Claims:1. A processor implemented method, comprising:
obtaining one or more known thermodynamics cycle parameters pertaining to a Vapour Compression Refrigeration System (VCRS), wherein the one or more known thermodynamics cycle parameters comprise information pertaining to pressure at a suction unit and a discharge unit of the VCRS and temperature at the discharge unit (202);
computing (i) a first enthalpy at the discharge unit using information pertaining to the pressure and the temperature at the discharge unit, and (ii) one or more saturation temperatures for the pressure at the suction unit and the discharge unit (204);
generating one or more prior distributions for degree of superheat and degree of sub-cooling of the VCRS (206);
computing a second enthalpy and a third enthalpy from the generated one or more prior distributions, the first enthalpy and the one or more saturation temperatures (208);
iteratively computing, using an Expectation Maximization (EM) technique, one or more posterior probability distributions based the generated one or more prior distributions, the second enthalpy, the third enthalpy, wherein the one or more posterior probability distributions are iteratively computed until an error pertaining to a KL divergence between a current iteration and a previous iteration reaches a pre-defined threshold (210);
computing a Maximum Likelihood Estimate (MLE) of the degree of superheat and degree of sub-cooling based the one or more posterior probability distributions (212); and
estimating a Coefficient of Performance (COP) of the VCRS based on the computed MLE (214).

2. The processor implemented method of claim 1, wherein the step of iteratively computing one or more posterior probability distributions comprises minimizing the KL Divergence error between the generated one or more prior distributions and the one or more posterior probability distributions.

3. The processor implemented method of claim 1, wherein the degree of superheat and the degree sub-cooling of the VCRS are pre-defined and obtained using at least one of a domain knowledge and one or more operation policies.

4. The processor implemented method of claim 1, wherein the step of iteratively computing, using an Expectation Maximization (EM) technique, one or more posterior probability distributions comprises performing a fixed point computation on the KL divergence error to obtain the one or more posterior probability distributions of the degree of superheat and degree of sub-cooling of the VCRS.

5. The processor implemented method of claim 1, further comprising identifying a value at a convergence as a value of the COP that jointly minimizes the KL divergence error between the one or more prior distributions and the one or more posterior probability distributions.

6. A system (100), comprising:
a memory (102) storing instructions;
one or more communication interfaces (106); and
one or more hardware processors (104) coupled to the memory (102) via the one or more communication interfaces (106), wherein the one or more hardware processors (104) are configured by the instructions to:
obtain one or more known thermodynamics cycle parameters pertaining to a Vapour Compression Refrigeration System (VCRS), wherein the one or more known thermodynamics cycle parameters comprise information pertaining to pressure at a suction unit and a discharge unit of the VCRS and temperature at the discharge unit;
compute (i) a first enthalpy at the discharge unit using the information pertaining to the pressure and the temperature at the discharge unit, and (ii) one or more saturation temperatures for the pressure at the suction unit and the discharge unit;
generate one or more prior distributions for degree of superheat and degree of sub-cooling of the VCRS;
compute a second enthalpy and a third enthalpy from the generated one or more prior distributions, the first enthalpy and the one or more saturation temperatures;
iteratively compute, using an Expectation Maximization (EM) technique, one or more posterior probability distributions based the generated one or more prior distributions, the second enthalpy, the third enthalpy, wherein the one or more posterior probability distributions are iteratively computed until an error pertaining to a KL divergence between a current iteration and a previous iteration reaches a pre-defined threshold;
compute a Maximum Likelihood Estimate (MLE) of the degree of superheat and degree of sub-cooling based the one or more posterior probability distributions; and
estimate a Coefficient of Performance (COP) of the VCRS based on the computed MLE.

7. The system of claim 6, wherein the one or more posterior probability distributions are iteratively computed to minimize the KL Divergence error between the generated one or more prior distributions and the one or more posterior probability distributions.

8. The system of claim 6, wherein the degree of superheat and the degree sub-cooling of the VCRS are pre-defined and obtained using at least one of a domain knowledge and one or more operation policies.

9. The system of claim 6, wherein the one or more posterior probability distributions are iteratively computed using the Expectation Maximization (EM) technique by performing a fixed point computation on the KL divergence error to obtain the one or more posterior probability distributions of the degree of superheat and degree of sub-cooling of the VCRS.

10. The system of claim 6, wherein the one or more hardware processors are further configured by the instructions to identify a value at a convergence as a value of the COP that minimizes the KL divergence error between the one or more prior distributions and the one or more posterior probability distributions.
, 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:
THERMODYNAMICS CYCLE PARAMETERS COMPUTATION BASED
PERFORMANCE ESTIMATION OF VAPOUR COMPRESSION REFRIGERATION SYSTEMS (VCRS)

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 Vapour Compression Refrigeration Systems (VCRS), and, more particularly, to thermodynamics cycle parameters computation based performance estimation of VCRS.

BACKGROUND
Vapour Compression Refrigeration Systems (VCRS) are traditionally well-known equipments which are commonly used in cooling the air in commercial premises and/or buildings, educational institutions, financial institutions, hospitals, restaurants and the like. Each such VCRS has at least a condenser, compressor racks, etc. As a practice, operation of the VCRS is controlled by various temperatures at various components of the VCRS so as to be able to operate at various conditions. Therefore, it is utmost important to estimate performance of VCRS to enable the VCRS operate at various conditions. For a system like VCRS to be able to operate and/or run smooth and cost-effectively, the performance should be at par and must be running efficiently. Traditional Performance Benchmarking of systems would include gathering of the required data for example, taking all system parameters, performing physics based calculations and providing benchmarking insights. The problem with the conventional approach is, it requires a large amount of data and it may be extremely hard to handle high volumes of data in a real time fashion. Moreover, most legacy systems may not be well instrumented to collect all the required data for performance estimation.

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. For example, in one aspect, there is provided a processor implemented method for thermodynamics cycle parameters computation based performance estimation of Vapour Compression Refrigeration Systems (VCRS). The processor implemented method comprises obtaining one or more known thermodynamics cycle parameters pertaining to a Vapour Compression Refrigeration System (VCRS), wherein the one or more known thermodynamics cycle parameters comprise information pertaining to pressure at a suction unit and a discharge unit of the VCRS and temperature at the discharge unit; computing (i) a first enthalpy (H_2) at the discharge unit using the information pertaining to the pressure and the temperature at the discharge unit, and (ii) one or more saturation temperatures for the pressure at the suction unit and the discharge unit; generating one or more prior distributions for degree of superheat and degree of sub-cooling of the VCRS; computing a second enthalpy (H_1) and a third enthalpy (H_4) from the generated one or more prior distributions, the first enthalpy and the one or more saturation temperatures; iteratively computing, using an Expectation Maximization (EM) technique, one or more posterior probability distributions based the generated one or more prior distributions, the second enthalpy (H_1) and the third enthalpy (H_4), wherein the one or more posterior probability distributions are iteratively computed until an error pertaining to a KL divergence between a current iteration and a previous iteration reaches a pre-defined threshold; computing a Maximum Likelihood Estimate (MLE) of the degree of superheat and degree of sub-cooling based the one or more posterior probability distributions; and estimating a Coefficient of Performance (COP) of the VCRS based on the computed MLE.
In an embodiment, the step of iteratively computing the one or more posterior probability distributions comprises minimizing a KL divergence between the generated one or more prior distributions and the one or more posterior probability distributions. In an embodiment, the degree of superheat and the degree sub-cooling of the VCRS are pre-defined and obtained using at least one of a domain knowledge and one or more operation policies.
In an embodiment, the step of iteratively computing, using an Expectation Maximization (EM) technique, one or more posterior probability distributions comprises performing a fixed point computation on a KL divergence error to obtain the one or more posterior probability distributions of the degree of superheat and degree of sub-cooling of the VCRS.
In an embodiment, a convergence is identified when a difference between a current iteration and a previous iteration of the KL divergence error reaches a pre-defined threshold.
In an embodiment, the processor implemented method may further comprise identifying a value at the convergence as a value of the COP that jointly minimizes the KL divergence error between the one or more prior distributions and the one or more posterior probability distributions.
In another aspect, there is provided a system for thermodynamics cycle parameters computation based performance estimation of Vapour Compression Refrigeration Systems (VCRS). The system comprises a memory storing instructions; one or more communication interfaces; and one or more hardware processors coupled to the memory via the one or more communication interfaces, wherein the one or more hardware processors are configured by the instructions to: obtain one or more known thermodynamics cycle parameters pertaining to a Vapour Compression Refrigeration System (VCRS), wherein the one or more known thermodynamics cycle parameters comprise information pertaining to pressure at a suction unit and a discharge unit of the VCRS and temperature at the discharge unit; compute (i) a first enthalpy (H_2) at the discharge unit using the information pertaining to the pressure and the temperature at the discharge unit, and (ii) one or more saturation temperatures for the pressure at the suction unit and the discharge unit; generate one or more prior distributions for degree of superheat and degree of sub-cooling of the VCRS; compute a second enthalpy (H_1) and a third enthalpy (H_4) from the generated one or more prior distributions, the first enthalpy and the one or more saturation temperatures; iteratively compute, using an Expectation Maximization (EM) technique, one or more posterior probability distributions based the generated one or more prior distributions, the second enthalpy (H_1), the third enthalpy (H_4), wherein the one or more posterior probability distributions are iteratively computed until an error pertaining to a KL divergence between a current iteration and a previous iteration reaches a pre-defined threshold; compute a Maximum Likelihood Estimate (MLE) of the degree of superheat and degree of sub-cooling based the one or more posterior probability distributions; and estimate a Coefficient of Performance (COP) of the VCRS based on the computed MLE.
In an embodiment, the one or more posterior probability distributions are iteratively computed to minimize a KL divergence between the generated one or more prior distributions and the one or more posterior probability distributions.
In an embodiment, the degree of superheat and the degree sub-cooling of the VCRS are pre-defined and obtained using at least one of a domain knowledge and one or more operation policies.
In an embodiment, the one or more posterior probability distributions are iteratively computed using the Expectation Maximization (EM) technique by performing a fixed point computation on a KL divergence error to obtain the one or more posterior probability distributions of the degree of superheat and degree of sub-cooling of the VCRS.
In an embodiment, a convergence is identified when a difference between a current iteration and a previous iteration of the KL divergence error reaches a pre-defined threshold.
In an embodiment, the one or more hardware processors are further configured by the instructions to identify a value at the convergence as a value of the cop that jointly minimizes the KL divergence error between the one or more prior distributions and the one or more posterior probability distributions.
In yet another aspect, there is provided one or more non-transitory machine readable information storage mediums comprising one or more instructions. The one or more instructions which when executed by one or more hardware processors causes obtaining one or more known thermodynamics cycle parameters pertaining to a Vapour Compression Refrigeration System (VCRS), wherein the one or more known thermodynamics cycle parameters comprise information pertaining to pressure at a suction unit and a discharge unit of the VCRS and temperature at the discharge unit; computing (i) a first enthalpy (H_2) at the discharge unit using the information pertaining to the pressure and the temperature at the discharge unit, and (ii) one or more saturation temperatures for the pressure at the suction unit and the discharge unit; generating one or more prior distributions for degree of superheat and degree of sub-cooling of the VCRS; computing a second enthalpy (H_1) and a third enthalpy (H_4) from the generated one or more prior distributions, the first enthalpy and the one or more saturation temperatures; iteratively computing, using an Expectation Maximization (EM) technique, one or more posterior probability distributions based the generated one or more prior distributions, the second enthalpy (H_1), the third enthalpy (H_4), wherein the one or more posterior probability distributions are iteratively computed until an error pertaining to a KL divergence between a current iteration and a previous iteration reaches a pre-defined threshold; computing a Maximum Likelihood Estimate (MLE) of the degree of superheat and degree of sub-cooling based the one or more posterior probability distributions; and estimating a Coefficient of Performance (COP) of the VCRS based on the computed MLE.
In an embodiment, the step of iteratively computing the one or more posterior probability distributions comprises minimizing a KL divergence between the generated one or more prior distributions and the one or more posterior probability distributions. In an embodiment, the degree of superheat and the degree sub-cooling of the VCRS are pre-defined and obtained using at least one of a domain knowledge and one or more operation policies.
In an embodiment, the step of iteratively computing, using an Expectation Maximization (EM) technique, one or more posterior probability distributions comprises performing a fixed point computation on a KL divergence error to obtain the one or more posterior probability distributions of the degree of superheat and degree of sub-cooling of the VCRS.
In an embodiment, a convergence is identified when a difference between a current iteration and a previous iteration of the KL divergence error reaches a pre-defined threshold.
In an embodiment, the one or more instructions which when executed by the one or more hardware processors may further cause identifying a value at the convergence as a value of the cop that jointly minimizes the KL divergence error between the one or more prior distributions and the one or more posterior probability distributions.
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 an exemplary block diagram of a system for computation of unknown thermodynamics cycle parameters and performance estimation of Vapour Compression Refrigeration Systems (VCRS) according to an example embodiment of the present disclosure.
FIG. 2 illustrates an exemplary method for computation of unknown thermodynamics cycle parameters and performance estimation of the Vapour Compression Refrigeration Systems (VCRS) using the system 100 of FIG. 1 according to an embodiment of the present disclosure.
FIG. 3A illustrates a pressure-enthalpy (P-H) graphical representation depicting of operational characteristics of a Heating, ventilation, air conditioning (HVAC) and Refrigeration (HVAC&R) system according to an example embodiment of the present disclosure.
FIG. 3B illustrates a temperature versus specific entropy (T-S) graphical representation depicting of operational characteristics of the Heating, ventilation, air conditioning (HVAC) and Refrigeration (HVAC&R) system according to an example embodiment of the present disclosure.
FIG. 4A illustrates a graphical representing depicting one or more prior distributions and one or more posterior probability distributions when value of K is 3.2 for a first iteration according to an example embodiment of the present disclosure.
FIG. 4B illustrates a graphical representing depicting the one or more prior distributions and the one or more posterior probability distributions after KL convergence that is indicative of a value of a Coefficient of Performance (COP) that jointly minimizes the KL divergence error between the one or more prior distributions and the one or more posterior probability distributions according to an example embodiment of the present disclosure.
FIG. 4C illustrates a graphical representation of a difference between a current iteration and a previous iteration of the KL divergence error reaching a pre-defined threshold according to an example embodiment of the present disclosure.
FIG. 5 depicts Coefficient of Performance (COP) of various VCRS according to an example 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.
As discussed above, traditional performance benchmarking of systems may not be efficient as the traditional approach, takes in all the system parameters and performs simple physics based calculations to compute the coefficient of performance (COP). Embodiments of the present disclosure provide systems and methods for computation of unknown parameters which are modeled probabilistically to get maximum likelihood estimates of the unknown parameters. Further the parameters are used as inputs to generate mathematical models (e.g., equation(s)) for computation of Coefficient of Performance (COP) specific to Vapour Compression Refrigeration Systems (VCRS).
A typical VCRS comprises an evaporator, a compressor, a condenser and a throttling device. A chemical refrigerant undergoes change in states to provide the required cooling effect. In the evaporator a low temperature low pressure liquid-gas mixture changes its state to low pressure and low temperature gas. Ideally the refrigerant should exit evaporator as superheated gas. However, in practice to avoid liquid refrigerant enter the compressor, evaporators are designed in a way such that the refrigerant exists as a superheated gas. This low pressure and low temperature superheated refrigerant is converted to high pressure, high temperature gas in compressor. In the condenser the refrigerant changes its state from high temperature high pressure gas to high temperature, high pressure liquid. In order to improve the net refrigeration effect, condenser is designed to exit the refrigerant in sub-cooled state. The subcooled liquid refrigerant passes through the throttling valve and is passively converted to low pressure and low temperature liquid/gas mixture and the cycle is repeated. To understand the method described, it is very important to understand the context. The suction pressure and the discharge pressure of the compressor is available and the discharge temperature of the compressor is also known. To complete the cycle, the temperature of the subcooled refrigerant and the superheated refrigerant needs to be estimated, which are unknown or not available at hand.
To estimate the missing parameters, the embodiments of the present disclosure utilize probabilistic reasoning. The prior distributions of degree of superheat and degree of sub-cooling is obtained from the manufacturer’s manual. The system implements (and/or executes) a fixed point computation to compute the Maximum Likelihood Estimates (MLE) of the posteriori distributions of degree of superheat and sub-cooling. In other words, is the fixed point computation is performed to compute the posteriori distribution by minimizing the Kullback–Leibler (KL) distance (or KL divergence error) between the prior and posteriori iteratively till convergence which gives an estimation of the COP of the VCRS.
Referring now to the drawings, and more particularly to FIGS. 1 through 5, 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. 1 illustrates an exemplary block diagram of a system 100 for computation of unknown thermodynamics cycle parameters and performance estimation of Vapour Compression Refrigeration Systems (VCRS) according to an example 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 may be one or more software processing modules and/or hardware processors.
In an embodiment, the hardware processors can be implemented as one or more microprocessors, microcomputers, microcontrollers, digital signal processors, central processing units, state machines, logic circuitries, and/or any devices that manipulate signals based on operational instructions. Among other capabilities, the processor(s) is configured to fetch and execute computer-readable instructions stored in the memory. In an embodiment, the device 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 device(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 device(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 database(s) 108 can be stored in the memory 102, wherein the database(s) 108 may comprise, but are not limited to information pertaining to one or more known thermodynamics cycle parameters, values pertaining to incomplete cycle parameters that are derived based on one or more prior distributions for degree of superheat and degree of sub-cooling of the VCRS, and the like.
FIG. 2, with reference to FIG. 1, illustrates an exemplary method for computation of unknown thermodynamics cycle parameters and performance estimation of Vapour Compression Refrigeration Systems (VCRS) using the system 100 of FIG. 1 according to an embodiment of the present disclosure. In an embodiment, the system(s) 100 comprises one or more data storage devices or the memory 102 operatively coupled to the one or more hardware processors 104 and is configured to store instructions for execution of steps of the method by the one or more processors 104. FIGS. 3A-3B, with reference to FIGS. 1-2, depict a pressure-enthalpy (P-H) and a temperature versus specific entropy (T-S) graphical representation of a Vapour Compression Refrigeration System (VCRS) according to an example embodiment of the present disclosure.
More particularly, FIGS. 3A-3B, depict operational characteristics of a Heating, ventilation, air conditioning (HVAC) and Refrigeration (HVAC&R) system. As mentioned above, a refrigeration system requires a minimum of four components namely an evaporator, a compressor, a condenser and a throttling device. A chemical refrigerant undergoes change in states to provide the required cooling effect. The lines joining points 2 and 7 in P-H graphical representation (also referred hereinafter as ‘P-H diagram’) and points 2 and 6 in T-S graphical representation (also referred hereinafter as ‘T-S diagram’) is the evaporator. In the evaporator, a low temperature low pressure liquid gas. Ideally the refrigerant should exit evaporator as saturated gas. However, in practice, to avoid liquid refrigerant enter the compressor, the evaporator are designed in a way such that the refrigerant exits as superheated gas. The lines joining points 2 and 3 in both the P-H and T-S diagram is the Compressor. The low pressure and low temperature superheated refrigerant is converted to high pressure and high temperature gas in compressor. The lines joining points 3 and 6 in the P-H diagram and points 3 and 5 in T-S diagram is the condenser. In the condenser, the refrigerant changes its state from high temperature, high pressure gas to high pressure, high temperature liquid. In order to improve the net effect condenser is designed to exit the refrigerant in sub-cooled state. The throttling valve is given by lines joining points 6 and 7 in the P-H diagram and lines joining points 5 and 6 in the T-S diagram. The subcooled liquid refrigerant passes through the throttling valve and is passively converted to low pressure and temperature liquid-gas mixture and the cycle is repeated.
The steps of the method of the present disclosure will now be explained with reference to the components of the system 100 as depicted in FIG. 1, and the P-H and T-S diagrams of FIGS. 3A and 3B respectively and the flow diagram of FIG. 2. The information that is available in the refrigeration cycle is the suction pressure, discharge pressure and discharge temperature. There parameters are hereinafter referred as “known thermodynamics cycle parameters”. Therefore, in an embodiment of the present disclosure, at step 202, the one or more hardware processors 104, obtain one or more known thermodynamics cycle parameters (as mentioned above) pertaining to a Vapour Compression Refrigeration System (VCRS), wherein the one or more known thermodynamics cycle parameters comprise information pertaining to pressure at a suction unit (also referred hereinafter as P_suction or Suction Pressure (Pa)), and a discharge unit (also referred hereinafter as P_discharge or Suction Pressure (Pa)) of the VCRS and temperature at the discharge unit (also referred hereinafter as T_discharge or Discharge Temperature (K).
From the P-H diagram, only Enthalpy (H_1) of the Refrigerant at the end of the Compressor (J/Kg) and Enthalpy (H_3) of the Refrigerant at the End of the condenser (J/Kg) are required to complete the Refrigeration Cycle.
In an embodiment of the present disclosure, at step 204, the one or more hardware processors 104 compute (i) a first enthalpy H_2 at the discharge unit using the pressure and the temperature at the discharge unit, and (ii) one or more saturation temperatures for the pressure at the suction unit and the discharge unit. From the law of thermodynamics, total load of a premise (say, a building under consideration) Q_Load is expressed by way of following example equation:
Q_Load=M_Evap (H_1-H_4) (1)
W_Comp=M_Comp ((H_2-H_1))/? (2)
where M_Evap is mass flow rate of the refrigerant through the evaporator (Kg/s), W_Comp is Compressor's Electrical Power (KW), M_Comp is mass flow rate of the refrigerant through the compressor (Kg/s), H_1, and H_4 are the unknown thermodynamics cycle parameters, and ? is Compressor Efficiency.
By utilizing equation (1) and (2), and re-arranging the terms, the following expression is obtained by way of example:
K=((H_2-H_1))/((H_1-H_4)) (3)
where K is an estimate of the refrigerant cycle COP. Now H_2 could be directly computed as the discharge pressure and the discharge temperature are known.
The missing variables (also referred hereinafter as “unknown thermodynamics cycle parameters”) are second enthalpy H_1 and third enthalpy H_4. To compute H_1 and H_4, the system 100 requires the suction temperature and the condenser exit temperature.
The above unknown parameters namely the suction temperature and the condenser exit temperature are further estimated using equation (3). Using equation (3), the following expressions are obtained:
H_1=(?(H?_4 K+H_2))/((1+K)) (4)
H_4=((H_1 (1+K)-H_2))/((K)) (5)
It may be noted that,
T_suction=T_suction^sat+SH, where SH is degree of superheat (6)
T_cond=T_dicharge^sat-SC, where SC is degree of sub-cooling (7)
where T_suction is Suction Temperature (K), T_suction^sat is Saturation temperature at Suction Pressure (K), T_cond is condenser Exit Temperature (K), and T_dicharge^sat is Saturation temperature at Discharge Pressure (K).
In an embodiment of the present disclosure, at step 206, the one or more hardware processors, generate one or more prior distributions for degree of superheat and degree of sub-cooling of the VCRS (see FIGS. 4A-4B). In an embodiment of the present disclosure, the degree of superheat and the degree sub-cooling of the VCRS are pre-defined and obtained using at least one of a domain knowledge and one or more operation policies. Below are illustrative example of expressions that are used for generation of the prior distributions of superheat and sub-cooling:
SH=N(µ_SH,s_SH) (8)
SC=N(µ_SC,s_SC) (9)
where µ_SH is mean of the superheat Distribution, s_SH is Standard Deviation of the superheat distribution, µ_SC is mean of the sub-cooling Distribution, and s_SC is Standard Deviation of the sub-cooling distribution.
From the above equations, given the degree of superheat and the degree of sub-cooling respectively, the suction temperature and condenser exit temperature are computed. In other words, in an embodiment of the present disclosure, at step 208, the one or more hardware processors 104 compute a second enthalpy (H_1) and a third enthalpy (H_4) from the generated one or more prior distributions, the first enthalpy and the one or more saturation temperatures. In an embodiment of the present disclosure, at step 210, the one or more hardware processors 104 iteratively compute, using an Expectation Maximization (EM) technique, one or more posterior probability distributions based the generated one or more prior distributions, the second enthalpy (H_1) and a third enthalpy (H_4) (see FIGS. 4A-4B). In an embodiment of the present disclosure, the step of iteratively computing one or more posterior probability distributions comprises minimizing KL Divergence between the generated one or more prior distributions and the one or more posterior probability distributions. In another embodiment of the present disclosure, the step of iteratively computing, using the Expectation Maximization (EM) technique, one or more posterior probability distributions comprises performing a fixed point computation on a KL divergence error to obtain the one or more posterior probability distributions of the degree of superheat and degree of sub-cooling of the VCRS. FIG. 4A depicts a graphical representation of one or more prior distributions and one or more posterior probability distributions pertaining to degree of superheat and degree of sub-cooling according to an example embodiment of the present disclosure. In the present disclosure, FIG. 4A, with reference to FIGS. 1 through FIG. 3B, illustrates a graphical representing depicting the one or more prior distributions and the one or more posterior probability distributions when value of K is 3.2 for a first iteration according to an example embodiment of the present disclosure. FIG. 4B, with reference to FIGS. 1 through FIG. 4A, illustrates a graphical representing depicting the one or more prior distributions and the one or more posterior probability distributions after KL convergence that is indicative of a value of the COP that jointly minimizes the KL divergence error between the one or more prior distributions and the one or more posterior probability distributions according to an example embodiment of the present disclosure. In an embodiment, the convergence is identified when a difference between a current iteration and a previous iteration of the KL divergence error reaches a pre-defined threshold. In an embodiment of the present disclosure, the number of iterations may be between 20 and 30. As per the experimental results conducted or performed by the embodiments of the present disclosure, the difference between the current and previous iteration's KL Divergence is 0.00134. In the further iteration the error was observed as 0.00108 and it yet further iteration the error was observed to be converging to converging to 0.00099, wherein the pre-defined threshold of convergence was set as 0.001. The value 0.00099 was compared to the pre-defined threshold of convergence (0.001), wherein in this case the convergence value 0.00099 is less than or equal to the pre-defined threshold of convergence (0.001). FIG. 4C, with reference to FIGS. 1 through 4B, illustrates a graphical representation of a difference between a current iteration and a previous iteration of the KL divergence error reaching a pre-defined threshold according to an example embodiment of the present disclosure. As depicted in FIG. 4C, along the x- axis is the iteration number, and along the Y axis, is plotted the difference between KL divergence error of current Iteration and the KL divergence error of previous iteration which is a convergence error. The process gets terminated when the convergence error is less than or equal to 0.0001.
In an embodiment of the present disclosure, the system 100 identifies a value at the convergence as a value of the COP that jointly minimizes the KL divergence error between the one or more prior distributions and the one or more posterior probability distributions. In an embodiment, the expression “jointly minimizes” refers to considering a first error and a second error wherein both the first and second error are computed to determine the KL divergence error for estimating the COP of the VCRS. In an embodiment of the present disclosure, the first error is referred as a sub-cooling error (or error pertaining to degree of sub-cooling) between the prior distributions and the posterior probability distributions and the second error is referred as superheat error (or error pertaining to degree of superheat) between the prior distributions and the posterior probability distributions. In an embodiment, the KL divergence error is based on the first error and the second error. In an example embodiment of the present disclosure, the KL divergence error is a summation of the first error (or error pertaining to degree of sub-cooling) and the second error (error pertaining to degree of superheat).
In an embodiment of the present disclosure, at step 212, the one or more hardware processors 104 compute a Maximum Likelihood Estimate (MLE) of the degree of superheat and degree of sub-cooling based the one or more posterior probability distributions. In an embodiment of the present disclosure, the MLE may be defined as a method of estimating parameters of a statistical model given observations, by finding the parameter values that maximize the likelihood of making the observations given the parameters. Hence, in the present disclosure, “Expectation” of the Posterior Probability Distributions are computed. Typically in refrigeration systems, the degree of superheat is a controlled variable, which means it has a set point and a dead band around it. In an embodiment of the present disclosure, the degree of superheat and the degree sub-cooling of the VCRS are pre-defined and obtained using at least one of a domain knowledge and one or more operation policies. In other words, from Manufacturer's specification, the acceptable values of sub-cooling and superheat are obtained, in one example embodiment. In an embodiment of the present disclosure, at step 214, the one or more hardware processors 104 estimate a Coefficient of Performance (COP) of the VCRS based on the computed MLE.
Below is an example experimental data conducted for a VCRS (e.g., Refrigerant Type R134A). From the P-H diagram of FIG. 3A, the Suction Pressure is 197197.0 (the line joining points 7 and 1) and Discharge Pressure: 1362452.0 (the line joining points 3 and 6), and Discharge Temperature 334.85 (temperature at point 3). The system 100 is configured by the instructions to calculate saturation temperature at suction pressure which is 262.7, and saturation temperature at discharge pressure which us 324.4 respectively. From the posterior probability distribution, MLE of the two unknown parameters are obtained as follows: (i) the degree of Superheat = 2.10 and (ii) the degree of sub-cooling = 6.15. The system 100 further computes suction temperature and condenser temperature by way of following example expression below:
Suction temperature = saturation temperature at suction pressure (262.7) + degree of Superheat (2.10) = 264.80 approximately and
Condenser temperature = saturation temperature at discharge pressure (324) - degree of sub-cooling (6.15) = 318 approximately.
The second enthalpy (H_1) and the third enthalpy (H_4) are further computed and obtained as 394199.8 (H_1) and 264179.4 (H_4) respectively.
Further, the system 100 computes the Coefficient of Performance (COP) of the VCRS based on the computed MLE. In the present disclosure, the value of COP is 3.1 which gave the lowest KL distance between the prior and posterior distributions.
FIG. 5, with reference to FIGS. 1 through 4C, depicts Coefficient of Performance (COP) of various VCRS according to an example embodiment of the present disclosure. More particularly, FIG. 5 depicts experimental data comprising COP cycle results conducted for 24 Chiller units according to an example embodiment of the present disclosure.
Below is an exemplary illustrative algorithm implemented by the embodiments of the present disclosure and the system 100:
Estimate_K(SuctionPressure, DischargePressure, DischargeTemperature):
saturation_temperature_suction <- PropsSI(SuctionPressure, Refrigerant)
saturation_temperature_discharge <- PropsSI(DischargePressure, Refrigerant)
H2 <- PropsSI(DischargePressure, DischargeTemperature, Refrigerant)
prior_sub-cooling <- Gaussian(sub-cooling_min, sub-cooling_max, std_deviations = 3)
prior_superheat <- Gaussian(superheating_min, superheating_max, std_deviations = 3)
posterior_sub-cooling_initialize <- initalize each sub-cooling_prob_val to 0
posterior_superheat_initialize <- initalize each superheat_prob_val to 0
Till Convergence:
posterior_sub-cooling_k <- {}
posterior_superheat_k <- {}
KL_error_k <- {}
KL_Distance_sub-cooling <- []
KL_Distance_superheat <- []
for eack k in K(K_min, K_max, steps_K):
posterior_sub-cooling <- posterior_sub-cooling_initialize
for each sh in superheat(superheat_min, superheat_max, steps_superheat):
suction_temperature <- saturation_temperature_suction + sh
H1 <- PropsSI(SuctionPressure, suction_temperature, Refrigerant)
H4 <- H1*(1+k)-H2*k
condensor_temperature <- PropsSI(H2, DischargePressure, Refrigerant)
sub-cooling <- saturation_temperature_discharge - condensor_temperature
if sub-cooling in (sub-cooling_min,sub-cooling_max):
posterior_probability_subcooling[subcooling] += prior_superheat[sh]
posterior_subcooling <- normalize(posterior_subcooling)
KL_temp_subcooling <- KL(posterior_subcooling, prior_subcooling)
append(KL_Distance_subcooling, KL_temp_subcooling)
for eack k in K(K_min, K_max, steps_K):
posterior_superheat <- posterior_superheat_initialize
for each sc in subcooling(subcooling_min, subcooling_max, steps_subcooling):
condensor_temperature <- saturation_temperature_discharge – sc
H0 <- PropsSI(DischargePressure, condensor_temperature, Refrigerant)
H1 <- (H4*k + H2)/(1+k)
suction_temperature <- PropsSI(H1, SuctionPressure, Refrigerant)
superheat <- suction_temperature - saturation_temperature_suction
if superheat in (superheat_min,superheat_max):
posterior_superheat[superheat] += prior_superheat[sc]
posterior_superheat <- normalize(posterior_superheat)
KL_temp_superheat <- KL(posterior_superheat, prior_superheat)
append(KL_Distance_superheat, KL_temp_superheat)
error_total <- KL_Distance_superheat + KL_Distance_subcooling
k* <- argmin(error_total)*steps_K + K_min
MAP_superheat <- posterior_superheat_k[k*]
MAP_subcooling <- posterior_subcooling_k[k*]
####for the next iteration####
prior_superheat, prior_subcooling <- MAP_superheat, MAP_subcooling
Return K, MAP_superheat, MAP_subcooling
Below is an illustrative methodology for computing second enthalpy H_1 by way of following example:
Suction Pressure = 197197.0 Pa
Discharge Pressure = 1362452.0 Pa
Refrigerant Type = R134A
Saturation Suction Temperature = 262.716 K
Saturation Discharge Temperature = 324.478 K
Discharge Temperature = 334.85 K
Following are to be noted:
The saturation temperature for any pressure given the refrigerant type can be calculated by looking up the refrigerant properties table. In an embodiment of the present disclosure, that is how ‘Saturation Suction Temperature’ and ‘Saturation Discharge Temperature’ are calculated.
To calculate the Enthalpy H_1, pressure and temperature are required. Defining the following parameters:
Suction Temperature = Saturation Suction Temperature + Degree of Superheat
Condenser Outlet Temperature = Saturation Discharge Temperature – Degree of Subcooling
Hence H_1 is calculated given the ‘Suction Temperature’ and 'Suction Pressure'. To calculate the ‘Suction Temperature’, ‘Degree of Superheat’ is used from the Prior Distribution of Superheat and similarly H_4, given the ‘Condenser Outlet Temperature’. To calculate the ‘Condenser Outlet Temperature’, the ‘Degree of Sub-cooling’ is utilized from the Prior Distribution of sub-cooling.
Now, consider the following tables, that demonstrate the calculation of H_1 and H_4 given the values of degree of superheat and degree of sub-cooling:
Subcooling Condenser Temperature H_4
4
4.5
5
5.5
6
6.5
7
7.5
8 320.478047
319.978047
319.478047
318.978047
318.478047
317.978047
317.478047
316.978047
316.478047 267453.77018
266683.59715
265915.36752
265149.04411
264384.59106
263621.97369
262861.1585
262102.11308
261344.80607

The above table has the H_4 value given the ‘Degree of Subcooling (SC)’ and the ‘Discharge Pressure’, which is the same for all the ‘SC’ values. Similarly H_1 is calculated which is demonstrated in the following table:
Superheat Suction Temperature H_1
1
1.5
2
2.5
3
3.5
4 325.478047
325.978047
326.478047
326.978047
327.478047
327.978047
328.478047 446972.73943
447425.69724
447879.00292
448332.65701
448786.66007
449241.01262
449695.7152

It is to be understood by a person having ordinary skill in the art or a person skilled in the art that the enthalpy H_1 may be first calculated and followed by H_4 or the enthalpy H_4 may be first calculated and followed by H_1. The calculation of H_1and H_4 may depend upon expressions (1), (2), (3), (4), (5), rearrangement thereof as depicted in expressions (4), and (5). In an embodiment of the present disclosure, all the values are calculated by looking up the Standard Refrigerant Property chart which has been encoded/ fed into the system 100 (e.g., a computing system) and accessed programmatically. It is to be understood by a person having ordinary skill in the art or a person skilled in the art that only few iterations as mentioned above are performed to provide details of computation of enthalpies H_1 and H_4 for estimation of COP of the VCRS, and there could be as many as iterations until the KL divergence reaches the pre-defined threshold. Such computation or calculation methodology/iteration(s) may vary as per the VCRS specification, and configuration set up thereof.
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.