Performance prediction method and system for two-stage compression refrigeration cycle system

Abstract

The invention provides a performance prediction method and system for a two-stage compression refrigeration system, and relates to the technical field of refrigeration system performance prediction. Constructing a multi-physical field coupling simulation model of the two-stage compression refrigeration cycle; obtaining a sample set of input parameters through Latin hypercube sampling; a sample set is input into the multi-physics field coupling simulation model, and the refrigeration power and the performance coefficient of the corresponding sample set in the stable refrigeration process are obtained; combining the refrigeration power and the performance coefficient with the sample set to construct a prediction data set; training by using the prediction data set and a neural network to construct a prediction model; optimizing the prediction model by using a particle swarm optimization algorithm; and inputting real-time input parameters into the optimized prediction model, and predicting the refrigeration power and the performance coefficient of the two-stage compression refrigeration cycle system. According to the method, the accuracy of prediction of the refrigeration power and the performance coefficient is improved, and the performance of the two-stage compression refrigeration cycle in a wide working condition range is accurately predicted and evaluated.

Description

Technical Field

[0001] This application relates to the field of refrigeration system performance prediction technology, and in particular to a performance prediction method for a two-stage compression refrigeration system and the two-stage compression refrigeration system itself. Background Technology

[0002] Refrigeration system design typically relies on single-point design based on rated operating conditions, achieving relatively good performance at the design point. However, during off-rated operation, due to the system's multi-loop, nonlinear, and strongly coupled characteristics, precise matching between components is difficult to achieve, impacting the efficient operation of the chiller unit. Currently, refrigeration systems consume a lot of energy and have insufficient control precision, indicating significant energy-saving potential. To achieve timely and effective optimization and adjustment of refrigeration system operation control, accurate prediction of refrigeration system performance is essential.

[0003] For achieving accurate prediction of refrigeration system performance, commonly used prediction methods include physical modeling and data-driven methods. Physical modeling methods rely on thermodynamic principles for energy consumption modeling and analysis. However, for more complex systems such as two-stage compression refrigeration, it is difficult to find the prediction logic, making its application challenging. Data-driven methods, on the other hand, do not depend on the internal structure and mechanism of the system and make predictions based on historical data, making them suitable for more complex refrigeration systems.

[0004] However, existing data-driven methods mostly rely on real-time monitoring data of the refrigeration system, which has a long sampling period and a narrow monitoring range, making it difficult to make accurate predictions for the entire range of refrigeration system operating conditions. Summary of the Invention

[0005] In view of the above problems, this application proposes a performance prediction method for a two-stage compression refrigeration system and a two-stage compression refrigeration system to solve the technical problem that existing methods lack the ability to make rapid predictions and accurate predictions across a wide range of operating conditions for refrigeration systems.

[0006] In a first aspect, embodiments of this application provide a performance prediction method for a two-stage compression refrigeration cycle system, including: Based on the structure and energy transfer process of the two-stage compression refrigeration cycle system, a multi-physics field coupled simulation model of the two-stage compression refrigeration cycle is constructed. Latin hypercube sampling is used to uniformly sample from the numerical range of the overall input parameters to obtain a sample set of input parameters; The sample set is input into the multiphysics coupling simulation model to obtain the refrigeration power and coefficient of performance of the two-stage compression refrigeration cycle system corresponding to the sample set during the stable refrigeration process. The cooling power and coefficient of performance are combined with the sample set to construct a prediction dataset; The prediction model is constructed by training the prediction dataset and neural network. The prediction model is used to predict the refrigeration power and coefficient of performance of the two-stage compression refrigeration cycle system under real-time input parameters. Based on the predicted dataset, the prediction model is optimized using the particle swarm optimization algorithm; The real-time input parameters are input into the optimized prediction model to predict the refrigeration power and coefficient of performance of the two-stage compression refrigeration cycle system.

[0007] Optionally, based on the structure and energy transfer process of the two-stage compression refrigeration cycle system, a multiphysics coupled simulation model of the two-stage compression refrigeration cycle is constructed, including: The components required in the two-stage compression refrigeration cycle system are determined, including: evaporator, low-pressure compressor, high-pressure compressor, condenser, subcooler, and expansion valve; Based on the design of the energy transmission process of each component, the connection relationship of each component is determined, and the structure of the two-stage compression refrigeration cycle system is obtained. Establish mathematical models for each of the aforementioned components; Based on the structure of the two-stage compression refrigeration cycle system and the energy transfer process, the multiphysics coupling simulation model is constructed using simulation technology.

[0008] Optionally, in the process of constructing the multiphysics coupled simulation model, each component in the two-stage compression refrigeration cycle system is regarded as an independent control body. The energy transfer process is simulated between the independent control bodies through parameter transfer to achieve coupled simulation, and the refrigerant physical property parameters are obtained in real time through the REFPROP software interface.

[0009] Optionally, a sample set of input parameters is obtained by uniformly sampling from the numerical input range of the overall input parameters using Latin hypercube sampling, including: Based on the requirements of the preset standard for the maximum load condition and low temperature condition of the vapor compression cycle, the numerical input range of the overall input parameters is determined; Based on the numerical input range of the overall input parameters, Latin hypercube sampling is used to uniformly sample the numerical input range of the overall input parameters to obtain a sample set of the input parameters. The overall input parameters include: chilled water mass flow rate, chilled water temperature, low-pressure compressor speed, low-pressure compressor guide vane opening, cooling water mass flow rate, and cooling water temperature.

[0010] Optionally, the sample set is input into the multiphysics coupled simulation model to obtain the cooling power and coefficient of performance of the two-stage compression refrigeration cycle system corresponding to the sample set during the steady-state cooling process, including: The sample set is input into the multiphysics coupling simulation model, and the multiphysics coupling simulation model outputs the current refrigeration power and coefficient of performance of the two-stage compression refrigeration cycle system. The multiphysics coupling simulation model is continuously run, and the output results when the multiphysics coupling simulation model is running stably are determined as the cooling power and performance coefficient of the two-stage compression refrigeration cycle system corresponding to the sample set during the stable refrigeration process.

[0011] Optionally, the cooling power and coefficient of performance are combined with the sample set to construct a prediction dataset, including: The cooling power and performance coefficient are combined with a sample set of input parameters, wherein the sample set includes six inputs: chilled water mass flow rate, chilled water temperature, low-pressure compressor speed, low-pressure compressor guide vane opening, cooling water mass flow rate, and cooling water temperature, and the cooling power and performance coefficient include the cooling power and performance coefficient corresponding to the six inputs; Based on the combination, the six inputs and the corresponding cooling power and coefficient of performance are saved as an Excel file, where column A is the number of the prediction dataset, columns B and G are the inputs, and columns H and I are the outputs, forming an eight-dimensional prediction dataset.

[0012] Optionally, the prediction model is constructed by training the prediction dataset and the neural network, including: Based on the prediction dataset, a prediction model is constructed using a backpropagation (BP) neural network. The BP neural network includes an input layer, a hidden layer, and an output layer. The specific steps involved in constructing the prediction model are as follows: The prediction dataset is shuffled and divided into training and testing sets according to a set ratio. The inputs are the six inputs, and the outputs are the cooling power and performance coefficients corresponding to the six inputs. The training dataset and the test dataset are normalized. Weighting coefficients are set for cooling power and coefficient of performance. By traversing the empirical range of hidden layer nodes and combining the weighting coefficients, the number of nodes with the smallest mean square error of the training set is selected as the optimal value for hidden layer node optimization. The BP neural network is trained based on the input layer after normalization and the hidden layer after optimization of hidden layer nodes. The trained BP neural network is used to predict and inversely normalize the test set to obtain the prediction model; The expression for selecting the number of nodes with the minimum mean square error of the training set as the optimal value based on the weight coefficients is as follows:

[0013] In the above formula, These represent the weighting coefficients for cooling power and coefficient of performance, respectively. Represents the total number of samples. This represents the true values ​​corresponding to the cooling power and coefficient of performance in the training set. This represents the predicted values ​​for cooling power and coefficient of performance.

[0014] Optionally, the prediction model is optimized using a particle swarm optimization algorithm based on the prediction dataset, including: Each particle represents a set of weights and thresholds in a backpropagation neural network, and the motion of the particles is simulated for optimization. The PSO population size, iteration number, and weight coefficients are set. The initial positions of the particles are randomly initialized, and the fitness is calculated using a fitness function. The optimal position of the initial individual is its own position, and the fitness function is the mean square error between the predicted output and the true value. The calculated particle fitness is searched, and the index of the particle with the lowest fitness is set as the global optimal position. By iterating through each particle, the velocity and position of the particles are updated using inertia, individual cognition, and social cognition. The initial individual optimal position and the global optimal position are updated by calculating the fitness of the current position and comparing it with the historical records; When the accuracy requirement is met or the maximum number of iterations is reached, the iteration ends, and the obtained optimal weights and optimal thresholds are substituted into the BP neural network for training.

[0015] Optionally, the PSO population size is 10; The number of iterations is 50; The weighting coefficient is: ; Both individual cognition and social cognition are set to 2; The inertia is set to 0.9.

[0016] In a second aspect, this application provides a two-stage compression refrigeration cycle system, wherein the two-stage compression refrigeration cycle system is used to predict the performance of the two-stage compression refrigeration cycle system as described in any of the first aspects, wherein the two-stage compression refrigeration cycle system is a two-stage compression refrigeration cycle system with incomplete cooling in the middle of a single throttling process, and includes: an evaporator, a low-pressure compressor, a high-pressure compressor, a condenser, a subcooler, and an expansion valve. The evaporator is connected to the low-pressure compressor, the expansion valve, and the subcooler respectively; the low-pressure compressor is also connected to the subcooler. The high-pressure compressor is connected to the subcooler and the condenser respectively; the condenser is also connected to the subcooler; the subcooler is also connected to the expansion valve. The low-pressure vapor from the evaporator first enters the low-pressure compressor, is compressed to an intermediate pressure pm, and then mixes with the saturated vapor from the subcooler in the pipeline. The mixture then enters the high-pressure compressor, where it is further compressed to a condensing pressure pk and then enters the condenser to condense into a liquid. The liquid flowing out of the condenser is divided into two paths: one path flows through the coil inside the subcooler, is subcooled by the refrigerant liquid outside the coil, and then flows to the expansion valve. The expansion valve throttles the liquid to the evaporation pressure p0 before it enters the evaporator, where it evaporates to produce a cooling effect; the other path flows through the gas injection valve, is throttled to the intermediate pressure pm, enters the subcooler, and evaporates to produce saturated vapor, which also subcools the high-pressure liquid inside the coil. The saturated vapor then mixes with the low-pressure vapor from the low-pressure compressor before entering the second stage.

[0017] Thirdly, this application provides an electronic device, including: a processor and a memory, wherein the memory stores computer-readable instructions, which, when loaded and executed by the processor, implement the two-stage compression refrigeration cycle system performance prediction method as described in the first aspect.

[0018] Fourthly, this application provides a computer-readable storage medium storing computer-readable instructions that are loaded and executed by a processor to implement the two-stage compression refrigeration cycle system performance prediction method as described in the first aspect.

[0019] This application achieves rapid simulation of a two-stage compression refrigeration cycle system across a wide operating range by constructing a multiphysics coupled simulation model. Based on the traditional structure and energy transfer process of a two-stage compression refrigeration cycle system, optimizations were made, and a novel approach was proposed to use simulation technology to construct the multiphysics coupled simulation model.

[0020] By determining the range of input parameter values ​​through parameter quantification analysis, and uniformly sampling within the range of input parameter values ​​using Latin hypercube sampling, the refrigeration power and coefficient of performance (COP) under different input parameters in a stable refrigeration process were obtained, effectively improving the accuracy of the performance prediction model for the two-stage compression refrigeration cycle system. A prediction model for refrigeration power and COP was constructed by training a BP neural network with a prediction dataset. The performance prediction model was then optimized using a particle swarm optimization algorithm, further improving the accuracy of refrigeration power and COP prediction. This enabled accurate prediction and evaluation of the performance of the two-stage compression refrigeration cycle over a wide operating range. Attached Figure Description

[0021] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which: Figure 1 This is a flowchart of a performance prediction method for a two-stage compression refrigeration cycle system, as exemplified in this application. Figure 2 This is a schematic diagram of the two-stage compression refrigeration cycle system as exemplified in this application. Figure 3 This is a flow chart of the energy transfer process of a two-stage compression refrigeration cycle system as described in this application. Figure 4 A schematic diagram of the BP neural network process optimized for the particle swarm optimization algorithm provided in this application example; Figures 5(a), 5(b), and 5(c) are comparison charts of the actual cooling power and the predicted cooling power of the refrigeration system in the example of this application. Figure 6 The image shows a comparison of the cooling power prediction error of the BP neural network without particle swarm optimization and the cooling power prediction error of the BP neural network with particle swarm optimization in this application example. Figures 7(a), 7(b), and 7(c) are comparison charts of the actual performance coefficients and model predicted performance coefficients of the refrigeration system in the example of this application; Figure 8 This is a comparison chart showing the performance coefficient prediction errors of a BP network without particle swarm optimization and the performance coefficient prediction errors of a BP neural network optimized with particle swarm optimization in this application example. In the diagram, 1-evaporator, 2-low-pressure compressor, 3-high-pressure compressor, 4-condenser, 5-subcooler, 6-expansion valve. Detailed Implementation

[0022] The embodiments of this application will now be described in detail. Examples of these embodiments are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0023] This application provides a performance prediction method for a two-stage compression refrigeration cycle system. This method can predict the refrigeration power and coefficient of performance (COP) of the two-stage compression refrigeration cycle system based on actual input parameters. This performance prediction method can be implemented using a performance prediction device for the two-stage compression refrigeration cycle system. This device can be any device with computing and data processing capabilities, such as a terminal or server. A flowchart of the proposed performance prediction method for the two-stage compression refrigeration cycle system is provided below. Figure 1 As shown, it includes: Step 101: Based on the structure and energy transfer process of the two-stage compression refrigeration cycle system, construct a multi-physics coupling simulation model of the two-stage compression refrigeration cycle.

[0024] The performance prediction method proposed in this application first requires constructing a multiphysics coupled simulation model of the two-stage compression refrigeration cycle based on its structure and energy transfer process. The prediction method is based on the two-stage compression refrigeration cycle system. This application proposes an optimized two-stage compression refrigeration cycle system, building upon the traditional two-stage compression refrigeration cycle system, which utilizes… Figure 1 The performance prediction method for the two-stage compression refrigeration cycle system shown is applied. This two-stage compression refrigeration cycle is a single-stage throttling cycle with incomplete intermediate cooling. See also... Figure 2 As shown, the two-stage compression refrigeration cycle system includes: evaporator 1, low-pressure compressor 2, high-pressure compressor 3, condenser 4, subcooler 5, and expansion valve 6. Evaporator 1 is connected to low-pressure compressor 2, expansion valve 6, and subcooler 5 respectively; low-pressure compressor 2 is also connected to subcooler 5; high-pressure compressor 3 is connected to subcooler 5 and condenser 4 respectively; condenser 4 is also connected to subcooler 5; subcooler 5 is also connected to expansion valve 6.

[0025] The working process of a two-stage compression refrigeration cycle system combined Figure 3 The energy transfer flow diagram shown can be better understood. During the cycle operation of the entire system, the low-pressure vapor from evaporator 1 first enters the low-pressure compressor 2. After being compressed to the intermediate pressure pm, the low-pressure vapor mixes with the saturated vapor from subcooler 5 in the pipeline, and then enters the high-pressure compressor 3, where it is further compressed to the condensing pressure pk, and then enters the condenser 4 to condense into liquid. The liquid coming out of the condenser 4 is divided into two paths: one path flows through the coil inside the subcooler 5, is subcooled by the refrigerant liquid outside the coil, and then is throttled to the evaporating pressure p0 by the expansion valve 6, where it evaporates in the evaporator to produce a cooling effect; the other path is throttled to the intermediate pressure pm by the gas injection valve, enters the subcooler 5 and evaporates in the subcooler, which subcools the high-pressure liquid in the coil. The throttled saturated vapor then mixes with the exhaust gas from the low-pressure compressor 1 and enters the second stage. Figure 2The diagram also schematically shows controller 7, which is used to receive various data and send corresponding control commands to various components.

[0026] Based on the structure and energy transfer process of the aforementioned two-stage compression refrigeration cycle system, a corresponding multiphysics coupling simulation model is constructed. In one embodiment of this application, a preferred method for constructing a multiphysics coupling simulation model of a two-stage compression refrigeration cycle includes: First, the necessary components for a two-stage compression refrigeration cycle system are identified, including: evaporator, low-pressure compressor, high-pressure compressor, condenser, subcooler, and expansion valve. Based on these components, the energy transfer process is designed, and the connection relationships between them are determined, resulting in the structure of the two-stage compression refrigeration cycle system. This part can be combined with... Figure 2 , Figure 3 To gain an intuitive understanding.

[0027] Based on the structure and energy transfer process, mathematical models of each component are established. Finally, based on the structure and energy transfer process of the two-stage compression refrigeration cycle system, a multi-physics coupling simulation model of the two-stage compression refrigeration cycle system can be constructed using simulation technology.

[0028] In this process, the establishment of mathematical models for each component can be accomplished using existing technologies. The embodiments in this application only exemplify the following methods and do not imply that only these exemplified methods can be used to establish mathematical models.

[0029] The mathematical model of evaporator 1, based on the refrigerant and chilled water sides, is as follows: The refrigerant in the evaporator tubes follows the law of conservation of energy, and its energy equation is expressed as follows:

[0030] In the above formula, M er This indicates the total mass of refrigerant in the evaporator. h er The average specific enthalpy of the refrigerant in the evaporator. t Indicates time, Q e This indicates the heat exchange capacity of the evaporator. m er This indicates the refrigerant mass flow rate in the evaporator. h er,o This indicates the refrigerant outlet ratio in the evaporator. h er,i This indicates the specific enthalpy of the refrigerant at the evaporator inlet. The heat exchange capacity of the evaporator... Q e The calculation formula is as follows:

[0031] In the above formula, K e This represents the average heat transfer coefficient of the evaporator. A e Δ represents the heat exchange area of ​​the evaporator. T e This represents the logarithmic mean heat transfer temperature difference of the evaporator. Wherein, the logarithmic mean heat transfer temperature difference Δ... Te The calculation formula is as follows:

[0032] In the above formula, T ew,i This indicates the inlet temperature of the chilled water in the evaporator. T e Indicates the evaporation temperature. T ew,o This indicates the chilled water outlet temperature of the evaporator.

[0033] The refrigerant in the evaporator also follows the law of conservation of mass, and its mass conservation equation can be expressed as follows:

[0034] In the above formula, M e0 This indicates the total mass of refrigerant in the evaporator at the previous moment. m er,i This indicates the mass flow rate into the evaporator at that moment. m er,o This indicates the mass flow rate exiting the evaporator at that moment.

[0035] The chilled water outside the pipes also follows the law of conservation of energy in the evaporator, and its energy equation is expressed as follows:

[0036] In the above formula, C w Indicates the specific heat of water. M er This indicates the mass of chilled water in the evaporator. m ew This indicates the mass flow rate of chilled water in the evaporator.

[0037] In this application, the model of condenser 4 is similar to that of evaporator 1, and mathematical models can be established for the refrigerant side inside the condenser tubes and the cooling water side outside the tubes, respectively.

[0038] In this application, the low-pressure compressor 2 can establish a mass flow model based on the compressor speed and the inlet guide vane angle:

[0039] In the above formula, ωThis indicates the angular velocity of the compressor spindle. v 1 indicates the specific volume of the gaseous refrigerant at the impeller inlet. α 1 represents the absolute airflow angle at the impeller blade inlet. β 1 indicates the relative airflow angle at the impeller blade inlet. r 1 indicates the impeller blade inlet radius. A 1 represents the impeller inlet flow area. k B Represents the blocking coefficient; where, ω It is the angular velocity of the compressor spindle rotation and the motor operating frequency. f Proportional v 1. This is related to the state of the refrigerant at the compressor inlet. α 1. Depends on the opening angle of the compressor inlet guide vane valve; under design conditions, β 1 is generally equal to the impeller inlet blade installation angle. β 1A , β A value of 1 is optimally set to 32°. r 1 A 1 k B It is a constant related to the geometry of the compressor, and a better setting is 0.12996.

[0040] The refrigerant condition at the outlet of low-pressure compressor 2 can be calculated using an efficiency model:

[0041] In the above formula, h 2 indicates the compressor outlet enthalpy. h 1 indicates the compressor inlet enthalpy. h 2s This represents the compressor outlet enthalpy under the isentropic assumption. η is The isentropic efficiency of the compressor can be obtained from the performance curve of the centrifugal compressor.

[0042] In this application, the high-pressure compressor 3 does not have a guide vane valve, and its mass flow rate is the sum of the mass flow rate of the low-pressure compressor 2 and the intermediate gas supply.

[0043] In this application, the mathematical model of the subcooler 5 is established based on the mass and energy balance equations for the inflow and outflow as follows: The refrigerant in the subcooler tubes follows the law of conservation of mass, and its mass equation is expressed as follows:

[0044] In the above formula, The mass flow rate of high-pressure compressor 3. This refers to the mass flow rate of the low-pressure compressor 2.

[0045] The refrigerant in the subcooler tubes follows the law of conservation of energy, and its energy equation is expressed as follows:

[0046] In the above formula, The mass flow rate of high-pressure compressor 3. The mass flow rate of low-pressure compressor 2, The enthalpy of the refrigerant liquid flowing out of the condenser and into the make-up valve can be obtained from the condensing pressure pk and the subcooling degree, which is set to 4°C. The enthalpy of the refrigerant liquid after cooling in the subcooler. It is the enthalpy of the saturated vapor that has been throttled after evaporation in the subcooler.

[0047] In this application, the mathematical model of expansion valve 6 is established based on the mass and energy balance equations for inflow and outflow as follows: The mass flow rate of the expansion valve is affected by the thermodynamic state of the refrigerant at the valve inlet and outlet and the opening degree of the expansion valve. Its calculation formula can be expressed as:

[0048] In the above formula, m v This indicates the mass flow rate of the expansion valve. C d This represents the flow coefficient of the expansion valve. A v This indicates the flow area of ​​the expansion valve. ρ v,in Δ represents the refrigerant density at the expansion valve inlet. p v This represents the pressure difference between the inlet and outlet of the expansion valve; where the flow coefficient is... C d It is related to many factors and is generally obtained through actual measurement or by consulting a handbook, or it can be calculated using empirical formulas:

[0049] In the above formula, ρ v,out This indicates the refrigerant density at the expansion valve outlet; When expansion valve 6 is operating stably, its inlet and outlet enthalpies remain equal, therefore the equation can be obtained:

[0050] In the above formula, h v,in This indicates the enthalpy of the refrigerant at the expansion valve inlet. h v,out This indicates the enthalpy of the refrigerant at the expansion valve outlet.

[0051] In this application, refrigerant property calculations are performed using REFPROP. The REFPROP software can query and calculate the physical properties of refrigerants. When two independent thermodynamic state parameters of a refrigerant in a certain state are known, the REFPROP program can be called using C, Fortran, or M languages ​​to perform property calculations and obtain all other property parameters of the refrigerant in that state.

[0052] In this application, existing simulation techniques can be employed. For example, preferably, a multiphysics coupling simulation model of a two-stage compression refrigeration cycle can be constructed using MatlabSimulink simulation software. When establishing the multiphysics coupling simulation model using MatlabSimulink, the MatlabSimulink module library can be used for quick and convenient model building. Simulation modules can be edited and modified according to model requirements, and connections to other simulation programs or third-party software can be made via API interfaces. When performing dynamic system simulations, users can select fixed or variable time steps and continuous or discrete sampling methods according to simulation needs. During the construction of the multiphysics coupling simulation model, each component in the two-stage compression refrigeration cycle system is treated as an independent control body. The energy transfer process between these independent control bodies is simulated through parameter transfer, achieving coupled simulation. Furthermore, refrigerant property parameters can be obtained in real time through the REFPROP software interface, thus enabling the construction of the multiphysics coupling simulation model.

[0053] The process of constructing the multiphysics coupled simulation model of the two-stage compression refrigeration cycle system described above differs from traditional technologies, which have no precedent for using simulation technology to construct a two-stage compression refrigeration cycle system. This is an innovative approach proposed in this application. The structure and energy transfer flow of the proposed two-stage compression refrigeration cycle system are optimized based on traditional technologies. Although the specific components used—evaporator 1, low-pressure compressor 2, high-pressure compressor 3, condenser 4, subcooler 5, and expansion valve 6—may be existing, the structure and energy transfer flow of the two-stage compression refrigeration cycle system constructed based on these six components are not entirely the same as those of traditional technologies. Those skilled in the art, upon seeing this concept of structure and energy transfer flow and combining it with knowledge in the field, can derive other deformable structures or energy transfer flows that fall within the scope of protection of this application.

[0054] Crucially, in traditional technologies, the performance research and optimization of chiller units can be conducted through both experimental and simulation methods. Experimental research is the most direct way to improve chiller unit performance, as it can be used to study and optimize specific units based on historical operating data. However, due to the differences between chillers during actual operation, experimental research methods lack universality and suffer from problems such as being time-consuming, costly, and having difficulty accurately measuring many parameters. Therefore, with the continuous development of computer technology, chiller unit simulation research has been further developed.

[0055] Simulation of chiller units primarily employs a model-based approach. This involves constructing mathematical models of each system component and then using computer software to model and simulate the chiller system. However, because the dynamic model of a chiller unit includes a time term, it is difficult to accurately calculate the spatiotemporal distribution of parameters for each component. Furthermore, considering complex geometric boundaries during the dynamic model construction process reduces the model's practicality. Conversely, using a fully lumped parameter method results in a significant discrepancy between the model's dynamic response and reality. In addition, the types of refrigerants and refrigeration cycles used in different practical application scenarios vary, leading to differences in model construction methods and assumptions. Consequently, the resulting simulation models differ, resulting in varying levels of accuracy.

[0056] Due to the aforementioned technical difficulties, it is challenging to construct a multiphysics coupled simulation model of a two-stage compression refrigeration cycle system using simulation technology. This application, however, utilizes simulation technology to construct a multiphysics coupled simulation model of a two-stage compression refrigeration cycle system, employing a two-stage vapor compression refrigeration cycle and using R1234yf as the refrigerant. In the multiphysics coupled simulation model of the two-stage compression refrigeration cycle system constructed in this application, each component is treated as a different control body. All control bodies adhere to the laws of mass and energy conservation. The input parameters of the control body are transmitted from the previous component, and after simulation calculations by each component model, the resulting output parameters are transmitted to the next component, thus enabling the cyclic operation of the entire chiller system.

[0057] In this model, evaporator 1 and condenser 4 adopt a dynamic lumped parameter model, while the centrifugal compressor (i.e., low-pressure compressor 2 and high-pressure compressor 3), expansion valve 6, and subcooler 5 adopt a steady-state lumped parameter model. For evaporator 1 and condenser 4, the following assumptions are made: heat exchange between the evaporator / condenser and the external environment is ignored; only heat exchange between the refrigerant and chilled / cooling water is considered; it is assumed that the refrigerant and chilled / cooling water undergo one-dimensional flow heat transfer within the tubes of evaporator 1 and condenser 4, and that this flow is homogeneous and saturated; it is assumed that the refrigerant is a pure working fluid and incompressible, and that the refrigerant charge is almost constant; and it is assumed that the refrigerant friction loss and the heat capacity of the evaporator tube wall are ignored.

[0058] The centrifugal compressor uses speed and inlet guide vanes to regulate flow. High-pressure compressor 3 does not have a guide vane valve; its mass flow rate is the sum of the low-pressure stage flow rate and the intermediate injection gas flow rate. Expansion valve 6 is an electronic expansion valve with a flow coefficient C. d The parameters are obtained from empirical formulas. Subcooler 5 adopts the following approach: heat exchange between the subcooler and the external environment is ignored; only heat exchange between the refrigerants within the subcooler is considered; the cold-end heat exchange temperature difference of the subcooler is given. The settings of all the above parameters and conditions are creatively proposed by the inventors after extensive research. Through these assumptions, this application simplifies the complex geometric boundaries in the dynamic model of the refrigeration system and constructs a multiphysics coupled simulation model of a two-stage compression refrigeration cycle system, thus setting a precedent for using simulation technology to construct a multiphysics coupled simulation model of a two-stage compression refrigeration cycle system.

[0059] Step 102: Obtain the sample set of input parameters by uniformly sampling from the numerical input range of the overall input parameters through Latin hypercube sampling.

[0060] After constructing multiple physical field coupling simulation models, Latin hypercube sampling is then used to uniformly sample from the overall numerical input range of the input parameters, thereby obtaining a sample set of the input parameters.

[0061] In one embodiment of this application, a preferred method for obtaining a sample set of input parameters includes: First, based on the requirements of the preset standard for the maximum load condition and low temperature condition of the vapor compression cycle, the numerical input range of the overall input parameters is determined. This preset standard can be the requirements of the national standard for the maximum load condition and low temperature condition of the vapor compression cycle, etc. Based on this preset standard, the numerical input range of the input parameters is determined, which can enable the two-stage compression refrigeration cycle system to operate stably within a wide operating range.

[0062] Based on the numerical input range of the overall input parameters, Latin hypercube sampling is used to uniformly sample the numerical input range of the overall input parameters, resulting in a sample set of input parameters. This overall input parameter set includes: chilled water mass flow rate, chilled water temperature, low-pressure compressor speed, low-pressure compressor guide vane opening, cooling water mass flow rate, and cooling water temperature. In one embodiment of this application, the sample set of input parameters is obtained through Latin hypercube sampling. Of course, other methods can also be used to obtain the sample set of input parameters; Latin hypercube sampling is simply a preferred method. Latin hypercube sampling (LHS) is a Monte Carlo sampling technique based on the idea of ​​"hierarchical randomness," which can achieve uniform coverage of samples in high-dimensional space, with efficiency far exceeding that of simple random sampling. Latin hypercube sampling can comprehensively cover and extract input parameters, avoiding waste of computational resources.

[0063] Step 103: Input the sample set into the multiphysics coupling simulation model to obtain the cooling power and coefficient of performance of the corresponding sample set in the two-stage compression refrigeration cycle system during the steady cooling process.

[0064] After obtaining the input sample set, the sample set is then input into the multiphysics coupling simulation model to obtain the cooling power and coefficient of performance of the corresponding sample set in the two-stage compression refrigeration cycle system during the stable cooling process.

[0065] In one embodiment of this application, the numerical range of the input parameters obtained in step 102 is used to input the sample set of input parameters (chilled water mass flow rate, chilled water temperature, low-pressure compressor speed, low-pressure compressor guide vane opening, cooling water mass flow rate, and cooling water temperature) into the aforementioned constructed multiphysics coupling simulation model of the two-stage compression refrigeration cycle. The multiphysics coupling simulation model can provide the current refrigeration power and performance coefficient of the system. The multiphysics coupling simulation model is continuously run, and the output result when the multiphysics coupling simulation model of the two-stage compression refrigeration cycle is stable is the refrigeration power and performance coefficient of the corresponding sample set of the two-stage compression refrigeration cycle system during the stable refrigeration process.

[0066] Step 104: Combine the cooling power and coefficient of performance with the sample set to construct the prediction dataset.

[0067] After the aforementioned three steps are completed, the cooling power and coefficient of performance are combined with the sample set to construct a prediction dataset. In one embodiment of this application, a preferred method for constructing the prediction dataset includes: The cooling power and coefficient of performance (COP) are combined with a sample set of input parameters. The sample set includes six inputs: chilled water mass flow rate, chilled water temperature, low-pressure compressor speed, low-pressure compressor guide vane opening, cooling water mass flow rate, and cooling water temperature. The cooling power and COP include the corresponding cooling power and COP for each of the six inputs. Based on the combination, the six inputs and their corresponding cooling power and COP are saved as an Excel file. Column A represents the prediction dataset number, columns B and G represent the inputs, and columns H and I represent the outputs. The resulting prediction dataset has an eight-dimensional shape.

[0068] Step 105: Use the prediction dataset and neural network to train and build a prediction model. The prediction model is used to predict the refrigeration power and coefficient of performance of the two-stage compression refrigeration cycle system under real-time input parameters.

[0069] Once the prediction dataset is obtained, it can be used to train a neural network to build a prediction model. The prediction model is used to predict the refrigeration power and coefficient of performance of a two-stage compression refrigeration cycle system under real-time input parameters.

[0070] In one embodiment of this application, a preferred method for constructing a prediction model includes: Based on the prediction dataset, a prediction model is constructed using a backpropagation neural network (BP neural network). The BP neural network includes an input layer, hidden layers, and an output layer. Naturally, it is understood that other neural networks can also be used to construct prediction models; the BP neural network is simply a preferred implementation.

[0071] In the process of building the prediction model, the prediction dataset is first shuffled and divided into training set and test set according to a set ratio; the input is the six inputs mentioned above, and the output is the cooling power and performance coefficient corresponding to the six inputs.

[0072] Next, the training and test datasets are normalized using the following expression:

[0073] In the above formula, This represents the normalized data. Indicates the minimum and maximum values ​​of the target range. Represents the original data. This represents the minimum and maximum values ​​of the original data.

[0074] After normalization, the hidden layer nodes are optimized. By traversing the empirical range of hidden layer nodes, the number of nodes with the smallest mean squared error (MSE) of the training set is selected as the optimal value. This step, for hidden layer node optimization, differs from the traditional process of training a model using a backpropagation (BP) neural network; it involves two quantities. Since traditional BP neural networks are generally single-quantity, the improved expression for hidden layer optimization is as follows:

[0075] In the above formula, This represents the weighting coefficients corresponding to cooling power and coefficient of performance. Represents the total number of samples. This represents the actual values ​​corresponding to the cooling power and coefficient of performance in the training set. This represents the predicted values ​​of cooling power and coefficient of performance.

[0076] After optimizing the hidden layers, the BP neural network is trained, and its expression is as follows:

[0077] In the above formula, Indicates the hidden layer number 1 The input of each neuron, This represents the weights from the input layer to the hidden layer. Indicates input features, This represents the hidden layer threshold. This indicates the output of the hidden layer. This represents the activation function, which is the tansig function in this application. Indicates the output layer number The input of each neuron, This represents the weights from the hidden layer to the output layer. Indicates the output layer threshold. This represents the final predicted output. This represents the output layer activation function, which is the purelin function in this application. Represents the weights from the output layer to the hidden layer. Update Indicates the learning rate. This represents the error term in the output layer.

[0078] The error backpropagation method is as follows: the prediction error of the output layer is calculated using the MSE calculation method described above. The error is backpropagated from the output layer to the hidden layer, and the weights and thresholds of each layer are adjusted using the Levenberg-Marquardt algorithm.

[0079] Use a trained BP neural network to predict and inversely normalize the test set: The trained BP neural network is used to predict the test set, and the prediction results of the test set are converted into the actual output values ​​by the above normalization process.

[0080] Step 106: Optimize the prediction model using the particle swarm optimization algorithm based on the prediction dataset.

[0081] After training and obtaining the prediction dataset, the prediction model needs to be optimized using the particle swarm optimization algorithm based on the prediction dataset so that the prediction model can make more accurate predictions.

[0082] In one embodiment of this application, a preferred method for optimizing a prediction model using a particle swarm optimization algorithm is combined with... Figure 4 The schematic diagram shown illustrates the process of optimizing a BP neural network using the particle swarm optimization algorithm, which includes: Each particle represents a set of weights and thresholds in a backpropagation (BP) network, and the particle motion is simulated for optimization. The PSO population size and number of iterations are set, and the initial positions of the particles are randomly initialized. Fitness is calculated using a fitness function, where the initial optimal position of an individual is its own position, and the fitness function is the mean squared error between the predicted and actual outputs. Preferably, the PSO population size can be set to 10; the number of iterations to 50; and the weight coefficients can be set as follows: .

[0083] The calculated particle fitness is searched, and the index of the particle with the lowest fitness is set as the global optimum (gbest). Further, each particle is traversed, and its velocity and position are updated using inertia, individual cognition, and social cognition. For the best results, both individual cognition and social cognition are set to 2, and inertia is set to 0.9. The fitness of the current position is then calculated and compared with historical records to update both the individual optimum and the global optimum.

[0084] When the accuracy requirement is met or the maximum number of iterations is reached, the iteration ends, and the obtained optimal weights and optimal thresholds are substituted into the above BP neural network for training.

[0085] The particle swarm optimization algorithm optimizes the initial weights and thresholds of the backpropagation (BP) neural network, addressing the problem of BP neural networks easily getting trapped in local optima and improving prediction accuracy. Applying the particle swarm optimization algorithm to optimize the performance prediction model of the two-stage compression-refrigeration cycle system yields better prediction results, with a significant reduction in error on the test set compared to the BP neural network.

[0086] To verify the effectiveness of the above performance prediction method, refer to Figures 5(a), 5(b), and 5(c) for a comparison of the actual cooling power of the refrigeration system and the predicted cooling power of the prediction model; the horizontal axis represents the test sample number, and the vertical axis represents the cooling capacity index value. Figure 5(a) is the actual value curve, Figure 5(b) is the predicted value curve of the prediction model without particle swarm optimization, and Figure 5(c) is the predicted value curve of the prediction model after optimization by particle swarm optimization. It can be seen that the prediction value of the prediction model after optimization by particle swarm optimization is more accurate.

[0087] Reference Figure 6 The chart shows a comparison of the cooling power prediction error of a BP neural network without particle swarm optimization (PSO) and with PSO optimization. The curve with the line and inverted triangle represents the cooling power prediction error of the BP neural network without PSO optimization, while the curve with the line and dots represents the cooling power prediction error of the BP neural network with PSO optimization. This further confirms that the prediction value of the prediction model optimized by PSO is more accurate.

[0088] Refer to Figures 7(a), 7(b), and 7(c) for a comparison of the actual performance coefficients and the model-predicted performance coefficients of the refrigeration system; the horizontal axis represents the test sample number, and the vertical axis represents the performance coefficient index value. Figure 7(a) is the actual value curve, Figure 7(b) is the predicted value curve of the prediction model without particle swarm optimization, and Figure 7(c) is the predicted value curve of the prediction model after optimization with particle swarm optimization. It can be seen that the prediction value of the prediction model after optimization with particle swarm optimization is more accurate.

[0089] Reference Figure 8 The chart shows a comparison of the prediction errors of BP neural network performance coefficients without and after optimization by the particle swarm optimization algorithm. The curve with the line and inverted triangle represents the prediction error curve of the BP neural network performance coefficients without optimization by the particle swarm optimization algorithm, while the curve with the line and dots represents the prediction error curve of the BP neural network performance coefficients after optimization by the particle swarm optimization algorithm. This further confirms that the prediction values ​​of the prediction model optimized by the particle swarm optimization algorithm are more accurate.

[0090] Step 107: Input the real-time input parameters into the optimized prediction model to predict the refrigeration power and coefficient of performance of the two-stage compression refrigeration cycle system.

[0091] After optimizing the prediction model, it can be applied to a practical two-stage compression refrigeration cycle system. Real-time input parameters are input into the optimized prediction model to predict the refrigeration power and coefficient of performance of the two-stage compression refrigeration cycle system, thereby obtaining the refrigeration power and coefficient of performance corresponding to the current real-time input parameters and realizing the system-wide prediction of the two-stage compression refrigeration cycle system.

[0092] Based on the above-described performance prediction method for a two-stage compression refrigeration cycle system, this application provides an electronic device including at least one processor and a memory. The memory stores a computer program, which, when executed by the at least one processor, causes the device to implement the performance prediction method for the two-stage compression refrigeration cycle system as described in steps 101-104 above. This electronic device can be an industrial control computer, an edge computing gateway, or a cloud server.

[0093] Based on the above-described performance prediction method for a two-stage compression refrigeration cycle system, this application provides a computer-readable storage medium, such as a USB flash drive, portable hard drive, read-only memory, random access memory, magnetic disk, or optical disk. The storage medium stores a computer program, which, when executed by one or more processors, implements the performance prediction method for the two-stage compression refrigeration cycle system as described in steps 101-104 above.

[0094] In summary, this application achieves rapid simulation of a two-stage compression refrigeration cycle system across a wide operating range by constructing a multiphysics coupled simulation model. Based on the traditional structure and energy transfer process of a two-stage compression refrigeration cycle system, optimizations were made, and a novel approach was proposed to use simulation technology to construct the multiphysics coupled simulation model.

[0095] By determining the input parameter value range through parameter quantification analysis, and uniformly sampling within the input parameter value range using Latin hypercube sampling, the refrigeration power and coefficient of performance (COP) under different input parameters in a stable refrigeration process were obtained, effectively improving the accuracy of the performance prediction model for a two-stage compression refrigeration cycle system. A prediction model for refrigeration power and COP was constructed by training a BP neural network with a prediction dataset. The performance prediction model was then optimized using a particle swarm optimization algorithm, further improving the accuracy of refrigeration power and COP prediction. This allows for accurate prediction and evaluation of the performance of the two-stage compression refrigeration cycle over a wide operating range, demonstrating broad application prospects and high practicality.

[0096] Although preferred embodiments of the present application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the present application.

[0097] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0098] The embodiments of this application have been described above with reference to the accompanying drawings. However, this application is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of this application without departing from the spirit and scope of the claims. All of these forms are within the protection scope of this application.

Claims

1. A method for predicting the performance of a two-stage compression refrigeration cycle system, characterized in that, include: Based on the structure and energy transfer process of the two-stage compression refrigeration cycle system, a multi-physics field coupled simulation model of the two-stage compression refrigeration cycle is constructed. Latin hypercube sampling is used to uniformly sample from the numerical range of the overall input parameters to obtain a sample set of input parameters; The sample set is input into the multiphysics coupling simulation model to obtain the refrigeration power and coefficient of performance of the two-stage compression refrigeration cycle system corresponding to the sample set during the stable refrigeration process. The cooling power and coefficient of performance are combined with the sample set to construct a prediction dataset; The prediction model is constructed by training the prediction dataset and neural network. The prediction model is used to predict the refrigeration power and coefficient of performance of the two-stage compression refrigeration cycle system under real-time input parameters. Based on the predicted dataset, the prediction model is optimized using the particle swarm optimization algorithm; The real-time input parameters are input into the optimized prediction model to predict the refrigeration power and coefficient of performance of the two-stage compression refrigeration cycle system.

2. The performance prediction method according to claim 1, characterized in that, Based on the structure and energy transfer process of the two-stage compression refrigeration cycle system, a multiphysics coupled simulation model of the two-stage compression refrigeration cycle is constructed, including: The components required in the two-stage compression refrigeration cycle system are determined, including: evaporator, low-pressure compressor, high-pressure compressor, condenser, subcooler, and expansion valve; Based on the design of the energy transmission process of each component, the connection relationship of each component is determined, and the structure of the two-stage compression refrigeration cycle system is obtained. Establish mathematical models for each of the aforementioned components; Based on the structure of the two-stage compression refrigeration cycle system and the energy transfer process, the multiphysics coupling simulation model is constructed using simulation technology.

3. The performance prediction method according to claim 2, characterized in that, In the process of constructing the multiphysics coupled simulation model, each component in the two-stage compression refrigeration cycle system is regarded as an independent control body. The energy transfer process is simulated between the independent control bodies through parameter transfer to achieve coupled simulation. The refrigerant physical property parameters are obtained in real time through the REFPROP software interface.

4. The performance prediction method according to claim 1, characterized in that, Latin hypercube sampling is used to uniformly sample the numerical range of the overall input parameters to obtain a sample set of input parameters, including: Based on the requirements of the preset standard for the maximum load condition and low temperature condition of the vapor compression cycle, the numerical input range of the overall input parameters is determined; Based on the numerical input range of the overall input parameters, Latin hypercube sampling is used to uniformly sample the numerical input range of the overall input parameters to obtain a sample set of the input parameters. The overall input parameters include: chilled water mass flow rate, chilled water temperature, low-pressure compressor speed, low-pressure compressor guide vane opening, cooling water mass flow rate, and cooling water temperature.

5. The performance prediction method according to claim 1, characterized in that, The sample set is input into the multiphysics coupled simulation model to obtain the cooling power and coefficient of performance of the two-stage compression refrigeration cycle system corresponding to the sample set during the steady-state cooling process, including: The sample set is input into the multiphysics coupling simulation model, and the multiphysics coupling simulation model outputs the current refrigeration power and coefficient of performance of the two-stage compression refrigeration cycle system. The multiphysics coupling simulation model is continuously run, and the output results when the multiphysics coupling simulation model is running stably are determined as the cooling power and performance coefficient of the two-stage compression refrigeration cycle system corresponding to the sample set during the stable refrigeration process.

6. The performance prediction method according to claim 1, characterized in that, The cooling power and coefficient of performance are combined with the sample set to construct a prediction dataset, including: The cooling power and performance coefficient are combined with a sample set of input parameters, wherein the sample set includes six inputs: chilled water mass flow rate, chilled water temperature, low-pressure compressor speed, low-pressure compressor guide vane opening, cooling water mass flow rate, and cooling water temperature, and the cooling power and performance coefficient include the cooling power and performance coefficient corresponding to the six inputs; Based on the combination, the six inputs and the corresponding cooling power and coefficient of performance are saved as an Excel file, where column A is the number of the prediction dataset, columns B and G are the inputs, and columns H and I are the outputs, forming an eight-dimensional prediction dataset.

7. The performance prediction method according to claim 6, characterized in that, The prediction model is constructed by training the prediction dataset and the neural network, including: Based on the prediction dataset, a prediction model is constructed using a backpropagation (BP) neural network. The BP neural network includes an input layer, a hidden layer, and an output layer. The specific steps involved in constructing the prediction model are as follows: The prediction dataset is shuffled and divided into training and testing sets according to a set ratio. The inputs are the six inputs, and the outputs are the cooling power and performance coefficients corresponding to the six inputs. The training dataset and the test dataset are normalized. Weighting coefficients are set for cooling power and coefficient of performance. By traversing the empirical range of hidden layer nodes and combining the weighting coefficients, the number of nodes with the smallest mean square error of the training set is selected as the optimal value for hidden layer node optimization. The BP neural network is trained based on the input layer after normalization and the hidden layer after optimization of hidden layer nodes. The trained BP neural network is used to predict and inversely normalize the test set to obtain the prediction model; The expression for selecting the number of nodes with the minimum mean square error of the training set as the optimal value based on the weight coefficients is as follows: In the above formula, These represent the weighting coefficients for cooling power and coefficient of performance, respectively. Represents the total number of samples. This represents the true values ​​corresponding to the cooling power and coefficient of performance in the training set. This represents the predicted values ​​for cooling power and coefficient of performance.

8. The performance prediction method according to claim 6, characterized in that, Based on the predicted dataset, the prediction model is optimized using a particle swarm optimization algorithm, including: Each particle represents a set of weights and thresholds in a backpropagation neural network, and the motion of the particles is simulated for optimization. The PSO population size, iteration number, and weight coefficients are set. The initial positions of the particles are randomly initialized, and the fitness is calculated using a fitness function. The optimal position of the initial individual is its own position, and the fitness function is the mean square error between the predicted output and the true value. The calculated particle fitness is searched, and the index of the particle with the lowest fitness is set as the global optimal position. By iterating through each particle, the velocity and position of the particles are updated using inertia, individual cognition, and social cognition. The initial individual optimal position and the global optimal position are updated by calculating the fitness of the current position and comparing it with the historical records; When the accuracy requirement is met or the maximum number of iterations is reached, the iteration ends, and the obtained optimal weights and optimal thresholds are substituted into the BP neural network for training.

9. The performance prediction method according to claim 8, characterized in that, The number of PSO populations is 10; The number of iterations is 50; The weighting coefficient is: ; Both individual cognition and social cognition are set to 2; The inertia is set to 0.

9.

10. A two-stage compression refrigeration cycle system, characterized in that, The two-stage compression refrigeration cycle system is used to predict the performance of the two-stage compression refrigeration cycle system according to any one of claims 1 to 9. The two-stage compression refrigeration cycle system is a two-stage compression refrigeration cycle system with incomplete cooling in the middle of a single throttling process, which includes: an evaporator, a low-pressure compressor, a high-pressure compressor, a condenser, a subcooler, and an expansion valve. The evaporator is connected to the low-pressure compressor, the expansion valve, and the subcooler respectively; the low-pressure compressor is also connected to the subcooler. The high-pressure compressor is connected to the subcooler and the condenser respectively; the condenser is also connected to the subcooler; the subcooler is also connected to the expansion valve. The low-pressure vapor from the evaporator first enters the low-pressure compressor, is compressed to an intermediate pressure pm, and then mixes with the saturated vapor from the subcooler in the pipeline. The mixture then enters the high-pressure compressor, where it is further compressed to a condensing pressure pk and then enters the condenser to condense into a liquid. The liquid flowing out of the condenser is divided into two paths: one path flows through the coil inside the subcooler, is subcooled by the refrigerant liquid outside the coil, and then flows to the expansion valve. The expansion valve throttles the liquid to the evaporation pressure p0 before it enters the evaporator, where it evaporates to produce a cooling effect; the other path flows through the gas injection valve, is throttled to the intermediate pressure pm, enters the subcooler, and evaporates to produce saturated vapor, which also subcools the high-pressure liquid inside the coil. The saturated vapor then mixes with the low-pressure vapor from the low-pressure compressor before entering the second stage.

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