Claims:1. A processor implemented method for optimizing thermal comfort in an uberized open plan space (200), the method comprising the steps of:
receiving, by one or more hardware processors, information pertaining to the uberized open plan space, wherein the open plan space includes a plurality of cells, each of the plurality of cells being served by a Heating, ventilation, and air conditioning (HVAC) actuator associated with a corresponding HVAC, and wherein the information comprises number of the plurality of cells therein and occupant preferred temperature at a given time obtained from a plurality of occupants intending to use the uberized open plan space (202);
iteratively solving a first optimization problem using the received information, by the one or more hardware processors, for each of the plurality of cells, such that energy consumption (EHVAC) by chillers and variable air volume (VAV) fans of the HVAC is minimized (204), wherein the first optimization problem is solved iteratively for each cell under consideration from the plurality of cells by :
selecting a first set-point to be used for each HVAC actuator serving a corresponding cell from the plurality of cells (204a);
predicting, by a pre-calibrated thermal model, temperature in each of the plurality of cells corresponding to the selected first set-point, wherein the pre-calibrated thermal model is based on parameters including electrical loads, ambient load, cooling load, lighting load and the laws of thermodynamics (204b);
computing the energy consumption (EHVAC) based on the predicted temperature in each of the plurality of cells (204c);
determining a first optimized set-point to be used for each HVAC actuator serving each of the plurality of cells such that the energy consumption (EHVAC) is minimum, the first optimized set-point providing a resultant cell temperature in each of the plurality of cells, such that the resultant cell temperature for the cell under consideration corresponds to a minimum occupant preferred temperature (204d); and
obtaining a time-averaged spatial temperature span as a time-average of a difference between a maximum resultant cell temperature and a minimum resultant cell temperature in the uberized open plan space based on the resultant cell temperature in each of the plurality of cells and a resulting span of a temperature field across the uberized open plan space (204e);
identifying, by the one or more hardware processors, a temperature field having a maximum time-averaged spatial temperature span amongst the plurality of cells as a template for assigning the plurality of occupants that have been sorted by the occupant preferred temperature (206); and
assigning, by the one or more hardware processors, each of the plurality of occupants to a cell in the plurality of cells such that ordering of the plurality of cells according to occupant preferred temperature is same as ordering of the plurality of cells according to a resultant cell temperature in the template (208).

2. The processor implemented method of claim 1 further comprising solving a second optimization problem using the received information, by the one or more hardware processors such that overall thermal discomfort for the plurality of occupants is optimized (210), wherein the second optimization problem is solved by:
selecting a second set-point to be used for each HVAC actuator serving a corresponding cell from the plurality of cells (210a);
predicting, by the pre-calibrated thermal model, temperature in each of the plurality of cells corresponding to the selected second set-point (210b);
computing the overall thermal discomfort based on the predicted temperature in each of the plurality of cells, wherein thermal discomfort for an occupant is based on the occupant preferred temperature and the resultant cell temperature in a cell assigned to the occupant (210c); and
determining a second optimized set-point to be used for each HVAC actuator serving a corresponding cell from the plurality of cells such that the overall thermal discomfort is minimized (210d).

3. The processor implemented method of claim 2, wherein solving the first optimization problem and the second optimization problem is subject to a plurality of constraints including (i) one-to-one mapping of the plurality of occupants to seats in the uberized open plan space; and (ii) mass flow rate of the HVAC actuator serving each of the plurality of cells is bound within pre-defined limits, the pre-defined limits corresponding to a minimum and a maximum HVAC flow rate.

4. The processor implemented method of claim 2, wherein the thermal discomfort for an occupant is defined as a squared difference between the occupant preferred temperature and the resultant cell temperature in the cell assigned to the occupant.

5. A system (100) comprising:
one or more data storage devices (102) operatively coupled to one or more hardware processors (104) and configured to store instructions configured for execution by the one or more hardware processors to:
receive information pertaining to the uberized open plan space, wherein the open plan space includes a plurality of cells, each of the plurality of cells being served by a Heating, ventilation, and air conditioning (HVAC) actuator associated with a corresponding HVAC, and wherein the information comprises number of the plurality of cells therein and occupant preferred temperature at a given time obtained from a plurality of occupants intending to use the uberized open plan space;
iteratively solve a first optimization problem using the received information, for each of the plurality of cells, such that energy consumption (EHVAC) by chillers and variable air volume (VAV) fans of the HVAC is minimized, wherein the one or more hardware processors are further configured to solve the first optimization problem iteratively for each cell under consideration from the plurality of cells by:
selecting a first set-point to be used for each HVAC actuator serving a corresponding cell from the plurality of cells;
predicting, by a pre-calibrated thermal model, temperature in each of the plurality of cells corresponding to the selected first set-point, wherein the pre-calibrated thermal model is based on parameters including electrical loads, ambient load, cooling load, lighting load and the laws of thermodynamics;
computing the energy consumption (EHVAC) based on the predicted temperature in each of the plurality of cells;
determining a first optimized set-point to be used for each HVAC actuator serving each of the plurality of cells such that the energy consumption (EHVAC) is minimum, the first optimized set-point providing a resultant cell temperature in each of the plurality of cells, such that the resultant cell temperature for the cell under consideration corresponds to a minimum occupant preferred temperature; and
obtaining a time-averaged spatial temperature span as a time-average of a difference between a maximum resultant cell temperature and a minimum resultant cell temperature in the uberized open plan space based on the resultant cell temperature in each of the plurality of cells and a resulting span of a temperature field across the uberized open plan space;
identify, a temperature field having a maximum time-averaged spatial temperature span amongst the plurality of cells as a template for assigning the plurality of occupants that have been sorted by the occupant preferred temperature; and
assign, each of the plurality of occupants to a cell in the plurality of cells such that ordering of the plurality of cells according to occupant preferred temperature is same as ordering of the plurality of cells according to a resultant cell temperature in the template.

6. The system of claim 5, wherein the one or more processors are further configured to solve a second optimization problem using the received information such that overall thermal discomfort for the plurality of occupants is optimized, wherein the one or more processors are further configured to the solve the second optimization problem by:
selecting a second set-point to be used for each HVAC actuator serving a corresponding cell from the plurality of cells;
predicting, by the pre-calibrated thermal model, temperature in each of the plurality of cells corresponding to the selected second set-point;
computing the overall thermal discomfort based on the predicted temperature in each of the plurality of cells, wherein thermal discomfort for an occupant is based on the occupant preferred temperature and the resultant cell temperature in a cell assigned to the occupant; and
determining a second optimized set-point to be used for each HVAC actuator serving a corresponding cell from the plurality of cells such that the overall thermal discomfort is optimized.

7. The system of claim 6, wherein the one or more processors are further configured to solve the first optimization problem and the second optimization problem subject to a plurality of constraints including (i) one-to-one mapping of the plurality of occupants to seats in the uberized open plan space; and (ii) mass flow rate of the HVAC actuator serving each of the plurality of cells is bound within pre-defined limits, the pre-defined limits corresponding to a minimum and a maximum HVAC flow rate.

8. The system of claim 6, wherein the thermal discomfort for an occupant is defined as a squared difference between the occupant preferred temperature and the resultant cell temperature in the cell assigned to the occupant.
, Description:FORM 2

THE PATENTS ACT, 1970
(39 of 1970)
&
THE PATENT RULES, 2003

COMPLETE SPECIFICATION
(See Section 10 and Rule 13)

Title of invention:

OPTIMIZING THERMAL COMFORT IN UBERIZED OPEN PLAN SPACES

Applicant

Tata Consultancy Services Limited
A company Incorporated in India under the Companies Act, 1956
Having address:
Nirmal Building, 9th floor,
Nariman point, Mumbai 400021,
Maharashtra, India

The following specification particularly describes the invention and the manner in which it is to be performed.
TECHNICAL FIELD
The disclosure herein generally relates to optimizing thermal comfort, and, more particularly, to systems and computer implemented methods for optimizing thermal comfort in uberized open plan spaces.

BACKGROUND
Office buildings are witnessing two emerging trends: uberization and personalization. Uberized or pay-as-you-use open plan spaces have no dedicated desk or workspace for a user. A user in need of a workspace has to reserve one in advance for a desired amount of time. Employees of the same organization or even across organizations can share such a hot-desked workspace. Users pay the workspace provider based on number of desks requested and duration of usage. Organizations are considering such uberized offices owing to the mounting costs of maintaining dedicated office spaces in prime locations that may not be 100% utilized at all times. Uberized office buildings also aim to provide personalized experience for the occupants using their facility.
Realizing a smart, comfort-based seat recommender system is relatively straight-forward if the individual workspaces are thermally decoupled, that is, workspaces have physical partitions separating them. However, the task becomes challenging if the building has an open plan with no partitions between the individual workspaces. In the absence of partitions, air and thus heat can mix freely across workspaces. As a consequence, the conditioned temperature of a workspace not only depends on the setting of the HVAC actuator serving that workspace but also on the settings of the actuators serving the neighboring workspaces. Therefore, the thermal comfort resulting at a given desk cannot be easily estimated and controlled in isolation.
Conventional methods explicitly focus on achieving individual thermal comfort by changing the temperature at the individual work space by climate control devices while some of the art deal with minimizing discomfort by using optimized temperature set point considering neighboring preferences. However assigning workspace to the users based on temperature preference while ensuring HVAC energy consumption is minimized continues to pose a challenge.

SUMMARY
Embodiments of the present disclosure present technological improvements as solutions to one or more of the above-mentioned technical problems recognized by the inventors in conventional systems.
In an aspect, there is provided a processor implemented method for optimizing thermal comfort in an uberized open plan space, the method comprising the steps of: receiving, by one or more hardware processors, information pertaining to the uberized open plan space, wherein the open plan space includes a plurality of cells, each of the plurality of cells being served by a Heating, ventilation, and air conditioning (HVAC) actuator associated with a corresponding HVAC, and wherein the information comprises number of the plurality of cells therein and occupant preferred temperature at a given time obtained from a plurality of occupants intending to use the uberized open plan space; iteratively solving a first optimization problem using the received information, by the one or more hardware processors, for each of the plurality of cells, such that energy consumption (EHVAC) by chillers and variable air volume (VAV) fans of the HVAC is minimized, wherein the first optimization problem is solved iteratively for each cell under consideration from the plurality of cells by : selecting a first set-point to be used for each HVAC actuator serving a corresponding cell from the plurality of cells; predicting, by a pre-calibrated thermal model, temperature in each of the plurality of cells corresponding to the selected first set-point, wherein the pre-calibrated thermal model is based on parameters including electrical loads, ambient load, cooling load, lighting load and the laws of thermodynamics; computing the energy consumption (EHVAC) based on the predicted temperature in each of the plurality of cells; determining a first optimized set-point to be used for each HVAC actuator serving each of the plurality of cells such that the energy consumption (EHVAC) is minimum, the first optimized set-point providing a resultant cell temperature in each of the plurality of cells, such that the resultant cell temperature for the cell under consideration corresponds to a minimum occupant preferred temperature; and obtaining a time-averaged spatial temperature span as a time-average of a difference between a maximum resultant cell temperature and a minimum resultant cell temperature in the uberized open plan space based on the resultant cell temperature in each of the plurality of cells and a resulting span of a temperature field across the uberized open plan space; identifying, by the one or more hardware processors, a temperature field having a maximum time-averaged spatial temperature span amongst the plurality of cells as a template for assigning the plurality of occupants that have been sorted by the occupant preferred temperature (206); assigning, by the one or more hardware processors, each of the plurality of occupants to a cell in the plurality of cells such that ordering of the plurality of cells according to occupant preferred temperature is same as ordering of the plurality of cells according to a resultant cell temperature in the template.
In another aspect, there is provided a system comprising: one or more data storage devices operatively coupled to one or more hardware processors and configured to store instructions configured for execution by the one or more hardware processors to: receive information pertaining to the uberized open plan space, wherein the open plan space includes a plurality of cells, each of the plurality of cells being served by a Heating, ventilation, and air conditioning (HVAC) actuator associated with a corresponding HVAC, and wherein the information comprises number of the plurality of cells therein and occupant preferred temperature at a given time obtained from a plurality of occupants intending to use the uberized open plan space; iteratively solve a first optimization problem using the received information, for each of the plurality of cells, such that energy consumption (EHVAC) by chillers and variable air volume (VAV) fans of the HVAC is minimized, wherein the one or more hardware processors are further configured to solve the first optimization problem iteratively for each cell under consideration from the plurality of cells by: selecting a first set-point to be used for each HVAC actuator serving a corresponding cell from the plurality of cells; predicting, by a pre-calibrated thermal model, temperature in each of the plurality of cells corresponding to the selected first set-point, wherein the pre-calibrated thermal model is based on parameters including electrical loads, ambient load, cooling load, lighting load and the laws of thermodynamics; computing the energy consumption (EHVAC) based on the predicted temperature in each of the plurality of cells; determining a first optimized set-point to be used for each HVAC actuator serving each of the plurality of cells such that the energy consumption (EHVAC) is minimum, the first optimized set-point providing a resultant cell temperature in each of the plurality of cells, such that the resultant cell temperature for the cell under consideration corresponds to a minimum occupant preferred temperature; and obtaining a time-averaged spatial temperature span as a time-average of a difference between a maximum resultant cell temperature and a minimum resultant cell temperature in the uberized open plan space based on the resultant cell temperature in each of the plurality of cells and a resulting span of a temperature field across the uberized open plan space; identify, a temperature field having a maximum time-averaged spatial temperature span amongst the plurality of cells as a template for assigning the plurality of occupants that have been sorted by the occupant preferred temperature; and assign, each of the plurality of occupants to a cell in the plurality of cells such that ordering of the plurality of cells according to occupant preferred temperature is same as ordering of the plurality of cells according to a resultant cell temperature in the template.
In yet another aspect, there is provided a computer program product comprising a non-transitory computer readable medium having a computer readable program embodied therein, wherein the computer readable program, when executed on a computing device, causes the computing device to: receive information pertaining to the uberized open plan space, wherein the open plan space includes a plurality of cells, each of the plurality of cells being served by a Heating, ventilation, and air conditioning (HVAC) actuator associated with a corresponding HVAC, and wherein the information comprises number of the plurality of cells therein and occupant preferred temperature at a given time obtained from a plurality of occupants intending to use the uberized open plan space; iteratively solve a first optimization problem using the received information, for each of the plurality of cells, such that energy consumption (EHVAC) by chillers and variable air volume (VAV) fans of the HVAC is minimized, wherein the one or more hardware processors are further configured to solve the first optimization problem iteratively for each cell under consideration from the plurality of cells by: selecting a first set-point to be used for each HVAC actuator serving a corresponding cell from the plurality of cells; predicting, by a pre-calibrated thermal model, temperature in each of the plurality of cells corresponding to the selected first set-point, wherein the pre-calibrated thermal model is based on parameters including electrical loads, ambient load, cooling load, lighting load and the laws of thermodynamics; computing the energy consumption (EHVAC) based on the predicted temperature in each of the plurality of cells; determining a first optimized set-point to be used for each HVAC actuator serving each of the plurality of cells such that the energy consumption (EHVAC) is minimum, the first optimized set-point providing a resultant cell temperature in each of the plurality of cells, such that the resultant cell temperature for the cell under consideration corresponds to a minimum occupant preferred temperature; and obtaining a time-averaged spatial temperature span as a time-average of a difference between a maximum resultant cell temperature and a minimum resultant cell temperature in the uberized open plan space based on the resultant cell temperature in each of the plurality of cells and a resulting span of a temperature field across the uberized open plan space; identify, a temperature field having a maximum time-averaged spatial temperature span amongst the plurality of cells as a template for assigning the plurality of occupants that have been sorted by the occupant preferred temperature; and assign, each of the plurality of occupants to a cell in the plurality of cells such that ordering of the plurality of cells according to occupant preferred temperature is same as ordering of the plurality of cells according to a resultant cell temperature in the template.
In accordance with an embodiment of the present disclosure, the one or more processors are further configured to solve a second optimization problem using the received information such that overall thermal discomfort for the plurality of occupants is optimized, wherein the one or more processors are further configured to the solve the second optimization problem by: selecting a second set-point to be used for each HVAC actuator serving a corresponding cell from the plurality of cells; predicting, by the pre-calibrated thermal model, temperature in each of the plurality of cells corresponding to the selected second set-point; computing the overall thermal discomfort based on the predicted temperature in each of the plurality of cells, wherein thermal discomfort for an occupant is based on the occupant preferred temperature and the resultant cell temperature in a cell assigned to the occupant; and determining a second optimized set-point to be used for each HVAC actuator serving a corresponding cell from the plurality of cells such that the overall thermal discomfort is optimized.
In accordance with an embodiment of the present disclosure, the one or more processors are further configured to solve the first optimization problem and the second optimization problem subject to a plurality of constraints including (i) one-to-one mapping of the plurality of occupants to seats in the uberized open plan space; and (ii) mass flow rate of the HVAC actuator serving each of the plurality of cells is bound within pre-defined limits, the pre-defined limits corresponding to a minimum and a maximum HVAC flow rate.
In accordance with an embodiment of the present disclosure, the thermal discomfort for an occupant is defined as a squared difference between the occupant preferred temperature and the resultant cell temperature in the cell assigned to the occupant.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS
The accompanying drawings, which are incorporated in and constitute a part of this disclosure, illustrate exemplary embodiments and, together with the description, serve to explain the disclosed principles.
FIG.1 illustrates a schematic representation of an open plan space with multiple actuators, as known in the art.
FIG.2 illustrates an exemplary block diagram of a system for optimizing thermal comfort in uberized open plan spaces, in accordance with an embodiment of the present disclosure.
FIG.3A through FIG.3C illustrates an exemplary flow diagram of a computer implemented method for optimizing thermal comfort in uberized open plan spaces, in accordance with an embodiment of the present disclosure.
FIG.4 illustrates variation in time-averaged spatial temperature span with assignment of a minimum occupant preferred temperature in various cells, in accordance with an embodiment of the present disclosure.
FIG.5A and FIG.5B illustrate thermal discomfort versus HVAC energy consumption for a 6 cells-6 HVAC actuators and a 16 cells-16 HVAC actuators respectively, in accordance with an embodiment of the present disclosure.

DETAILED DESCRIPTION OF EMBODIMENTS
Exemplary embodiments are described with reference to the accompanying drawings. In the figures, the left-most digit(s) of a reference number identifies the figure in which the reference number first appears. Wherever convenient, the same reference numbers are used throughout the drawings to refer to the same or like parts. While examples and features of disclosed principles are described herein, modifications, adaptations, and other implementations are possible without departing from the spirit and scope of the disclosed embodiments. It is intended that the following detailed description be considered as exemplary only, with the true scope and spirit being indicated by the following claims.
Uberized open plan spaces may typically have occupants with conflicting thermal comfort preferences. In the absence of partitions, it is difficult to realize an arbitrary combination of occupants’ comfort preferences even with dedicated Heating, ventilation, and air conditioning (HVAC) actuators because of air mixing. Occupant preferred temperatures were seen to vary in the range 19-25? through occupant participation.
In the art, works have focused on energy and user comfort based on occupancy-driven control, user participation with comfort personalization and fairness. Occupancy-driven control involves exploiting dynamically sensed or inferred unoccupied periods as against a naive fixed schedule based HVAC operation. Control actions are usually occupancy based ventilation and/or use of a higher set-back temperature. Both reactive and model-predictive-control approaches have been considered resulting in energy savings of up to 35%. Under the premise that optimal HVAC control needs user feedback, various works have explored user participatory mechanisms and personalized comfort temperatures. Some of these include: framework for carrying user’s favorite comfort preference along with them and participatory approach to develop a comfort temperature set-point for each user and an optimum set-point algorithm in case a group of users occupy a room. Personalized comfort profiles may work fine when each user has a dedicated comfort control mechanism. Although there are algorithms to estimate optimum set-point for a group of users in the same room, they may be unfair to some users particularly when the user preferred comfort profiles are skewed. In some art, a fairness metric was proposed by considering the loss in comfort experienced by the users over time.
Again, most of the related work have focussed on shared spaces with a single HVAC actuator. In works where an optimal HVAC control for shared spaces with multiple actuators was proposed, all the users were assumed to have the same comfort profiles (that is, the same temperature set-point). Therefore, the problem of spatial assignment of users and the need to maintain different temperatures in occupied spaces did not arise.
In accordance with the present disclosure, discomfort of the occupants is minimized with respect to their respective preferences by assigning seats or workspaces with favorable neighborhoods. Addressing this problem requires a global view rather than allowing each HVAC actuator to act in isolation. The present disclosure addresses the problem of assigning workspaces based on individual thermal comfort preferences of the occupants in uberized open plan offices to minimize the discomfort levels. An optimization problem has been formulated with thermodynamic constraints for air-mixing and heat transfer across cells. Further a two-phase heuristic that exploits a time-averaged spatial temperature span of the open plan space and assigns occupants to workspaces by identifying a temperature field with a maximum time-averaged spatial temperature span is provided such that energy consumption by the HVAC is minimized and the overall thermal discomfort is minimized . In the context of the present disclosure, the expressions ‘seat’ and ‘workspace’ may be interchangeably used. Likewise, the expressions ‘users’ and ‘occupants’ may also be interchangeably used.
FIG.1 illustrates a schematic representation of an open plan space with multiple HVAC actuators, as known in the art. In the context of the present disclosure, HVAC actuators imply controllable end devices such as Variable air volumes (VAVs), cassette air-conditioners, or fan coil units. The area served by an HVAC actuator is referred to hereinafter as a cell and all the cells when taken together, cover the entire open plan space. It is assumed that the temperature and humidity ratio remains uniform within a cell. As illustrated in FIG.1, there are no physical partitions between the various cells. Without the loss of generality, it is assumed that each cell has a single workspace housing a single occupant with one comfort setting. Practically each cell may house one or more occupants. Let N be the number of occupants across the M cells, with N = M (some of the cells may be unoccupied).
It is assumed that users reserve their workspace in advance (at least a few hours before the day begins). They also indicate their preferred thermal comfort setting. First a case where users reserve their workspaces for the entire day is considered. The same may be extended to a case where users reserve the space for a few hours. Notations used hereinafter are described in Table 1 below.
Table 1: Notations
Symbol Description
t Time instant
M Number of cells
N Number of occupants
Aij Indicator variable if occupant i is assigned to cell j
A N X M matrix of assignments
T8 Ambient dry-bulb temperature
Ti Realized temperature in cell i
T_i^P Preferred temperature of user in cell i
Di User discomfort in cell i
D Global discomfort
EHVAC Total energy consumption (chiller + fans)
m ?i VAV mass flow-rate in cell i
It is assumed that each occupant indicates his/her thermal comfort preferences in the form of a temperature setting. Given the input temperature preferences TP of all users, the problem for the facility manager is to decide on the following for each cell: 1) assigning each user to a cell; and 2) determining the temperature set-point to be used for the HVAC actuator serving that cell, so that the overall thermal discomfort for all the users is minimized (ideally, should be zero).
While the decision of assigning users to cells (represented as matrix A) is clearly required, the reason for the second decision of temperature set-points to be used (the vector TS) is subtle. Suppose, post the assignment of users to cells, each user is allowed to set his or her preferred temperature in his cell independent of the choice of the users in adjoining cells. Due to air mixing with other neighboring cells, maintaining the preferred temperatures may not be thermodynamically feasible. Therefore, a centralized mechanism is needed to decide the set-point to be used in each cell; both accounting for user preferences and respecting thermodynamic limitations.
Accordingly, the present disclosure identifies a first optimization problem that needs to be solved as:
min-(A,T_S )??D(A,T_S )=?_(i=1)^N¦D_i ?
(1)
subject to the following constraints:
?i,j?_(j=1)^(j=M)¦?A_ij=1? and ?_(i=1)^(i=N)¦?A_ij=1?
(2)
?i m ?_min=m ?_i=m ?_max
(3)
T=f(m ?,T_8,A)
(4)
The objective function of equation (1) accounts for the global discomfort seen by all users. In accordance with the present disclosure, a convex function is chosen for the discomfort defined at cell i as D_i=((T_i^P-T_i )^2, i.e. the squared difference between the occupant preferred temperature and a resultant cell temperature. It may be noted by one skilled in the art that Fanger’s comfort metric or user participation can be used to quantify the thermal comfort. Fanger’s metric is a function of four environment parameters and two personal parameters. Such approach may warrant extensive sensorization. Generally assumptions are made for four out of the six parameters. Moreover, it is noted that Fanger’s discomfort can be empirically approximated to a quadratic function in room air temperature with other parameters being fixed. Hence, in accordance with the present disclosure, a quadratic function is chosen in room temperature for discomfort. In addition, user participation may help when the user preferences are likely to change over time. In the description hereinafter, it is assumed that the user preferences do not change with time.
Equations (2) through (4) represent constraints for solving the optimization problem of equation (1). Particularly, equation (2) indicates that the mapping of users to seats should be one-to-one. Equation (3) indicates that the mass flow rates of all the HVAC actuators are bounded within pre-defined limits corresponding to a minimum (typically zero) and a maximum (based on design) HVAC flow rate. Equation (4) states that the thermodynamic constraints should be followed in the temperature evolution of a cell. In the present disclosure the constraint represented by equation (4) is addressed by use of a thermal model described later in the description. Specifically, the temperature evolution is modelled from first principles using the heat balance equation provided by D.B.Crawley et al. in ‘Energyplus: Energy simulation program’ published in ASHRAE journal, 42:49-56, 2000.
The optimization problem has a complex nonlinear objective function with integer (assignment matrix A) decision variables. Assigning users to cells based on preferred temperatures, to a coarse approximation, can be thought of as a seating problem with preferred neighbors; with the objective being to maximize preferences being satisfied. In the problem under consideration, users having similar preferred temperatures will prefer each other as neighbors. Solving the problem of assigning similar temperatures is now equivalent to finding a Hamiltonian path in the preference graph, which is NP (nondeterministic polynomial time) hard. Thus it may be inferred that the problem under consideration is at least of the same complexity. It is also noted that conventional solvers do not scale beyond a few cells for a direct formulation.
Referring now to the drawings, and more particularly to FIG.2 through FIG.5B, where similar reference characters denote corresponding features consistently throughout the figures, there are shown preferred embodiments and these embodiments are described in the context of the following exemplary system and/or method.
FIG.2 illustrates an exemplary block diagram of a system 100 for optimizing thermal comfort in uberized open plan spaces in accordance with an embodiment of the present disclosure. In an embodiment, the system 100 includes one or more processors 104, communication interface device(s) or input/output (I/O) interface(s) 106, and one or more data storage devices or memory 102 operatively coupled to the one or more processors 104. The one or more processors 104 that are hardware processors can be implemented as one or more microprocessors, microcomputers, microcontrollers, digital signal processors, central processing units, state machines, graphics controllers, logic circuitries, and/or any devices that manipulate signals based on operational instructions. Among other capabilities, the processor(s) are configured to fetch and execute computer-readable instructions stored in the memory. In the context of the present disclosure, the expressions ‘processors’ and ‘hardware processors’ may be used interchangeably. In an embodiment, the system 100 can be implemented in a variety of computing systems, such as laptop computers, notebooks, hand-held devices, workstations, mainframe computers, servers, a network cloud and the like.
The I/O interface(s) 106 can include a variety of software and hardware interfaces, for example, a web interface, a graphical user interface, and the like and can facilitate multiple communications within a wide variety of networks N/W and protocol types, including wired networks, for example, LAN, cable, etc., and wireless networks, such as WLAN, cellular, or satellite. In an embodiment, the I/O interface(s) can include one or more ports for connecting a number of devices to one another or to another server.
The memory 102 may include any computer-readable medium known in the art including, for example, volatile memory, such as static random access memory (SRAM) and dynamic random access memory (DRAM), and/or non-volatile memory, such as read only memory (ROM), erasable programmable ROM, flash memories, hard disks, optical disks, and magnetic tapes. In an embodiment, one or more modules (not shown) of the system 100 can be stored in the memory 102.
FIG.3A through FIG.3C illustrates an exemplary flow diagram for a computer implemented method 200 for optimizing thermal comfort in uberized open plan spaces, in accordance with an embodiment of the present disclosure. In an embodiment, the system 100 includes one or more data storage devices or memory 102 operatively coupled to the one or more processors 104 and is configured to store instructions configured for execution of steps of the method 200 by the one or more processors 104. The steps of the method 200 will now be explained in detail with reference to the components of the system 100 of FIG.2. Although process steps, method steps, techniques or the like may be described in a sequential order, such processes, methods and techniques may be configured to work in alternate orders. In other words, any sequence or order of steps that may be described does not necessarily indicate a requirement that the steps be performed in that order. The steps of processes described herein may be performed in any order practical. Further, some steps may be performed simultaneously.
In accordance with an embodiment of the present disclosure, the one or more processors 104 are configured to receive, at step 202, information pertaining to the uberized open plan space, wherein the open plan space includes a plurality of cells, each of the plurality of cells being served by a Heating, ventilation, and air conditioning (HVAC) actuator associated with a corresponding HVAC. In the context of the present disclosure, the received information comprises number of the plurality of cells in the uberized open plan space and occupant preferred temperature at a given time obtained from a plurality of occupants intending to use the uberized open plan space.
The optimization problem as determined in the present disclosure is solved in two parts as described herein after. In accordance with an embodiment, the one or more processors 104, are configured to iteratively solve a first optimization problem, at step 204, using the received information in step 202, such that energy consumption (EHVAC) by chillers and variable air volume (VAV) fans of the HVAC is minimized. In an embodiment, the first optimization problem is solved iteratively for each cell under consideration from the plurality of cells by firstly selecting a first set-point to be used, at step 204a, for each HVAC actuator serving a corresponding cell from the plurality of cells. A pre-calibrated thermal model then predicts the temperature in each of the plurality of cells corresponding to the selected first set-point at step 204b. The energy consumption (EHVAC) is then computed at step 204c based on the predicted temperature in each of the plurality of cells. A first optimized set-point to be used for each HVAC actuator serving each of the plurality of cells is determined at step 204d, such that the energy consumption (EHVAC) is minimum.
In an embodiment, the first optimized set-point provides a resultant cell temperature in each of the plurality of cells such that the resultant cell temperature for the cell under consideration corresponds to a minimum occupant preferred temperature. As described earlier, due to cross-cell air mixing, temperatures across multiple cells are coupled. Due to these thermodynamic constraints; the ambient boundary conditions; distribution of internal non-user heat-sources; and the geometry of the open plan space; there exists a natural temperature field even in the absence of users and controlled conditioning of the open plan space. In accordance with the present disclosure, the coldest or the minimum occupant preferred temperature is assigned to each cell iteratively. For each assignment of the coldest or the minimum occupant preferred temperature to the cell under consideration, temperatures of all remaining cells are computed to obtain a time-averaged spatial temperature span at step 204e, wherein the time-averaged spatial temperature span is time-average of a difference between a maximum resultant cell temperature and a minimum resultant cell temperature in the uberized open plan space based on the resultant cell temperature in each of the plurality of cells and a resulting span of the temperature field across the uberized open plan space. The first optimization problem is solved such that the energy consumption (EHVAC) is minimized subject to meeting the coldest user preferred temperature in the cell under consideration. The presence of the user requiring the coldest preferred temperature acts as a lens that helps magnify and tease out the maximum temperature span possible in the room, which may not be computationally recognizable otherwise due to miniscule temperature differences across the cells.
In accordance with the present disclosure, the one or more hardware processors 104 are configured to identify, at step 206, a temperature field having a maximum time-averaged spatial temperature span amongst the plurality of cells as a template for assigning the plurality of occupants that have been sorted by the occupant preferred temperature.
In accordance with the present disclosure, the one or more hardware processors 104 are configured to assign, at step 208, each of the plurality of occupants to a cell in the plurality of cells such that ordering of the plurality of cells according to occupant preferred temperature TP is same as ordering of the plurality of cells according to a resultant cell temperature in the template (which in turn is based on the maximum time-averaged spatial temperature span T_F^* . Accordingly, the assignment matrix A is obtained.
In accordance with an embodiment, the one or more processors 104, are further configured to iteratively solve a second optimization problem, at step 210, using the received information such that overall thermal discomfort for the plurality of occupants is optimized. In an embodiment, the second optimization problem is solved by firstly selecting a second set-point to be used for each HVAC actuator serving a corresponding cell from the plurality of cells at step 210a. The pre-calibrated thermal model then predicts, temperature in each of the plurality of cells corresponding to the selected second set-point at step 210b. The overall thermal discomfort is computed at step 210c based on the predicted temperature in each of the plurality of cells, wherein thermal discomfort for an occupant is based on the occupant preferred temperature and the resultant cell temperature in a cell assigned to the occupant. Particularly, as stated earlier, in an embodiment, the thermal discomfort for an occupant may be defined as a squared difference between the occupant preferred temperature and the resultant cell temperature in the cell assigned to the occupant. A second optimized set-point to be used for each HVAC actuator serving a corresponding cell from the plurality of cells is then determined at step 210d, such that the overall thermal discomfort is minimized.
In accordance with the present disclosure, as explained with reference to equations (2) through (4) solving the first optimization problem and the second optimization problem is subject to the represented plurality of constraints.

EXPERIMENTAL SETUP AND EVALUATION
Baselines considered: The method of the present disclosure was evaluated along the dimensions of thermal discomfort and energy consumption. The method of the present disclosure was compared against a brute-force technique that evaluates against all possible seat assignments for small problem instances; and against a Monte-Carlo sampling based evaluation for realistic problem instances.
Office layouts considered: The performance of the method of the present disclosure and their respective baselines were evaluated on a 16 cells layout derived from a real-world office set-up. In addition to this 16-actuators setup, a synthetic layout of the same size was considered but with just six cells and six actuators. The synthetic 6 cells set-up was considered to identify the optimum user assignment through an exhaustive combinatorial enumeration. Since enumerating and evaluating all 16! ways of assigning users to workspaces was not feasible, 100 random assignments of users to workspaces was considered to serve as a baseline for the 16-actuator case.
Comfort preferences considered: For both the synthetic and the real-world layouts, two distinct user comfort preference profiles were evaluated - one with a low co-efficient of variation (CV) of around 2% and a second with a high co-efficient of variation (CV) of around 8%, wherein the CV is the ratio of the standard deviation to the mean. The cell comfort preferences were picked to be within the temperature range of 22? to 26?. The low CV case mimics a scenario where all the user preferences are close to each other while the high CV case reflects the scenario where the user preferences are more diverse.
RESULTS
Preprocessing for Assigning Users (AU): FIG.4 illustrates variation in time-averaged spatial temperature span with assignment of a minimum occupant preferred temperature in various cells, in accordance with an embodiment of the present disclosure. It was observed that the time-averaged spatial temperature span was achieved when the user is located at the left bottom corner. This is due to placing the coldest occupant preferred temperature user farthest from the locations of expected high heat loads such as the perimeter zone with glazing.
Performance of Assigning Users (AU): The energy and overall thermal discomfort that results from different user-to-cell assignment combinations are considered here. FIG.5A and FIG.5B illustrate thermal discomfort versus HVAC energy consumption for a 6 cells-6 HVAC actuators and a 16 cells-16 HVAC actuators respectively, in accordance with an embodiment of the present disclosure. Each point in the scatter plots results from the assignment of users to cells. FIG.5A for the 6 HVAC actuators case has 100 randomly chosen user assignments. The results are shown for low CV (represented as circles) and high CV (represented as squares) in the occupant preferred temperature. Following are the observations based on FIG. 5A and 5B:
Because each point uses the same set-point assignment method, the energy-comfort spread is caused by the difference in user assignments.
For the low CV scenario, there is noticeable spread in energy with little spread in the discomfort. Because the user preferred temperatures vary within a narrow range, the resultant cell temperatures can be closely matched with comfort profiles for any assignment of users to workspaces. This leads to a lower overall thermal discomfort. The spread in the energy for nearly the same discomfort is a result of assigning users with lower temperature preferences in regions expected to have high heat loads. As mentioned earlier, maintaining a lower temperature in a region expected to have high heat loads, for instance perimeter cells with windows, can consume more energy.
For the same minimum discomfort, the spread in energy is almost 7-8%. This is shown in the region labeled R1 in FIG.5A and R2 in FIG.5B. This suggests that a facility manager can seek to reduce energy even while maintaining the same (minimum) discomfort with just a good seating plan.
There is a considerable spread in both energy and discomfort when there is high CV in the user preferred temperatures. This indicates that arbitrary assignment of users can be suboptimal both in terms of energy and discomfort. Hence, there is a need for a good user-to-cell assignment strategy as provided in the present disclosure.
Points P1 and P2 in FIG.5A identify the results of the method of the present disclosure ( user assignment and set-point assignment) for the two cases of low CV and high CV in user preferred temperatures respectively. It is noted that all possible assignments for the 6-HVAC actuator case, the heuristic method (AU) achieves the lowest discomfort at P1 and P2. Further, it also achieves the lowest energy consumption among all points with the same minimum discomfort. Similarly, points P3 and P4 identified by the method of the present disclosure minimize the discomfort for the 16 HVAC actuators case in FIG.5B.
The results presented herein above give the best possible global comfort that can be achieved if a facility manager were to assign the users to respective workspaces in accordance with the present disclosure. However, it is possible that, in addition to preferred temperatures, the users may have other preferences such as choosing a specific location in the room, that is, sit with colleagues or have good view of outside. In such case, if the neighboring users preferred temperatures are incompatible, the global discomfort can only increase. The proposed approach is generic and capable of handling such scenarios.
The written description describes the subject matter herein to enable any person skilled in the art to make and use the embodiments. The scope of the subject matter embodiments is defined by the claims and may include other modifications that occur to those skilled in the art. Such other modifications are intended to be within the scope of the claims if they have similar elements that do not differ from the literal language of the claims or if they include equivalent elements with insubstantial differences from the literal language of the claims.
It is to be understood that the scope of the protection is extended to such a program and in addition to a computer-readable means having a message therein; such computer-readable storage means contain program-code means for implementation of one or more steps of the method, when the program runs on a server or mobile device or any suitable programmable device. The hardware device can be any kind of device which can be programmed including e.g. any kind of computer like a server or a personal computer, or the like, or any combination thereof. The device may also include means which could be e.g. hardware means like e.g. an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or a combination of hardware and software means, e.g. an ASIC and an FPGA, or at least one microprocessor and at least one memory with software modules located therein. Thus, the means can include both hardware means and software means. The method embodiments described herein could be implemented in hardware and software. The device may also include software means. Alternatively, the embodiments may be implemented on different hardware devices, e.g. using a plurality of CPUs.
The embodiments herein can comprise hardware and software elements. The embodiments that are implemented in software include but are not limited to, firmware, resident software, microcode, etc. The functions performed by various modules described herein may be implemented in other modules or combinations of other modules. For the purposes of this description, a computer-usable or computer readable medium can be any apparatus that can comprise, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device.
The illustrated steps are set out to explain the exemplary embodiments shown, and it should be anticipated that ongoing technological development will change the manner in which particular functions are performed. These examples are presented herein for purposes of illustration, and not limitation. Further, the boundaries of the functional building blocks have been arbitrarily defined herein for the convenience of the description. Alternative boundaries can be defined so long as the specified functions and relationships thereof are appropriately performed. Alternatives (including equivalents, extensions, variations, deviations, etc., of those described herein) will be apparent to persons skilled in the relevant art(s) based on the teachings contained herein. Such alternatives fall within the scope and spirit of the disclosed embodiments. Also, the words “comprising,” “having,” “containing,” and “including,” and other similar forms are intended to be equivalent in meaning and be open ended in that an item or items following any one of these words is not meant to be an exhaustive listing of such item or items, or meant to be limited to only the listed item or items. It must also be noted that as used herein and in the appended claims, the singular forms “a,” “an,” and “the” include plural references unless the context clearly dictates otherwise.
Furthermore, one or more computer-readable storage media may be utilized in implementing embodiments consistent with the present disclosure. A computer-readable storage medium refers to any type of physical memory on which information or data readable by a processor may be stored. Thus, a computer-readable storage medium may store instructions for execution by one or more processors, including instructions for causing the processor(s) to perform steps or stages consistent with the embodiments described herein. The term “computer-readable medium” should be understood to include tangible items and exclude carrier waves and transient signals, i.e., be non-transitory. Examples include random access memory (RAM), read-only memory (ROM), volatile memory, nonvolatile memory, hard drives, CD ROMs, DVDs, flash drives, disks, and any other known physical storage media.
It is intended that the disclosure and examples be considered as exemplary only, with a true scope and spirit of disclosed embodiments being indicated by the following claims.