform at least the operations described herein. In some embodiments, the one or more processors may be shared by multiple circuits (e.g., circuit A and circuit B may comprise or otherwise share the same processor which, in some example embodiments, may execute instructions stored, or otherwise accessed, via different areas of memory). Alternatively or additionally, the one or more processors may be structured to perform or otherwise execute certain operations independent of one or more co-processors. In other example embodiments, two or more processors may be coupled via a bus to enable independent, parallel, pipelined, or multi-threaded instruction execution. Each processor may be implemented as one or more general-purpose processors, application specific integrated circuits (ASICs), field programmable gate arrays (FPGAs), digital signal processors (DSPs), or other suitable electronic data processing components structured to execute instructions provided by memory. The one or more processors may take the form of a single core processor, multi-core processor (e.g., a dual core processor, triple core processor, quad core processor, etc.), microprocessor, etc. In some embodiments, the one or more processors may be external to the apparatus, for example the one or more processors may be a remote processor (e.g., a cloud based processor). Alternatively or additionally, the one or more processors may be internal and/or local to the apparatus. In this regard, a given circuit or components thereof may be disposed locally (e.g., as part of a local server, a local computing system, etc.) or remotely (e.g., as part of a remote server such as a cloud based server). To that end, a “circuit” as described herein may include components that are distributed across one or more locations.

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.

Claims

1. A controller for heating, ventilating, or air conditioning (HVAC) equipment using a plurality of values of a predicted heating or cooling load of the HVAC equipment at a plurality of time steps within a time period, 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; generating a calibration model that relates the predicted heating or cooling load to actual heating or cooling load using the plurality of values of the predicted heating or cooling load and the plurality of values of the actual heating or cooling load;using the calibration model to calculate calibrated values of the predicted heating or cooling load of the HVAC equipment; andoperating the HVAC equipment using the calibrated values of the predicted heating or cooling load.

2. The controller of claim 1, wherein using the calibration model to calculate the calibrated values of the predicted heating or cooling load comprises performing an equation-based calibration process comprising: providing the plurality of values of the predicted heating or cooling load as inputs to the calibration model; andcalculating adjusted values of the predicted heating or cooling load as outputs of the calibration model.

3. The controller of claim 1, wherein using the calibration model to calculate the calibrated values of the predicted heating or cooling load comprises performing a based calibration process comprising: obtaining adjusted model parameters by modifying parameters of a predictive model based on parameters of the calibration model;replacing the parameters of the predictive model with the adjusted model parameters to generate a calibrated predictive model; andusing the calibrated predictive model to directly output the calibrated values of the predicted heating or cooling load.

4. The controller of claim 1, wherein generating the calibration model comprises performing a regression process using the plurality of values of the predicted heating or cooling load at the plurality of time steps and the plurality of values of the actual heating or cooling load at the plurality of time steps to generate values of parameters of the calibration model.

5. The controller of claim 4, wherein generating the calibration model comprises further comprises: determining whether the parameters of the calibration model are practical in representing physics of building thermal dynamics; andadjusting the values of the parameters of the calibration model in response to determining that the values of the parameters of the calibration model are not practical in representing the physics of the building thermal dynamics.

6. The controller of claim 1, the operations further comprising obtaining initial states of a predictive model by running the predictive model for a previous time period prior to the time period comprising the plurality of time steps.

7. The controller of claim 1, wherein using a predictive model to calculate the plurality of values of the predicted heating or cooling load comprises: determining whether the HVAC equipment are on or off at each time step of the time period;setting a value of the predicted heating or cooling load to zero for each time step during which the HVAC equipment are off during the time period; andusing the predictive model to calculate a value of the predicted heating or cooling load for each time step during which the HVAC equipment are on during the time period.

8. The controller of claim 1, wherein operating the HVAC equipment using the calibrated values of the predicted heating or cooling load comprises: using the calibrated values of the predicted heating or cooling load to plan a sequence of control actions for the HVAC equipment over a future time period; andoperating the HVAC equipment over the future time period using the sequence of control actions.

9. The controller of claim 1, wherein operating the HVAC equipment using the calibrated values of the predicted heating or cooling load comprises performing an optimization-based control process using the calibrated values of the predicted heating or cooling load to generate control actions for the HVAC equipment over a future time period.

10. The controller of claim 1, wherein operating the HVAC equipment using the calibrated values of the predicted heating or cooling load comprises: estimating a cost savings resulting from operating the HVAC equipment in accordance with the calibrated values of the predicted heating or cooling load; andusing the cost savings to perform a measurement and verification process for the HVAC equipment.

11. A method for operating heating, ventilating, or air conditioning (HVAC) equipment using a predictive model for the HVAC equipment to calculate a plurality of values of a predicted heating or cooling load of the HVAC equipment at a plurality of time steps within a time period, the method comprising: obtaining a plurality of values of an actual heating or cooling load of the HVAC equipment at the plurality of time steps within the time period;generating a calibration model that relates the predicted heating or cooling load to the actual heating or cooling load using the plurality of values of the predicted heating or cooling load and the plurality of values of the actual heating or cooling load;using the calibration model to calculate calibrated values of the predicted heating or cooling load of the HVAC equipment; andoperating the HVAC equipment using the calibrated values of the predicted heating or cooling load.

12. The method of claim 11, wherein using the calibration model to calculate the calibrated values of the predicted heating or cooling load comprises performing an equation-based calibration process comprising: providing the plurality of values of the predicted heating or cooling load as inputs to the calibration model; andcalculating adjusted values of the predicted heating or cooling load as outputs of the calibration model.

13. The method of claim 11, wherein using the calibration model to calculate the calibrated values of the predicted heating or cooling load comprises performing a based calibration process comprising: obtaining adjusted model parameters by modifying parameters of the predictive model based on parameters of the calibration model;replacing the parameters of the predictive model with the adjusted model parameters to generate a calibrated predictive model; andusing the calibrated predictive model to directly output the calibrated values of the predicted heating or cooling load.

14. The method of claim 11, wherein generating the calibration model comprises performing a regression process using the plurality of values of the predicted heating or cooling load at the plurality of time steps and the plurality of values of the actual heating or cooling load at the plurality of time steps to generate values of parameters of the calibration model.

15. The method of claim 14, wherein generating the calibration model comprises further comprises: determining whether the parameters of the calibration model are practical in representing physics of building thermal dynamics; andadjusting the values of the parameters of the calibration model in response to determining that the values of the parameters of the calibration model are not practical in representing the physics of the building thermal dynamics.

16. The method of claim 11, further comprising obtaining initial states of the predictive model by running the predictive model for a previous time period prior to the time period comprising the plurality of time steps.

17. The method of claim 11, wherein using the predictive model to calculate the plurality of values of the predicted heating or cooling load comprises: determining whether the HVAC equipment are on or off at each time step of the time period;setting a value of the predicted heating or cooling load to zero for each time step during which the HVAC equipment are off during the time period; andusing the predictive model to calculate a value of the predicted heating or cooling load for each time step during which the HVAC equipment are on during the time period.

18. The method of claim 11, wherein operating the HVAC equipment using the calibrated values of the predicted heating or cooling load comprises: using the calibrated values of the predicted heating or cooling load to plan a sequence of control actions for the HVAC equipment over a future time period; andoperating the HVAC equipment over the future time period using the sequence of control actions.

19. The method of claim 11, wherein operating the HVAC equipment using the calibrated values of the predicted heating or cooling load comprises performing an optimization-based control process using the calibrated values of the predicted heating or cooling load to generate control actions for the HVAC equipment over a future time period.

20. A controller for heating, ventilating, or air conditioning (HVAC) equipment using a predicted heating or cooling load of the HVAC equipment, the controller comprising: a calibration model configured to relate the predicted heating or cooling load to an actual heating or cooling load using values of the predicted heating or cooling load and values of the actual heating or cooling load;a processor configured to use the calibration model to calculate calibrated values of the predicted heating or cooling load of the HVAC equipment andto operate the HVAC equipment using the calibrated values of the predicted heating or cooling load.