US20200080744A1

US20200080744A1 - Method for creating demand response determination model for hvac system and method for implementing demand response

Info

Publication number: US20200080744A1
Application number: US16/224,806
Authority: US
Inventors: YoungSeok SOHN; Youngjin Kim; Ye Eun JANG
Original assignee: SEOKYOUNG SYSTEMS
Current assignee: SEOKYOUNG SYSTEMS
Priority date: 2018-09-12
Filing date: 2018-12-19
Publication date: 2020-03-12
Also published as: KR20200034023A; KR102198817B1

Abstract

A method for implementing a demand response (DR) for a HVAC system in a building is provided. The method comprises: creating a zone temperature determination model that outputs temperatures of the building by considering an input power provided to the HVAC system and a thermal state of the building; generating objective functions for a power supply schedule in which optimal solutions vary with electricity prices and the thermal state, wherein the power supply schedule includes linear equations for emulating the zone temperature determination model; determining the optimal solutions to the objective functions based on a plurality of electricity price profiles and thermal state profiles; and creating a demand response determination model for taking the electricity price profiles and the thermal state profiles as input and producing a power supply schedule for the HVAC system as output.

Description

CROSS-REFERENCE TO RELATED APPLICATION

This application is based on and claims the benefit of priority to Korean Patent Application No. 10-2018-0109099, filed on Sep. 12, 2018, the disclosure of which is incorporated herein in its entirety by reference.

BACKGROUND OF THE INVENTION

Field of the Invention

The present invention relates to implement a demand response for a heating, ventilation, and air-conditioning (HVAC) system in a building, and more particularly, to a method of utilizing a supervised learning for an improved demand response for the HVAC system in the building.

Related Art

Buildings have high thermal capacity, and thus heating, ventilation, and air-conditioning (HVAC) systems in the buildings can be used for a demand response (DR). However, it is particularly difficult to employ the demand response in the HVAC system in a multi-zone building, because using an HVAC system as a demand response resource requires different temperature models for each zone dependent on the thermal conditions of the building and facility management in the building and these models should reflect the physical characteristics in detail.

SUMMARY OF THE INVENTION

An aspect of the present invention is to provide a method for creating a demand response determination model for an HVAC system, that can easily and quickly produce an optimal schedule of input power to the HVAC system by training an artificial neural network based on data built up through machine learning under normal building management conditions, emulating the trained artificial neural network into a mathematical formula using a piecewise linear equation, and applying this mathematical formula for a price-based demand response scheduling optimization problem.
Another aspect of the present invention is to provide a method for implementing demand response that can easily and quickly produce an optimal schedule of input power to the HVAC system by training an artificial neural network based on data built up through machine learning under normal building management conditions, emulating the trained artificial neural network into a mathematical formula using a piecewise linear equation, and applying this mathematical formula for a price-based demand response scheduling optimization problem.
However, the problems to be solved by the present inventive concept are not limited to the above, and it may be variously extended without departing from the spirit and scope of the present inventive concept.
An exemplary embodiment of the present invention provides a method for implementing a demand response (DR) for a heating, ventilation, and air-conditioning (HVAC) system in a building, the method comprising: creating a zone temperature determination model that outputs temperatures of the building by considering an input power provided to the HVAC system and a thermal state of the building, wherein the zone temperature determination model is created by training a first artificial neural network based on a plurality of first training data sets; generating objective functions for a power supply schedule in which optimal solutions vary with electricity prices and the thermal state, wherein the power supply schedule includes linear equations for emulating the zone temperature determination model; determining the optimal solutions to the objective functions based on a plurality of electricity price profiles and thermal state profiles; and creating a demand response determination model that outputs the power supply schedule for the HVAC system by considering the electricity price profiles and the thermal state profiles, wherein the demand response determination model is created by training a second artificial neural network based on a plurality of second training data sets each including the electricity price profiles, thermal state profiles, and determined optimal solutions.
In an aspect, the building comprises multiple zones, and the zone temperature determination model outputs temperatures for each of the multiple zones.
In an aspect, each of the plurality of first training data sets includes information related to an existing input power provided to the HVAC system and the thermal state of the building and information related to temperatures for the multiple zones dependent on the existing input power provided to the HVAC system and the thermal state of the building.
In an aspect, the thermal state of the building comprises at least one of an atmospheric temperature, daylight hours, a wind force, a humidity, a thermal load on the building, and/or building usage schedules.
In an aspect, the information related to the existing input power provided to the HVAC system and the thermal state of the building is obtained from a building energy management system (BEMS).
In an aspect, an input layer of the first artificial neural network comprises the input power provided to the HVAC system from a predetermined first time to the present time, the thermal state from a predetermined second time to the present time, and the temperatures for the multiple zones from a third predetermined time to the present time.
In an aspect, the first artificial neural network model is implemented as a deep nonlinear auto-regressive network (D-NARX).
In an aspect, the first artificial neural network comprises a plurality of hidden layers, wherein one of more of the hidden layers uses a sigmoid function or rectified linear unit (ReLU) function as an activation function.
In an aspect, the first artificial neural network comprises a pre-processor for normalizing input data and a post-processor for de-normalizing output data.
In an aspect, the first artificial neural network comprises one or more weight coefficients and one or more bias values, wherein the weight coefficients and the bias values are determined based on normalized mean squared errors (NMSE).
In an aspect, the weight coefficients and bias values are determined for each zone.
In an aspect, the linear equations for emulating the zone temperature determination model comprise piecewise linear equations which are generated by locally linearizing the activation functions respectively corresponding to the hidden layers included in the first artificial neural network.
In an aspect, the power supply schedule is determined in such a way as to maintain the temperatures of the multiple zones within a predetermined range and minimize the total electricity cost according to time-varying electricity prices.
In an aspect, the objective functions are used to determine the power supply schedule for the HVAC system and the temperatures for the multiple zones as the optimal solutions, in order to minimize the total electricity cost and the sum of surpluses from a predetermined boundary temperature.
In an aspect, the temperature boundary condition for each of the multiple zones allows a first offset for the lower limit of the boundary temperature and a second offset for the upper limit of the boundary temperature, and the first and second offsets are set differently for each of the multiple zones.
In an aspect, the first offset does not exceed a first reinforced offset, and the second offset does not exceed a second reinforced offset.
In an aspect, in the objective function, the HVAC system input power is set to zero for predetermined hours that there are no people in the building.
In an aspect, the electricity price profiles include information on time-varying electricity prices, and the thermal state profiles include information on the time-varying thermal state of the building.
In an aspect, in the determining of optimal solutions to objective functions for a power supply schedule, optimal solutions to objective functions for a power supply schedule are determined by using mixed-integer linear programing (MILP).
Another exemplary embodiment of the present invention provides a method for implementing a demand response (DR) for a heating, ventilation, and air-conditioning (HVAC) system in a building, the method comprising: obtaining an electricity price prediction profile including information related to time-varying electricity prices and a thermal state prediction profile including information related to an time-varying thermal state of the building; and determining a power supply schedule for the HVAC system in the building based on the information related to the time-varying electricity prices and the information related to the time-varying thermal state of the building.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flowchart of an algorithm for optimal demand response scheduling according to an exemplary embodiment of the present invention.

FIG. 2 is a flowchart of a method for creating a demand response determination model for a heating, ventilation, and air-conditioning (HVAC) system according to an exemplary embodiment of the present invention.

FIG. 3 is a flowchart of a method for implementing a demand response for the HVAC system according to an exemplary embodiment of the present invention.

FIG. 4 shows an architecture of a first artificial neural network according to an exemplary embodiment of the present invention.

FIG. 5 is a detail view of a J-th hidden layer in FIG. 4.

FIG. 6 is a detail view of a K-th hidden layer in FIG. 4.

FIG. 7 is a detail view of an L-th hidden layer in FIG. 4.

FIG. 8 is an exemplary view of a piecewise linear approximation of a sigmoid function as an activation function.

FIG. 9 is an exemplary view of a piecewise linear approximation of an ReLU function as an activation function.

FIG. 10 shows the processing of a data set for optimal solutions to objective functions.

FIG. 11 shows the processing of a training data set used to train a second artificial neural network.

FIG. 12 shows the determination of an optimal demand response schedule using the trained second artificial neural network.

FIG. 13 shows an optimal demand response algorithm according to an exemplary embodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

Examples of various embodiments are illustrated and described further below. It will be understood that the description herein is not intended to limit the claims to the specific embodiments described. On the contrary, it is intended to cover alternatives, modifications, and equivalents as may be included within the spirit and scope of the present disclosure as defined by the appended claims.
It will be understood that, although the terms “first”, “second”, “third”, and so on may be used herein to describe various elements, components, regions, layers and/or sections, these elements, components, regions, layers and/or sections should not be limited by these terms. These terms are used to distinguish one element, component, region, layer or section from another element, component, region, layer or section. Thus, a first element, component, region, layer or section described below could be termed a second element, component, region, layer or section, without departing from the spirit and scope of the present disclosure.
It will be understood that when an element or layer is referred to as being “connected to”, or “coupled to” another element or layer, it can be directly on, connected to, or coupled to the other element or layer, or one or more intervening elements or layers may be present. In addition, it will also be understood that when an element or layer is referred to as being “between” two elements or layers, it can be the only element or layer between the two elements or layers, or one or more intervening elements or layers may also be present.
The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the present disclosure. As used herein, the singular forms “a” and “an” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises”, “comprising”, “includes”, and “including” when used in this specification, specify the presence of the stated features, integers, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, operations, elements, components, and/or portions thereof. As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items. Expression such as “at least one of” when preceding a list of elements may modify the entire list of elements and may not modify the individual elements of the list.
Unless otherwise defined, all terms including technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this inventive concept belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present disclosure. The present disclosure may be practiced without some or all of these specific details. In other instances, well-known process structures and/or processes have not been described in detail in order not to unnecessarily obscure the present disclosure.
Overview
According to an aspect of the present invention, there is provided a method of using a heating, ventilation, and air-conditioning (HVAC) system in a multi-zone building for an optimal demand response through a machine learning.
In the method disclosed according to an aspect of the present invention, a first artificial neural network may be trained based on data built up under normal building management conditions, the trained first artificial neural network may be emulated into a mathematical formula using a piecewise linear equation, and this mathematical formula may be used for a price-based demand response scheduling optimization problem. A scheduling optimization problem may be solved for a variety of electricity prices and the thermal conditions of the building, and a resultant optimal solution to the objective function may be used to train a second artificial neural network (e.g., a deep neural network) which will be used for determining an optimal demand response schedule. According to an aspect of the present invention, this algorithm may be called a supervised-learning-aided meta-prediction (SLAMP). An machine learning-based strategies according to an exemplary embodiment of the present invention may be actually applied without sacrificing residents' thermal preferences and cost-effective operation.
More specifically, according to an aspect of the present invention, a novel method that allows a heating, ventilation, and air-conditioning (HVAC) system in a multi-zone commercial building to optimally participate in a demand response through a machine learning. This method involves continuous scheduling of in input power for the HVAC system with respect to time, by which the temperatures of the zones are maintained within a certain range and optimally determined with respect to time-varying electricity prices.
To predict how the temperatures in the zones change with changes in the input power for the HVAC system, a first artificial neural network (ANN) model using a feedback loop, time-delayed input, and multiple hidden layers may be implemented. Using a supervised learning algorithm, the above first artificial neural network model is trained on building management data for the building under normal conditions, and then emulated by a set of piecewise linear equations. For optimal demand response scheduling, an optimization problem may be formulated as a linear equation, and a globally optimal solution may be found using mixed-integer linear programming (MILP). Optimal solutions found on a profile of a variety of electricity prices and the thermal state of the building is used to train a second artificial neural network (e.g., a deep neural network) model, and afterwards the second artificial neural network is used to instantly produce an optimal demand response schedule without solving any optimization problem. This may be collectively called a supervised-learning-aided meta-prediction (SLAMP) algorithm.
According to the SLAMP algorithm according to an aspect of the present invention, the proposed algorithm is advantageous in that it may be instantly applied to various types of HVAC systems and commercial buildings because it uses a machine learning technique, not a physics-based modeling method. Moreover, emulation of the first artificial neural network with a feedback loop, pre- and post-processors of data, and hidden layers may be included as a primary technical characteristic of the algorithm, whereby an optimization problem may be formulated as a linear equation, and a globally optimal solution may be found using mixed-integer linear programming. Furthermore, a method of supervised-learning-aided meta-prediction according to an aspect of the present invention allows for instantly producing an optimal schedule of input power to an HVAC system dependent on the thermal state of the building for 24 hours and varying electricity prices. This may significantly reduce calculation time and help a distribution system manager by controlling the overall load demand on the HVAC system within a distribution network through electricity price signals.
Supervised Learning of Thermal Response from Multi-Zone Building for an HVAC System Operation
FIG. 1 is a flowchart of an algorithm for an optimal demand response scheduling according to an exemplary embodiment of the present invention. That is, FIG. 1 is a schematic view of a machine learning-based demand response strategic algorithm according to an aspect of the present invention. The algorithm according to an aspect of the present invention may be largely divided into three stages. To begin with, a first artificial neural network is implemented for modeling the operation of a heating, ventilation, and air-conditioning (HVAC) system and the thermal state of a building. Afterwards, by emulating the first artificial neural network by a linear equation, an optimization problem is formulated, and an optimal solution is found. Next, a supervised-learning-aided meta-prediction algorithm is implemented using the found optimal solution in order to produce an optimal demand response schedule.
Referring to FIG. 1, in order to implement the algorithm according to an aspect of the present invention, data from a building energy management system (BEMS) concerning the HVAC system operation and thermal conditions (weather, zone temperatures, etc.) of a target multi-zone building (step 10).
For instance, a first artificial neural network model (see FIG. 4) may be trained for estimating zone temperatures under given operating conditions (e.g., a profile of power supply) of the HVAC system and thermal conditions (e.g., the environmental values of the building, including atmospheric temperature, daylight hours, etc.) which are obtained from the BEMS (step 20). Afterwards, the first artificial neural network model may be emulated by linear and piecewise linear equations (by using pre- and post-processors; see Mathematical Formulas 2 to 11) (step 30). Using this, an optimization problem for a price-based demand response scheduling may be formulated (see Mathematical Formulas 5 to 25) (step 40). Optimal solutions to Mathematical Formulas 5 to 25 may be found using mixed-integer linear programming (MILP) (step 50). The above steps 20 to 50 may be called as an artificial neural network emulation method 1 for estimating zone temperatures based on the operation of the HVAC system and thermal conditions.
Referring again to FIG. 1, optimal solutions to objective functions may be found for a plurality of thermal conditions and electricity price profiles. Concretely speaking, optimal solutions to formulated optimization objective functions for price-based demand response scheduling in Mathematical Formulas 5 to 25 (step 50) may be iteratively found for the thermal conditions of the building and various profiles of electricity prices (step 60) (see Part 1 of Algorithm 1 in FIG. 13). Based on the thermal conditions of the building, the various profiles of electricity prices, and the found optimal solutions, a second artificial neural network (e.g., deep neural network) for optimal demand response scheduling of the HVAC system may be trained (step 70) (see Part 2 of Algorithm 1 in FIG. 13). The above steps 50 to 70 may be called a supervised-learning-aided meta-prediction (SLAMP) method.
Afterwards, based on the trained second artificial neural network, an optimal demand response schedule for the HVAC system reflecting time-varying electricity prices and the thermal conditions of the building may be quickly and easily produced (step 80).
According to another aspect of the present invention, the above-described algorithm may be defined in two separate methods: one is creating a demand response determination model for the HVAC system and the other is implementing demand response for the HVAC system based on the created model.
FIG. 2 is a flowchart of a method for creating a demand response determination model for a heating, ventilation, and air-conditioning (HVAC) system according to an exemplary embodiment of the present invention. As shown in FIG. 2, the method for creating a demand response determination model for the HVAC system according to an exemplary embodiment of the present invention is a method for creating a demand response (DR) determination model for the HVAC system in a building, and the building may have multiple zones. Still, the method according to an exemplary embodiment of the present invention may also be applied to a building with a single zone.
To begin with, a first artificial neural network may be trained based on a plurality of first training data sets, whereby a zone temperature determination model for taking the input power to the HVAC system and the thermal state of the building as input and producing output temperatures for the building may be created (step 210). That is, the zone temperature determination model may be created by considering an input power provided to the HVAC system and a thermal state of the building, where the zone temperature determination model may be created by training a first artificial neural network based on a plurality of first training data sets.
Afterwards, objective functions for a power supply schedule including linear equations for emulating the above-created zone temperature determination model may be generated whose optimal solutions vary with electricity prices and thermal state (step 220), and the optimal solutions to the above-generated objective functions may be determined based on a plurality of electricity price profiles and thermal state profiles (step 230). Here, the power supply schedule may include linear equations for emulating the zone temperature determination model.
Next, a second artificial neural network may be trained based on a plurality of second training data sets each including the electricity price profiles, thermal state profiles, and determined optimal solutions, whereby a demand response determination model for taking the electricity price profiles and the thermal state profiles as input and producing a power supply schedule for the HVAC system as output may be created (step 240). That is, the demand response determination model may be created by considering the electricity price profiles and the thermal state profiles, where the demand response determination model may be created by training a second artificial neural network based on a plurality of second training data sets each including the electricity price profiles, thermal state profiles, and determined optimal solutions.
FIG. 3 is a flowchart of a method for implementing demand response for a heating, ventilation, and air-conditioning (HVAC) system according to an exemplary embodiment of the present invention. As shown in FIG. 3, the method for implementing demand response for the HVAC system according to an exemplary embodiment of the present invention is a method for implementing demand response (DR) for the HVAC system in a building, and the building may have multiple zones. Still, the method according to an exemplary embodiment of the present invention may also be applied to a building with a single zone.
To begin with, an electricity price prediction profile including information related to time-varying electricity prices and a thermal state prediction profile including information related to an time-varying thermal state of the building may be obtained (step 310), and a power supply schedule for the HVAC system in the building may be determined based on the information related to the time-varying electricity prices and the information related to the time-varying thermal state of the building (step 320). This determination may be made based on the above-explained demand response determination model.
Now, each of the steps of the above-described algorithm and/or method according to the exemplary embodiments of the present invention will be described in more detail.

Artificial Neural Network Architecture and Training

As stated above with reference to FIG. 2, in the method for creating a demand response determination model for a heating, ventilation, and air-conditioning (HVAC) system according to an exemplary embodiment of the present invention, a zone temperature determination model for taking the input power to the HVAC system and the thermal state of the building as input and producing output temperatures for the building may be created first by training a first artificial neural network based on a plurality of first training data sets (step 210). If the building has multiple zones, the zone temperature determination model may output temperatures for the multiple zones.
Regarding this, the architecture and training of the first artificial neural network for creating a zone temperature determination model will be described in detail first. FIG. 4 shows an architecture of a first artificial neural network according to an exemplary embodiment of the present invention. FIG. 5 is a detail view of a J-th hidden layer in FIG. 4. FIG. 6 is a detail view of a K-th hidden layer in FIG. 4. FIG. 7 is a detail view of an L-th hidden layer in FIG. 4.
The indoor temperature T_z ^tin each zone z at a certain time t may be determined by the thermal state E^tof the multi-zone building and the input power P^tto the HVAC system for a period from the previous time t−τ to the present time t. If the building's thermal state E^tand the input power P^tto the facilities are the same, the indoor temperature T_z ^t−1at the previous time directly affects the current temperature T_z ^t. That is, the current temperature T_z ^tis an output from a state-space model for the thermodynamic design of the building and at the same time is used as a state variable. From this, it can be seen that an artificial neural network model is suitable for thermodynamic design because it takes the input power and thermal state in the past as inputs and has a feedback loop of the indoor temperature.
Regarding this, each of the first training data sets for training the first artificial neural network may include information related to an existing input power provided to the HVAC system and the thermal state of the building and information related to temperatures for the multiple zones dependent on the existing input power provided to the HVAC system and the thermal state of the building.
More specifically, as shown in FIGS. 4 to 7, an input layer of the first artificial neural network may include, as input neurons, the input power to the HVAC system from a predetermined first time until the present time, the thermal state from a predetermined second time to the present time, and the temperatures for the multiple zones from a third predetermined time until the present time.
Moreover, to increase the accuracy of the model, multiple hidden layers using a sigmoid function or rectified linear unit (ReLU) function as an activation function may be used. As a result, as shown in FIGS. 4 to 7, the first artificial neural network model may be implemented as a deep nonlinear auto-regressive network (D-NARX) with exogenous inputs. Also, other types of multilayer networks may be partially modified and applied to the algorithm.
According to an aspect, the first artificial neural network model may include a pre-processor for normalizing input data and a post-processor for de-normalizing output data.
Specifically, the first artificial neural network model may include a pre-processor for normalizing an input data set X_z ^t. This prevents the learning rate of the artificial neural network from slowing down due to the vanishingly small gradient in the learning algorithm. Based on the validity of building management data from the building energy management system (BEMS), the thermal state E^tof the building may include at least one of an atmospheric temperature, daylight hours, a wind force, a humidity, a thermal load on the building, and/or building usage schedules. These factors have different value ranges. The post-processor is used to transform the normalized indoor temperature y_z ^tback to the range of the original temperature T_z ^t.
As shown in FIGS. 4 to 7, the first artificial neural network may include one or more weight coefficients and one or more bias values. During a learning process, the weight coefficients IW_jiz, HW_kjz, and LW_lz, and the bias values b_j(k)zand o_zmay be determined for all neurons (input, hidden, and output neurons) based on normalized mean squared errors (NMSE).
$\begin{matrix} e (T_{z}, T_{z}^{'}) = 1 - \frac{\sqrt{\sum_{t = 1}^{N_{T}} {(T_{z}^{t} - T_{z}^{t^{'}})}^{2}}}{\sqrt{\sum_{t = 1}^{N_{T}} {(T_{z}^{t} - T_{z, avg}^{})}^{2}}} where T_{z, avg} = \frac{1}{N_{T}} \sum_{t = 1}^{N_{T}} T_{z}^{t} & [Mathematical Formula 1] \end{matrix}$
where T_z ^t′ is the model-predicted value of the indoor temperature T_z ^t, and N_Tis the total number of training (or test) data sets. The weight values and the bias values may be set constant during a scheduling period (1h≤t≤N_H). The weight coefficients and bias values for the first artificial neural network may be determined for each of the multiple zones included in the building, and therefore the first artificial neural network model may have different weight coefficients and bias values for each zone. All zones may have the same input (except the previous indoor temperature T_z ^t−1), the same activation functions, and the same network architecture.

Piecewise Linear Emulation of Trained Artificial Neural Network

Referring again to FIG. 2, in the method for creating a demand response determination model for an HVAC system according to an exemplary embodiment of the present invention, linear equations for emulating the above-described zone temperature determination model created by training the first artificial neural network may be obtained (step 220).
As explained above with reference to FIGS. 4 to 7, the first artificial neural network according to an aspect of the present invention includes a plurality of hidden layers, and at least one of the hidden layers may use a sigmoid function or rectified linear unit (ReLU) function as an activation function. According to an aspect, the linear equations for emulating the zone temperature determination model may include piecewise linear equations which are generated by locally linearizing the activation functions respectively corresponding to the hidden layers included in the first artificial neural network.
Concretely speaking, the zone temperature determination model of the trained first artificial neural network is emulated by linear equations and piecewise linear equations and applied to an optimization problem dealt with in the step 220 of FIG. 2. Referring to FIGS. 4 to 7, the output n_jz ^tof a j-th hidden neuron in the first hidden layer may be calculated by the following Mathematical Formula 2, where x_iz ^tdenotes normalized input data of an i-th input neuron at a specific time t in a specific zone Z.
$\begin{matrix} n_{jz}^{t} = \sum_{i = 1}^{N_{I}} {IW}_{jiz} x_{iz}^{t} + b_{jz}, \forall j \in H_{1 z}, \forall t, \forall z, & [Mathematical Formula 2] \end{matrix}$
Similarly, the output n_kz ^tof a k-th hidden neuron may be calculated by the following Mathematical Formula 3 by using the output m_jz ^tof the activation function of the previous hidden neuron (j, j=k−1).
$\begin{matrix} n_{kz}^{t} = \sum_{j = 1}^{N_{J}} {HW}_{kjz} m_{jz}^{t} + b_{kz}, \forall k \in H_{Kz}, \forall t, \forall z . & [Mathematical Formula 3] \end{matrix}$
where the output m_jz ^tof the j-th hidden neuron in Mathematical Formula 3 may be represented as n_jz ^t, and may be calculated by the first or second column of the following Mathematical Formula 4 depending on the type of the activation function. A sigmoid function and an ReLu function may be respectively represented by the first and second lines of Mathematical Formula 4.
$\begin{matrix} F_{J} : m_{jz}^{t} = \frac{2}{1 + \exp (- 2 \cdot n_{jz}^{t})} - 1, \forall j, \forall t, \forall z, F_{J} : m_{jz}^{t} = \max (0, n_{jz}^{t}), \forall j, \forall t, \forall z . & [Mathematical Formula 4] \end{matrix}$
FIG. 8 is an exemplary view of a piecewise linear approximation of a sigmoid function as an activation function. FIG. 9 is an exemplary view of a piecewise linear approximation of an ReLU function as an activation function. As shown in FIGS. 8 and 9, the activation functions of all hidden neurons may be represented by local linearization by the following Mathematical Formulas 5 to 8.
$\begin{matrix} m_{jz}^{t} - \sum_{s = 1}^{N_{S}} l_{s} q_{sjz}^{t} = F_{J, \min}, \forall j, \forall t, \forall z, & [Mathematical Formula 5] \\ - q_{1 jz}^{t} + (r_{1} - r_{0}) w_{1 jz}^{t} \leq 0, \forall j, \forall t, \forall z, q_{1 jz}^{t} \leq (r_{1} - r_{0}), \forall j, \forall t, \forall z, & [Mathematical Formula 6] \\ - q_{sjz}^{t} + (r_{s} - r_{(s - 1)}) w_{sjz}^{t} \leq 0, \forall s \in [2, \dots, (N_{S} - 1)], \forall j, \forall t, \forall z, q_{sjz}^{t} - (r_{s} - r_{(s - 1)}) w_{(s - 1) jz}^{t} \leq 0, \forall s \in [2, \dots, (N_{S} - 1)], \forall j, \forall t, \forall z, & [Mathematical Formula 7] \\ - q_{N_{s} jz}^{t} \leq 0, \forall j, \forall t, \forall z, q_{N_{s} jz}^{t} - (r_{N_{s}} - r_{(N_{s} - 1)}) w_{(N_{s} - 1) jz}^{t} \leq 0, \forall j, \forall t, \forall z . & [Mathematical Formula 8] \end{matrix}$
In Mathematical Formula 5, N_Sdenotes the number of piecewise linear blocks, F_J,minis the minimum value of F_J, and l_Sis the local linearization of the gradient of the output m_jz ^tof the activation function for an s-th linear segment of n_jz ^t. In Mathematical Formulas 6 to 8, q_sjz ^tdenotes the input of the activation function for the s-th linear segment of n_jz ^t, and w_sjz ^tdenotes a binary variable for completing local linearization. Similarly, the output of the output neuron is as shown in the following Mathematical Formula 9. Here, N_Lis the number of neurons in the last hidden layer.
$\begin{matrix} y_{z}^{t} = \sum_{l = 1}^{N_{L}} {LW}_{lz} \cdot m_{lz}^{t} + o_{z}, \forall t, \forall z, & [Mathematical Formula 9] \end{matrix}$
To put it simply, the activation function F₀for the output layer may be set as a linear identity function. Here, it is assumed that the first artificial neural network successfully reflects the thermodynamic design of the building by multiple hidden layers.
Mathematical Formulas 10 and 11 are formulated that represent the aforementioned pre- and post-processors. Here, X_iz and X_iz represent the maximum and minimum values of training data X_iz ^t, and T_z and T_z denote the maximum and minimum values of the indoor temperature T_z ^tin the training data. Mathematical Formulas 2 to 11 may be applied to other types of artificial neural networks or activation functions without loss of universality.
$\begin{matrix} - \frac{2}{(\overline{X_{iz}} - \underline{X_{iz}})} X_{iz}^{t} + x_{iz}^{t} = - \frac{2 \underline{X_{iz}}}{(\overline{X_{iz}} - \underline{X_{iz}})} - 1, \forall i, \forall t, \forall z, & [Mathematical Formula 10] \\ - \frac{(\overline{T_{z}} - \underline{T_{z}})}{2} y_{z}^{t} + T_{z}^{t} = \frac{(\overline{T_{z}} - \underline{T_{z}})}{2} + \underline{T_{z}}, \forall t, \forall z, & [Mathematical Formula 11] \end{matrix}$

Supervised Learning-Aided Demand Response for HVAC System in Multi-Zone Building

Formulation of Optimization Problem Using Trained Artificial Neural Network

Referring again to FIG. 2, in the method for creating a demand response determination model for an HVAC system according to an exemplary embodiment of the present invention, objective functions for a power supply schedule including linear equations for emulating the above-described zone temperature determination model created by training the first artificial neural network may be generated whose optimal solutions vary with electricity prices and thermal state (step 220). That is, an optimization problem may be formulated by using the trained artificial neural network.
In the above-described algorithm and/or method according to the exemplary embodiments of the present invention, the optimal solution to the objective function represented by the following Mathematical Formula 12 may be found by using the emulated first artificial neural network model, in order to optimally manage the HVAC system in the multi-zone building using price-based demand response.
$\begin{matrix} \underset{P^{t}, T_{z}^{t}}{\arg \min} J_{DR} = \sum_{t = 1}^{N_{H}} C_{E}^{t} P^{t} + \sum_{z = 1}^{N_{Z}} \sum_{t = 1}^{N_{H}} C_{V}^{t} (Δ T_{z}^{tH} + Δ T_{z}^{tL}) & [Mathematical Formula 12] \end{matrix}$
Here, constraints to consider may be set, and examples of these constraints are as follows.
Constraints on Indoor Temperature T_z ^t(Mathematical Formulas 13 to 15)
T _z ^t −ΔT _z ^tH ≤T _z,max ^t , ∀t, ∀z, [Mathematical Formula 13]
−T _z ^t −ΔT _z ^tL ≤−T _z,min ^t , ∀t, ∀z, [Mathematical Formula 14]
HT_z,min ^t≤T_z ^t≤HT_z,max ^t, ∀t, ∀z, [Mathematical Formula 15]
Constraints on the Relationship Between Indoor Temperature T_z ^tand HVAC System Input Power Pt
Along with Mathematical Formulas 5 to 11, the constraints for the following Mathematical Formulas 16 to 22 are presupposed.
$\begin{matrix} n_{jz}^{t} - \sum_{i \in X_{Cz}}^{N_{Cz}} {IW}_{jiz} x_{iz}^{t} - \sum_{i \in X_{Fz}}^{N_{Fz}} {IW}_{jiz} x_{iz}^{t} = \sum_{i \in X_{Ez}}^{N_{Ez}} {IW}_{jiz} x_{iz}^{t} + b_{jz}, \forall j \in H_{1 z}, \forall t, \forall z, & [Mathematical Formula 16] \\ n_{jz}^{t} = r_{0} + \sum_{s = 1}^{N_{S}} q_{sjz}^{t}, \forall j \in H_{1 z}, \forall t, \forall z, & [Mathematical Formula 17] \\ - \sum_{j = 1}^{N_{J}} {HW}_{kjz} m_{jz}^{'} + \sum_{s = 1}^{N_{S}} q_{skz}^{'} = b_{kz} - r_{o}, \forall k \in H_{K (= J + 1 \geq 2) z}, \forall t, \forall z, & [Mathematical Formula 18] \\ X_{iz}^{t} - T_{z}^{(t - i \cdot Δ t)} = 0, \forall i \in X_{Fz}, \forall t \geq (i + 1) Δ t, \forall z, & [Mathematical Formula 19] \\ X_{iz}^{t} = T_{z, pre}^{(N_{H} + (t - i Δ t))}, \forall i \in X_{Fz}, \forall t \leq i \cdot Δ t, \forall z, & [Mathematical Formula 20] \\ - 1 \leq x_{iz}^{t} \leq 1, \forall i \in {X_{Cz}, X_{Fz}}, \forall t, \forall z & [Mathematical Formula 21] \\ - 1 \leq y_{z}^{t} \leq 1, \forall t, \forall z, & [Mathematical Formula 22] \end{matrix}$
Constraints on Time-Delayed Input Power (Mathematical Formulas 23 to 25)
X _iz ^t =P ^{(t−(i−1)Δt)} , ∀i ∈ X _Cz , ∀t, ∀z, [Mathematical Formula 23]
X _iz ^{(t+(i−1)·Δt)} −X _(i+1)z ^(t+i·Δt)=0, ∀i ∈ X _Cz, 1h≤t<t _e , ∀z, [Mathematical Formula 24]
X _iz ^t=0, ∀i ∈ X _Cz , t≤(i−1)·Δt, N _H−(i−1)·Δt≤t≤N _H , ∀z. [Mathematical Formula 25]
A power supply schedule produced according to the algorithm and/or method according to one exemplary embodiment of the present invention may be determined in such a way as to maintain the temperatures of the multiple zones in the building within a predetermined range and minimize the total electricity cost relative to time-varying electricity prices. Therefore, according to an aspect, the objective functions acting as criteria for achieving optimal demand response may be used to determine the power supply schedule for the HVAC system and the temperatures for the multiple zones as the optimal solutions, in order to minimize the total electricity cost and the sum of surpluses from a predetermined boundary temperature.
More specifically, referring to FIG. 12, the objective function in Mathematical Formula 12 may be largely divided into two terms. The first term is the sum of time-varying electricity prices C_E ^tmultiplied by the input power P^tto the HVAC system for 24 hours, the goal of which is to lower facility management costs.
The second term in Mathematical Formula 12 represents the penalty for the temperature difference ΔT_z ^tHor ΔT_z ^tLwhich is the surplus generated when the indoor temperature T_z ^tcorresponding to the input power exceeds the maximum limit T_z,max ^tor minimum limit T_z,min ^t. The first and second terms respectively correspond to Mathematical Formulas 13 and 14. In other words, the temperature boundary condition may be alleviated by including the temperature difference ΔT_z ^tHor ΔT_z ^tLin Mathematical Formula 12, by which this optimization problem can be solved reliably. To put it another way, in an objective function for an algorithm and/or method according to an aspect of the present invention, the temperature boundary condition for each of the multiple zones is designed to allow a first offset against the lower limit of the boundary temperature and a second offset for the upper limit of the boundary temperature, whereby the temperature boundary condition may be alleviated.
Here, the maximum and minimum limits or the first and second offsets may be set differently for each of the multiple zones in the building, based on the thermal preferences of residents in each zone. However, the boundary condition may be reinforced as in Mathematical Formula 15, in order to prevent an excessive increase or decrease in temperature. Thus, the first offset may be set to not exceed a first reinforced offset, and the second offset may be set to not exceed a second reinforced offset. The values of the first and second reinforced offsets may be set the same as in Mathematical Formula 15, or may be set different from each other.
The second constraint for Mathematical Formulas 16 to 22 describes the relationship between the input power P^t, which is one of the input variables for the trained first artificial neural network model, and the temperature T_z ^tof each zone, which is the output variable. Particularly, Mathematical Formula 16 is an equivalent expression of Mathematical Formula 2, in which the input variables x_z ^tmay include a controllable variable P^t, a feedback variable T_z ^t−1, and an environmental input variable E^t. Moreover, Mathematical Formula 17 shows that the activation function input n_jz ^tin Mathematical Formula 16 is equivalent to the sum of q_sjz ^t: i.e., the value assigned in the linear blocks, where r₀is an arbitrarily large negative number, as shown in FIGS. 8 and 9. Analogously, it can be seen that Mathematical Formula 3 is equivalently expressed as Mathematical Formula 18 using the linear expression n_kz ^t=r₀+Σ_sq_skz ^tof the activation function input n_kz ^texisting in another layer.
Mathematical Formulas 19 and 20 reflect a feedback loop of the indoor temperature T_z ^t. Mathematical Formula 19 represents the relationship between the feedback input variable X_iz ^t(i ∈ X_F _z) of the trained artificial neural network model and the output variable T_z ^t. Time-varying electricity prices C_Eare applied when calculating management costs, and, in an exemplary embodiment of the present invention, when electricity prices vary by the hour, the unit sampling time Δt may be set to 1 hour. As in Mathematical Formula 20, X_iz ^t(i ∈ X_F _z) may be set for the temperature T_z ^(N ^H ^{+(t−i·Δt))}predicted a day ago. Furthermore, Mathematical Formula 21 represents that the controllable variable and feedback input variable obtained from Mathematical Formula 10 have a value between −1 and 1. It means that the variable P^tfor the input power is larger than or equal to 0 and has a value lower than the rated power P_rated. This way, the maximum and minimum values of the normalized variable y_z ^tcan be found from Mathematical Formula 22. Here, the normalized variable y_z ^tmay be linked to Mathematical Formula 18 via Mathematical Formulas 5 to 9, and be reverse-transformed to the indoor temperature by using Mathematical Formula 11.
To apply the trained artificial neural network to an optimization problem, Mathematical Formulas 23 and 24 involve constraints on input neurons for time-delayed input power to the HVAC system. Moreover, Mathematical Formula 25 may reflect shutting down the HVAC system during after-office hours t≥t_Ewhen there are almost no people in the building and running the HVAC system for pre-cooling early in the morning before people arrive their offices in the building. Accordingly, in the objective function, the HVAC system input power for predetermined hours when there are no people in the building may be set to zero according to the settings.
The optimization problems in Mathematical Formulas 5 to 25 may be actually applied to a variety of building models without any major modifications. But it should be noted that, for example, five variables IW_jiz, HW_kjz, LW_iz, b_j(k)z, and o_zfor the first artificial neural network may vary with the thermodynamic design of the building and the load characteristics of the HVAC system. Since mathematical Formulas 5 to 25 contain a linear equation and binary variables, optimization problems according to the algorithm and/or method according to an aspect of the present invention may be solved using mixed-integer linear programing (MILP). This way, an optimal demand response schedule may be produced.
Referring again to FIG. 2, in a method for creating a demand response determination model for an HVAC system according to an exemplary embodiment of the present invention, optimal solutions to objective functions for a plurality of electricity price profiles and thermal state profiles may be determined (step 230). Here, an electricity price prediction profile may contain information on time-varying electricity prices, and a thermal state prediction profile may contain information on the time-varying thermal state. The intervals of varying electricity prices and/or thermal states may differ according to implementations—for example, information specifying that electricity prices vary by the hour. The intervals of electricity prices and the intervals of thermal states may be the same or different. Meanwhile, in the step (step 230) of determining optimal solutions to objective functions for a power supply schedule, as shown in FIG. 2, optimal solutions to objective functions for a power supply schedule may be determined by using mixed-integer linear programing (MILP).

Optimal Demand Response Using Supervised-Learning-Aided Meta-Prediction

Referring again to FIG. 2, optimal solutions to objective functions for a plurality of electricity price profiles and thermal state profiles may be determined (step 230). A second artificial neural network may be trained based on a plurality of second training data sets each including the electricity price profiles, thermal state profiles, and determined optimal solutions, whereby a demand response determination model for taking the electricity price profiles and the thermal state profiles as input and producing a power supply schedule for the HVAC system as output may be created (step 240).
Concretely speaking, given an electricity price C_E ^tand an environmental variable E^t(e.g., thermal condition), the optimal solutions to Mathematical Formulas 5 to 25 may be found immediately through the SLAMP method (see Algorithm 1 in FIGS. 10 to 12 and FIG. 13). This significantly reduces the time taken to produce an optimal demand response schedule, and allows a distribution facility manager to set optimal electricity prices at a number of buses in a distribution network. This is because the profile of the overall load demand on the HVAC system across a distribution network may be predicted, and the SLAMP method, as mentioned previously, may be implemented by artificial neural network emulation using building management data.
Notably, as can be seen from Part 1 of Algorithm 1 in FIG. 13, the optimization problems in Mathematical Formulas 5 to 25 may be solved offline through iteration. As a result, optimal solutions P^tand T_z ^tmay be found, and the corresponding operating cost E_c=Σ_tC_E ^t·P^tand the temperature penalty term T_V=Σ_zΣ_tC_V ^t(ΔT_z ^tH+ΔT_z ^tL) associated with the difference with the boundary temperature may be calculated by using the past data in the current input m=[t, C_E ^t, E^t]. As shown in FIG. 10, an input m from a BEMS database 1010, for example, may be extended into data M=[t, C_E ^t, E^t, T_z,opt ^t, P_opt ^t] for training the second artificial neural network (e.g., deep neural network) model by an SLAMP algorithm 1020, and then re-processed into input data I and output data O. To improve the performance of the deep neural network model, the input data I may be extended by including time-delayed data in training data M. Then, as shown in FIG. 11, the input data I and output data O that can be obtained from the data in the database 1110 may be randomly mixed so that training data D_rand test data C_E ^tD_efor the deep neural network model 1120 include various profiles of electricity prices C_E ^tand environmental variables E^t, and the corresponding optimal schedule for the indoor temperature T_z ^tand the input power P^t.
Referring again to FIG. 13, in Part 2, the deep neural network is trained and tested by using the training data D_rand the test data C_E ^tD_e, respectively. The training and the testing are performed on network parameters W(c), and the parameters include time delay τ in input data I, the number of hidden layers G, and the activation functions F and hidden neurons U of each layer. After the optimal input power P^tis meta-predicted, the corresponding indoor temperature T_z ^tmay be derived through a zone temperature determination model which trains the first artificial neural network model (1240 in FIG. 12, see FIGS. 4 to 7).
In an aspect of the present invention, the performance of the deep neural network may be evaluated by using the input power P^t, indoor temperature T_z ^t, operating cost E^c, and weighted sum of penalty terms Tv (e_c, as in Mathematical Formula 1) on all daily profiles in the input data D. A set W* for deriving the maximum value e* of a normalized mean square error NMSE may be selected from among a number parameter sets W(c) to implement a deep neural network model N*. Lastly, an optimal demand response schedule for the input power P^tand indoor temperature T_z ^tmay be produced based on the predicted values of the electricity price C_E ^tand environmental variable E^tfor the next scheduling period (see FIG. 12). As shown in FIG. 12, when a price profile 1210 and an environmental variable 1220 are inputted, the optimal power supply and the optimal temperature for each zone may be derived based on a deep neural network 1230 and artificial neural networks 1240.
As explained above, according to an aspect of the present invention, a novel, machine learning-based algorithm and/or method for optimal demand response for an HVAC system in a multi-zone building is disclosed. A first artificial neural network model in the algorithm and/or method may be trained based on a supervised learning algorithm to reflect a complex thermodynamic design of the building, and may be emulated using a piecewise linear equation. This way, an optimization problem may be formulated, and therefore an optimal solution may be found using mixed-integer linear programming. Here, the optimal solution may be found based on past data on electricity prices and the thermal state of the building. Optimal solutions found on a plurality of electricity prices and the thermal state of the building are used to train a second artificial neural network (e.g., deep neural network) model in the SLAMP method, and this model allows for producing an optimal input power schedule for the HVAC system. The SLAMP method is effective for optimal demand response scheduling, given its actual applicability, operating cost, and calculation time. Moreover, the SLAMP method reflects time-varying electricity prices and residents' thermal preferences, thereby ensuring the load shifting function of the HVAS system.
The above-described method for creating a demand response determination model for an HVAC system and method for implementing demand response according to an exemplary embodiment of the present invention may be implemented by a computing device. The computing device may include a processor, a memory, and a transceiver. The memory may store commands for implementing the above methods, and the commands, when executed by the processor, may perform the above methods.
The disclosed technology may have the following effects. However, since it does not represent that a specific embodiment should include all the following effects or should include only the following effects, it should not be understood that the scope of the disclosed technology is limited thereby.
The above-described method for creating a demand response determination model for an HVAC system and method for implementing demand response according to an exemplary embodiment of the present invention can easily and quickly produce an optimal schedule of input power to the HVAC system by training an artificial neural network based on data built up through machine learning under normal building management conditions, emulating the trained artificial neural network into a mathematical formula using a piecewise linear equation, and applying this mathematical formula for a price-based demand response scheduling optimization problem.
That is, demand response determination according to an exemplary embodiment of the present invention may be instantly applied to various types of HVAC systems and commercial buildings by using a machine learning technique, not a physics-based modeling method.
Moreover, an artificial neural network with a feedback loop, pre- and post-processors of data, and hidden layers may be emulated, whereby an optimization problem may be formulated as a linear equation, and a globally optimal solution may be found using mixed-integer linear programming.
Furthermore, a method of supervised-learning-aided meta-prediction according to an exemplary embodiment of the present invention allows for instantly producing an optimal schedule of input power to an HVAC system dependent on the thermal state of the building for 24 hours and varying electricity prices. This may significantly reduce calculation time and help a distribution system manager by controlling the overall load demand on the HVAC system within a distribution network through electricity price signals.
The method according to an embodiment of the present invention can be implemented as computer-readable instructions on a computer-readable recording medium. The computer-readable recording medium comprises all kinds of recording media storing data which can be interpreted by a computer system. For example, the computer-readable recording medium may include a Read Only Memory (ROM), a Random Access Memory (RAM), a magnetic tape, a magnetic disk, a flash memory, an optical data storage device, and the like. In addition, the computer-readable recording medium may be distributed in computer systems connected to a computer network, and may be stored and executed as a code readable in a distribution manner.
While the present invention has been described with reference to the accompanying drawings and exemplary embodiments, it is to be understood that the invention is not limited by the accompanying drawings and embodiments. It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
In particular, the described features may be implemented within digital electronic circuitry, or computer hardware, firmware, or combinations thereof. The features may be implemented in a computer program product embodied in a storage device in a machine-readable storage device, for example, for execution by a programmable processor. Also, the features may be performed by a programmable processor executing a program of instructions for performing functions of the described embodiments, by operating on input data and generating an output. The described features may be implemented in at least one computer programs that can be executed on a programmable system including at least one programmable processor, at least one input device, and at least one output device which are combined to receive data and directives from a data storage system and to transmit data and directives to the data storage system. A computer program includes a set of directives that can be used directly or indirectly within a computer to perform a particular operation on a certain result. A computer program may be written in any form of programming language including compiled or interpreted languages, and may be used in any form included as modules, elements, subroutines, or other units suitable for use in other computer environments or independently operable programs.
Suitable processors for execution of the program of directives include, for example, both general-purpose and special-purpose microprocessors, and a single processor or one of multiple processors of other type of computer. In addition, storage devices suitable for implementing the computer program directives and data implementing the described features include, for example, semiconductor memory devices such as EPROM, EEPROM, and flash memory devices, magnetic devices such as internal hard disks and removable disks, magneto-optical disks, and all forms of nonvolatile memories including CD-ROM and DVD-ROM disks. The processor and memory may be integrated within Application-Specific Integrated Circuits (ASICs) or added by ASICs.
While the present invention has been described on the basis of a series of functional blocks, it is not limited by the embodiments described above and the accompanying drawings, and it will be apparent to those skilled in the art that various substitutions, modifications and variations can be made without departing from the scope of the present invention.
The combination of the above-described embodiments is not limited to the above-described embodiments, and various forms of combination in addition to the above-described embodiments may be provided according to implementation and/or necessity.
In the above-described embodiments, the methods are described on the basis of a flowchart as a series of operations or blocks, but the present invention is not limited to the order of the operations, and some operations may occur in different orders or at the same time unlike those described above. It will also be understood by those skilled in the art that the operations shown in the flowchart are not exclusive, and other operations may be included, or one or more operations in the flowchart may be omitted without affecting the scope of the present invention.
The above-described embodiments include examples of various aspects. While it is not possible to describe every possible combination for expressing various aspects, one of ordinary skill in the art will recognize that other combinations are possible. Accordingly, it is intended that the present invention include all alternatives, modifications and variations that fall within the scope of the following claims.

Claims

What is claimed is:

1. A method for implementing a demand response (DR) for a heating, ventilation, and air-conditioning (HVAC) system in a building, the method comprising:

creating a zone temperature determination model that outputs temperatures of the building by considering an input power provided to the HVAC system and a thermal state of the building, wherein the zone temperature determination model is created by training a first artificial neural network based on a plurality of first training data sets;

generating objective functions for a power supply schedule in which optimal solutions vary with electricity prices and the thermal state, wherein the power supply schedule includes linear equations for emulating the zone temperature determination model;

determining the optimal solutions to the objective functions based on a plurality of electricity price profiles and thermal state profiles; and

creating a demand response determination model that outputs the power supply schedule for the HVAC system by considering the electricity price profiles and the thermal state profiles, wherein the demand response determination model is created by training a second artificial neural network based on a plurality of second training data sets each including the electricity price profiles, thermal state profiles, and determined optimal solutions.

2. The method of claim 1, wherein the building comprises multiple zones, and the zone temperature determination model outputs temperatures for each of the multiple zones.

3. The method of claim 2, wherein each of the plurality of first training data sets includes information related to an existing input power provided to the HVAC system and the thermal state of the building and information related to temperatures for the multiple zones dependent on the existing input power provided to the HVAC system and the thermal state of the building.

4. The method of claim 1, wherein the thermal state of the building comprises at least one of an atmospheric temperature, daylight hours, a wind force, a humidity, a thermal load on the building, and/or building usage schedules.

5. The method of claim 3, wherein the information related to the existing input power provided to the HVAC system and the thermal state of the building is obtained from a building energy management system (BEMS).

6. The method of claim 2, wherein an input layer of the first artificial neural network comprises the input power provided to the HVAC system from a predetermined first time to the present time, the thermal state from a predetermined second time to the present time, and the temperatures for the multiple zones from a third predetermined time to the present time.

7. The method of claim 6, wherein the first artificial neural network model is implemented as a deep nonlinear auto-regressive network (D-NARX).

8. The method of claim 1, wherein the first artificial neural network comprises a plurality of hidden layers,

wherein one or more of the hidden layers uses a sigmoid function or rectified linear unit (ReLU) function as an activation function.

9. The method of claim 1, wherein the first artificial neural network comprises a pre-processor for normalizing input data and a post-processor for de-normalizing output data.

10. The method of claim 2, wherein the first artificial neural network comprises one or more weight coefficients and one or more bias values,

wherein the weight coefficients and the bias values are determined based on normalized mean squared errors (NMSE).

11. The method of claim 10, wherein the weight coefficients and bias values are determined for each zone.

12. The method of claim 1, wherein the linear equations for emulating the zone temperature determination model comprise piecewise linear equations which are generated by locally linearizing the activation functions respectively corresponding to the hidden layers included in the first artificial neural network.

13. The method of claim 2, wherein the power supply schedule is determined in such a way as to maintain the temperatures of the multiple zones within a predetermined range and minimize the total electricity cost according to time-varying electricity prices.

14. The method of claim 13, wherein the objective functions are used to determine the power supply schedule for the HVAC system and the temperatures for the multiple zones as the optimal solutions, in order to minimize the total electricity cost and the sum of surpluses from a predetermined boundary temperature.

15. The method of claim 2, wherein the temperature boundary condition for each of the multiple zones allows a first offset for the lower limit of the boundary temperature and a second offset for the upper limit of the boundary temperature, and the first and second offsets are set differently for each of the multiple zones.

16. The method of claim 15, wherein the first offset does not exceed a first reinforced offset, and the second offset does not exceed a second reinforced offset.

17. The method of claim 1, wherein, in the objective function, the HVAC system input power is set to zero for predetermined hours that there are no people in the building.

18. The method of claim 1, wherein the electricity price profiles include information on time-varying electricity prices, and the thermal state profiles include information on the time-varying thermal state of the building.

19. The method of claim 1, wherein, in the determining of optimal solutions to objective functions for a power supply schedule, optimal solutions to objective functions for a power supply schedule are determined by using mixed-integer linear programing (MILP).

20. A method for implementing a demand response (DR) for a heating, ventilation, and air-conditioning (HVAC) system in a building, the method comprising:

obtaining an electricity price prediction profile including information related to time-varying electricity prices and a thermal state prediction profile including information related to an time-varying thermal state of the building; and

determining a power supply schedule for the HVAC system in the building based on the information related to the time-varying electricity prices and the information related to the time-varying thermal state of the building.