Air-supplementing enthalpy-increasing heat pump system and entropy production multi-objective optimization method thereof

Abstract

The invention discloses an air-supplementing enthalpy-increasing heat pump system, and relates to the technical field of heat pump systems. An outlet of a compressor is sequentially connected with a condenser, a first expansion valve and an evaporator. The system is further provided with an air supply branch, the inlet end of the air supply branch is connected with a pipeline between the condenser and the first expansion valve, the outlet end of the air supply branch is connected with a middle air supply port of the compressor, and the second expansion valve is arranged at the inlet end of the air supply branch. The entropy production multi-objective optimization method comprises the following steps: 1, building a test bed, and collecting thermodynamic parameters; 2, establishing and correcting a system entropy production and performance coefficient calculation model; 3, determining a control variable and a security constraint; 4, carrying out data normalization processing, and constructing a comprehensive evaluation function; 5, performing iterative optimization, and outputting a Pareto optimal leading edge; and 6, screening control parameters, and verifying adaptability. According to the method, a comprehensive optimization index combining multi-process entropy production and COP is constructed, so that the system runs in an area with the highest performance coefficient and the lowest total entropy production in the compression process while avoiding liquid impact and overheating risks.

Description

Technical Field

[0001] This invention relates to the field of heat pump system technology, specifically to a gas-injection enthalpy-increasing heat pump system and its entropy production multi-objective optimization method. Background Technology

[0002] Economized Vapor Injection (EVI) systems significantly expand the operating temperature range of air-source heat pumps by introducing an intermediate injection flow between the first and second stages of compression in the compressor. In low ambient temperatures during winter, EVI systems effectively enhance heating capacity; in high ambient temperatures during summer, they improve cooling capacity; and simultaneously reduce compressor discharge temperature, enhancing system stability and reliability.

[0003] In existing EVI systems, the intermediate injection pressure directly determines the injection volume, which in turn determines the relative injection volume, thus affecting the compressor's shaft power consumption and discharge volume. The discharge volume not only affects the discharge temperature but also directly relates to the output level of heating or cooling capacity. Furthermore, the state of the refrigerant at the injection port also directly determines the injection volume: when the injection flow is gaseous, the inflow is determined by the pressure difference; when the injection flow contains droplets or is in a two-phase region, the actual inflow and degree of vaporization are further constrained by thermodynamic processes. Therefore, the injection pressure and injection state jointly determine the injection volume and relative injection volume.

[0004] On the other hand, outdoor ambient temperature also affects system performance. In heating mode, ambient temperature determines the evaporation temperature; in cooling mode, ambient temperature determines the condensation temperature. These changes further affect the refrigerant flow rate in the system cycle, thus altering the relative gas injection rate. Therefore, it is necessary to systematically analyze the impact of parameters such as gas injection pressure, gas injection status, and ambient temperature on the relative gas injection rate, and further analyze the effect of the relative gas injection rate on the performance of the gas injection enthalpy-enhancing air source heat pump system, based on which optimization strategies can be proposed.

[0005] Existing research on enthalpy-increasing heat pump systems mainly focuses on aspects such as the design of the refrigerant injection structure, economizer loop control, refrigerant injection flow regulation, and exhaust temperature control. However, relying on empirical thresholds or single performance indicators lacks a unified metric that can comprehensively measure the irreversible losses and operational patterns of the system. This often makes it impossible to simultaneously consider system energy efficiency and operational safety under different environmental conditions. Especially when the refrigerant at the injection port is unsaturated (containing droplets or in the two-phase region), existing control logic struggles to accurately assess its combined impact on the refrigerant injection volume, mixing process, and secondary compression process, easily leading to control instability or performance degradation.

[0006] Entropy production is a fundamental physical quantity that measures the irreversibility of a thermodynamic process, comprehensively reflecting losses in compression, heat transfer, and mixing. Compared to traditional control methods that optimize solely based on exhaust temperature or the coefficient of performance (COP), the analytical approach centered on minimizing the total entropy production of the compression process addresses the thermodynamic essence, providing a unified description of the system's energy efficiency and irreversible losses. In a gas-feed enthalpy-increasing system, the entropy production of each process is coupled, and the state of the gas feed directly affects the entropy production levels of mixing and secondary compression, thus determining the overall system performance. Summary of the Invention

[0007] The purpose of this invention is to provide a gas-injection enthalpy-increasing heat pump system and its entropy production multi-objective optimization method. By constructing a comprehensive optimization index that combines multi-process entropy production and COP, a quantitative balance between gas injection pressure, dryness, and energy efficiency is achieved, thereby determining the optimal gas injection state point. This allows the system to operate in the region with the highest coefficient of performance and the lowest total entropy production during the compression process while avoiding the risks of liquid slugging and overheating.

[0008] To achieve the above objectives, the present invention adopts the following technical solution.

[0009] A gas-injection enthalpy-increasing heat pump system includes a compressor, a condenser, a first expansion valve, an evaporator, and a second expansion valve.

[0010] The compressor is a two-stage gas injection and enthalpy-increasing compressor. The compressor outlet is connected to the condenser, the first expansion valve, and the evaporator in sequence through pipelines, and returns from the evaporator to the compressor inlet to form the main circuit.

[0011] The system also has a gas supply branch. The inlet end of the gas supply branch is connected to the pipeline between the condenser and the first expansion valve, and the outlet end is connected to the intermediate gas supply port of the compressor. The second expansion valve is located at the inlet end of the gas supply branch.

[0012] Furthermore, the gas replenishment branch also includes a heat absorption pipe installed on the compressor casing. The outlet end of the gas replenishment branch is connected to the intermediate gas replenishment port of the compressor through the heat absorption pipe, so that the refrigerant in the gas replenishment branch enters the compressor through the heat absorption pipe, thereby achieving a cooling effect on the compressor and recovering heat energy.

[0013] Furthermore, an economizer is installed between the main circuit and the make-up gas branch. One end of the economizer is connected to the main circuit, and the other end is connected to the part between the second expansion valve and the heat absorption pipe on the make-up gas branch. This is used to utilize the heat from the main circuit to partially vaporize the refrigerant in the make-up gas branch.

[0014] A multi-objective optimization method for entropy production in a gas-fuel-injection enthalpy-increasing heat pump system, based on the aforementioned heat pump system, includes the following steps: S1. Set up a heat pump system test bench and collect core thermodynamic parameters under stable operating conditions; S2. Establish the system entropy production model and the system performance coefficient calculation model, and use the parameters collected in S1 to correct the model; S3. Determine the control variables and security constraints with the goal of minimizing entropy production and maximizing system performance coefficients; S4. Data normalization processing and construction of a comprehensive evaluation function; S5. Use a non-dominated sorting genetic algorithm to iteratively find the optimal solution and output the Pareto optimal frontier. S6. Select control parameters according to actual needs, feed them back to the system for dynamic operation, and verify the adaptability under changing operating conditions.

[0015] Furthermore, in step S1, both the condenser and evaporator on the test bench adopt water bath heat exchange. A condensing side water tank and a condensing side water pump are provided on one side of the condenser. The condensing side water pump is used to drive the heat exchange medium in the condensing side water tank to exchange heat with the condenser.

[0016] Furthermore, in step S2, the system entropy production model includes the entropy production model of the first-stage compression process of the two-stage compressor, the entropy production model of the gas injection evaporation process, the entropy production model of the gas injection mixing process, and the entropy production model of the second-stage compression process. The entropy production of each stage is calculated using the thermodynamic parameters of each stage and then summed to obtain the total entropy production of the system.

[0017] During model correction, the error between the entropy production and system performance coefficients calculated by the model and the measured values ​​derived from the collected parameters in step S1 does not exceed the preset range.

[0018] Furthermore, in step S3, the control variables include the opening degree of the first expansion valve, the opening degree of the second expansion valve, and the flow rate of the condensate side water pump.

[0019] Safety constraints include refrigerant dryness constraints at the gas injection inlet, compressor suction superheat constraints, condenser outlet refrigerant subcooling constraints, intermediate gas injection pressure constraints, and compressor efficiency constraints, which are used to avoid the risk of liquid slugging or overheating in the system.

[0020] Furthermore, in step S4, the data normalization process targets the total entropy production of the compression process and the system performance coefficients. The normalized data is uniformly mapped to the same standard interval.

[0021] The comprehensive evaluation function is used to balance the two objectives of minimizing entropy production and maximizing system performance coefficients, and the priority of the two objectives is adjusted by setting weight coefficients.

[0022] Furthermore, in step S5, the non-dominated sorting genetic algorithm adopts the NSGA-II algorithm, and outputs the Pareto optimal front when the iteration termination condition is reached.

[0023] Furthermore, in step S6, the selection of control parameters is based on a preset weight bias. The preset weights include stability weight and energy efficiency weight, and the sum of stability weight and energy efficiency weight is fixed. By adjusting the values ​​of stability weight and energy efficiency weight, one can switch between energy efficiency priority mode, stability priority mode, or a balanced mode of both.

[0024] By adopting the above technical solution, the present invention has the following beneficial effects: 1. This invention can accurately handle complex working conditions where the gas supply is in a two-phase region or contains droplets, solving the problem that existing technologies cannot accurately assess its impact, and significantly improving the stability and performance of the system under varying working conditions. 2. This invention constructs a multi-objective optimization model with the dual objectives of minimizing entropy production and maximizing COP. This model can simultaneously take into account the improvement of system energy efficiency and the control of irreversible losses, and achieve a balance between energy utilization and operational stability, breaking through the limitations of traditional methods that only adjust a single performance index. 3. This invention introduces a performance optimization method for partially gas-supplemented enthalpy-increasing heat pump systems based on entropy production analysis and multi-objective optimization. Starting from the thermodynamic essence, it establishes a systematic and quantifiable performance optimization mechanism, which enables the control strategy to break free from dependence on empirical parameters and has stronger universality and robustness. 4. This invention achieves a quantitative balance between make-up gas pressure, make-up gas dryness, and energy efficiency through a control strategy that couples entropy production and COP, thereby determining the optimal make-up gas state point. This allows the system to operate in the region with the highest performance coefficient and the lowest total entropy production during compression while avoiding the risks of liquid slugging and overheating. The optimized system can adaptively adjust the make-up gas volume and flow distribution according to changes in external temperature and load, ensuring that the system operates in a high-efficiency and safe range under different operating conditions, thereby improving system reliability and equipment lifespan. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the overall structure of the heat pump system in this invention.

[0026] Figure 2 This is a schematic diagram of the gas injection and compression process of a two-stage compressor.

[0027] Figure 3 This is a flowchart of the simulation model establishment process in this invention.

[0028] Figure 4 This is a flowchart of the multi-objective optimization process of the heat pump system in this invention.

[0029] Figure 5 This is a flowchart of the non-dominated sorting genetic algorithm in this invention.

[0030] Figure description: 1. Compressor, 2. Condenser, 21. Condensing side water tank, 22. Condensing side water pump, 3. First expansion valve, 4. Evaporator, 41. Evaporating side water tank, 42. Evaporating side water pump, 5. Second expansion valve, 6. Economizer. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of the present invention clearer, the features and performance of a gas-injection enthalpy-increasing heat pump system and its entropy production multi-objective optimization method are further described in detail below with reference to the accompanying drawings and embodiments.

[0032] Please see the appendix Figures 1-5 A gas-injection enthalpy-increasing heat pump system includes a compressor 1, a condenser 2, a first expansion valve 3, an evaporator 4, and a second expansion valve 5.

[0033] Compressor 1 is a two-stage gas injection and enthalpy-increasing compressor. The outlet of compressor 1 is connected to condenser 2, first expansion valve 3 and evaporator 4 in sequence through pipelines, and returns from evaporator 4 to compressor 1 inlet to form the main circuit.

[0034] The system is also equipped with a gas supply branch. The inlet end of the gas supply branch is connected to the pipeline between the condenser 2 and the first expansion valve 3, and the outlet end is connected to the intermediate gas supply port of the compressor 1. The second expansion valve 5 is located at the inlet end of the gas supply branch.

[0035] The gas replenishment branch also includes a heat absorption pipe installed on the casing of compressor 1. The outlet end of the gas replenishment branch is connected to the middle gas replenishment port of compressor 1 through the heat absorption pipe. This allows the refrigerant in the gas replenishment branch to enter compressor 1 through the heat absorption pipe, thereby achieving a cooling effect on compressor 1 and recovering heat energy.

[0036] An economizer 6 is installed between the main circuit and the make-up gas branch. One end of the economizer 6 is connected to the main circuit, and the other end is connected to the part between the second expansion valve 5 and the heat absorption pipe on the make-up gas branch. It is used to utilize the heat of the main circuit to partially vaporize the refrigerant in the make-up gas branch.

[0037] A multi-objective optimization method for entropy production in a gas-replenishing enthalpy-increasing heat pump system, based on the aforementioned heat pump system, includes the following steps.

[0038] S1. Construct a heat pump system test bench and collect core thermodynamic parameters under stable operating conditions. Both the condenser 2 and evaporator 4 on the test bench utilize water bath heat exchange. The condenser 2 has a condensing-side water tank 21 and a condensing-side water pump 22 on one side. The condensing-side water pump 22 drives the heat exchange medium in the condensing-side water tank 21 to exchange heat with the condenser 2. Similarly, the evaporator 4 has an evaporating-side water tank 41 and an evaporating-side water pump 42 on one side. The evaporating-side water pump 42 drives the heat exchange medium in the evaporating-side water tank 41 to exchange heat with the evaporator 4.

[0039] S2. Establish the system entropy production model and the system performance coefficient calculation model, and use the parameters collected in S1 to correct the model.

[0040] The system entropy production model includes entropy production models for the first-stage compression process, the gas injection evaporation process, the gas injection mixing process, and the second-stage compression process of the two-stage compressor. The entropy production of each stage is calculated using the thermodynamic parameters of each stage, and then summed to obtain the total entropy production of the system. During model correction, the error between the entropy production and system performance coefficients calculated by the model and the measured values ​​derived from the parameters collected in step S1 does not exceed a preset range.

[0041] S3. Determine the control variables and safety constraints with the goal of minimizing entropy production and maximizing system performance coefficients.

[0042] The control variables include the opening degree of the first expansion valve 3, the opening degree of the second expansion valve 5, and the flow rate of the condenser-side water pump 22. Safety constraints include refrigerant dryness constraints at the makeup gas inlet, superheat constraints at the compressor 1 suction gas, subcooling constraints at the condenser 2 outlet, intermediate makeup gas pressure constraints, and compressor 1 efficiency constraints, which are used to avoid the risk of liquid slugging or overheating in the system.

[0043] S4. Data normalization processing and construction of a comprehensive evaluation function.

[0044] Data normalization processes target the total entropy production and system performance coefficients during the compression process, mapping the normalized data to the same standard interval. A comprehensive evaluation function balances the two objectives of minimizing entropy production and maximizing system performance coefficients, adjusting their priority by setting weighting coefficients.

[0045] S5. Use a non-dominated sorting genetic algorithm for iterative optimization and output the Pareto optimal front. The non-dominated sorting genetic algorithm adopts the NSGA-II algorithm, and outputs the Pareto optimal front when the iteration termination condition is reached.

[0046] S6. Select the optimal control parameters according to actual needs, feed them back to the system for dynamic operation, and verify the adaptability under varying operating conditions. The selection of optimal control parameters is based on preset weightings, which include stability weights and energy efficiency weights. The sum of stability weights and energy efficiency weights is fixed. By adjusting the values ​​of stability weights and energy efficiency weights, one can switch between energy efficiency priority mode, stability priority mode, or a balanced mode of both.

[0047] In specific implementation, this invention proposes a gas-injection enthalpy-increasing heat pump system and its entropy production multi-objective optimization method. The method is characterized by using the online estimation results of the system performance coefficient (COP) and the total entropy production of the compression process as dual objective functions. It combines multi-process entropy production with system energy efficiency characteristics to construct a comprehensive optimization model that balances energy efficiency improvement and irreversible loss reduction. The non-dominated sorting genetic algorithm II (NSGA-II) is then used to perform multi-objective optimization on the constructed model to achieve optimal opening settings for the first expansion valve 3 and the second expansion valve 5, as well as the flow rate of the condenser-side water pump 22, thereby determining the optimal dryness range for gas injection. Based on the theoretical foundation of minimizing entropy production and maximizing COP, this method enhances the system's adaptability and operational stability under varying operating conditions through synergistic optimization of energy efficiency and irreversibility.

[0048] A gas-injection enthalpy-increasing heat pump system includes a compressor 1, a condenser 2, a first expansion valve 3, an evaporator 4, a second expansion valve 5, and an economizer 6. The main circuit of the system comprises a two-stage gas-injection enthalpy-increasing compressor 1, a condenser 2, an evaporator 4, and a first expansion valve 3. The gas-injection branch section includes a second expansion valve 5 and an economizer 6. The second expansion valve 5 controls the pressure of the working fluid entering the economizer 6. The system also includes a gas-injection control system for controlling the dryness of the gas injection. The gas-injection control system consists of the compressor 1, the second expansion valve 5, the economizer 6, the gas-injection branch pipeline, and temperature and pressure sensors sequentially arranged along the gas-injection direction on the gas-injection branch pipeline.

[0049] The experimental platform for the gas-fuel-injection enthalpy-increasing heat pump system includes a refrigerant circulation system, a constant-temperature water bath circulation system, an experimental control system, and a data acquisition system. The constant-temperature water bath circulation system includes a condenser-side water tank 21 and a condenser-side water pump 22 for heat exchange with the condenser 2, and an evaporator-side water tank 41 and an evaporator-side water pump 42 for heat exchange with the evaporator 4. Figure 1 As shown.

[0050] Specifically, both the condensation and evaporation sides of this experiment employ liquid cooling, thus requiring two constant-temperature water baths. The condensation side (high-temperature side) water bath exchanges heat with the refrigerant in condenser 2, requiring a higher water bath temperature; therefore, pure water is selected as the heat exchange medium for the high-temperature side water bath. The evaporation side (low-temperature side) water bath exchanges heat with the refrigerant in evaporator 4, requiring a lower water bath temperature and necessitating a liquid with a lower freezing point. Therefore, ethylene glycol solution with a low freezing point is selected as the heat exchange medium, enabling a low-temperature water bath environment of -20°C.

[0051] The main components of a gas-injection enthalpy-increasing heat pump system (refrigerant circulation system) include a scroll compressor 1 with an intermediate gas injection port, a condenser 2, a first expansion valve 3, an evaporator 4, a second expansion valve 5, and an economizer 6. Figure 1 As shown. The system flow consists of two parts: the main loop and the make-up gas branch. In the main loop, the refrigerant flows in the following order: Compressor 1 draws in low-temperature, low-pressure refrigerant vapor, compresses it into superheated refrigerant vapor through a first-stage compression process, and mixes it with gaseous refrigerant injected from the make-up gas branch between the first and second-stage compression processes. Then, it undergoes a second-stage compression to become high-temperature, high-pressure superheated refrigerant vapor, which is then fed into condenser 2. The superheated refrigerant vapor entering condenser 2 releases heat and condenses into high-temperature, high-pressure liquid refrigerant. Subsequently, most of the high-temperature, high-pressure liquid refrigerant releases heat through economizer 6 and becomes subcooled liquid refrigerant. After being throttled and depressurized into a two-phase state by the first expansion valve 3, it enters evaporator 4. The two-phase refrigerant absorbs heat in evaporator 4 to become low-temperature, low-pressure refrigerant vapor, which is then drawn in by the compressor to complete the main cycle.

[0052] The refrigerant flow sequence in the make-up gas branch is as follows: a small portion of the high-temperature, high-pressure liquid refrigerant generated by condensation in condenser 2 enters the make-up gas branch, is throttled by the second expansion valve 5 to medium-pressure, low-dryness wet vapor, and then partially vaporizes by absorbing the heat released by the refrigerant in the main circuit through economizer 6. It then further vaporizes by absorbing the heat from compressor 1 through the heat absorption pipe, and finally enters compressor 1 from the middle make-up gas port to mix with the refrigerant that has undergone one stage of compression in the main circuit, thus completing the cycle of the make-up gas branch.

[0053] The system operates under given target conditions, and real-time data on pressure, temperature, and flow rate of compressor 1, condenser 2, evaporator 4, economizer 6, and the gas injection branch are collected. Figure 1 In this model, T represents the temperature sensor, P represents the pressure sensor, and subscripts represent positions. Parameters for each state point are calculated based on a refrigerant property database. During actual operation and analysis, to ensure the reliability and comparability of the thermodynamic analysis, the system undergoes a sufficient dynamic transition process after each expansion valve adjustment until all key system parameters reach a relatively stable state. Only under stable system operating conditions are the corresponding state points selected for subsequent system COP and entropy production analysis. This avoids the unsteady-state effects introduced by transient processes, ensuring that the calculated entropy production reflects the true irreversible loss characteristics of the gas-fueled enthalpy-increasing compression process under steady-state conditions.

[0054] The working principle of the gas-injection enthalpy-increasing heat pump system is theoretically analyzed, and a thermodynamic model of the main components is established. Based on the processes of primary compression, gas-injection evaporation contact, gas-injection mixing, and secondary compression, the entropy production of each process is calculated and accumulated to obtain the total entropy production of the system compression process. Furthermore, the functional relationship between the total entropy production and the gas injection amount, intermediate gas injection pressure, and gas injection state is derived.

[0055] Open system Entropy change of the system after time satisfy, (1) (2) in, For mass entropy flow, The unit is , The entropy of the input substances in the system, expressed in units of . , The entropy carried away by matter leaving the system, in units of . , For the algebraic sum of (thermal) entropy flows, The unit is , Entropy production, unit: .

[0056] Specifically, the refrigerant mass flow rate through the evaporator is The refrigerant mass flow rate through the condenser is Refrigerant mass flow rate through the gas supply branch The relative air replenishment volume is defined as .

[0057] like Figure 2 As shown, in the first-stage compression process of compressor 1, the product after the first-stage compression (i.e., Figure 2 (The position of the number 2 in the middle) Refrigerant pressure enthalpy value and entropy Therefore, (3) in, Before primary compression (i.e.) Figure 2 The position of the number 1 in the middle) indicates the pressure of the refrigerant, in units of , The specific volume of the refrigerant before the first stage of compression, in units of... , This is the specific volume of the refrigerant after the first stage of compression, in units of... , is the isentropic index of the refrigerant. This refers to the theoretical suction volume of the compressor, in units of... , The volume ratio of the first-level compressed content.

[0058] The entropy production of the first-order compression process can be further obtained from the entropy balance equation. for, (4) in, The entropy value of the refrigerant before the first stage of compression, in units of... , This refers to the amount of heat dissipated from the casing to the air during the first stage of compression, measured in units of... , Temperature of the outer surface of the compressor housing during the first stage of compression, in units of... .

[0059] During the replenishment and mixing process, such as Figure 1 As shown, the high-pressure liquid refrigerant at the outlet of condenser 2 enters the make-up gas branch and is controlled and throttled to the intermediate pressure by the second expansion valve 5. During the throttling process, the refrigerant partially vaporizes, forming a two-phase mixed flow with liquid as the main phase and gas as the auxiliary phase. The temperature of this mixed flow is close to the saturated liquid temperature, belonging to an unsaturated state, and possessing strong heat absorption and vaporization potential. By adjusting the opening of the second expansion valve 5 to regulate the intermediate pressure, the dryness of the makeup gas flow can be flexibly controlled, achieving precise regulation of the subsequent heat exchange and enthalpy increase processes.

[0060] The two-phase unsaturated refrigerant (makeup gas flow) passing through the second expansion valve 5 partially vaporizes after recovering heat from the main circuit via the economizer 6. The temperature of the makeup gas is obtained by the controller and monitored by the temperature controller. The pressure sensor detected the replenishment pressure. Calculate the refrigerant dryness after passing through Economist 6 but not entering the heat absorption pipe. , Based on refrigerant dryness Calculate the enthalpy value of the corresponding gas replenishment state point. and entropy , respectively, (5) (6) in, This refers to the enthalpy of the refrigerant that passes through the economizer 6 in the make-up gas branch but does not enter the heat absorption line, expressed in units of... , and They are respectively at intermediate pressure The enthalpy of the refrigerant at its saturation point when the dryness fraction is 0 and 1, respectively, in units of... , This is the intermediate pressure, in units of , The entropy value of the refrigerant that passes through the economizer 6 in the make-up gas branch but does not enter the heat absorption line is expressed in units of 1. , and They are respectively at intermediate pressure The entropy values ​​of the refrigerant at the saturation point when the dryness fraction is 0 and 1, respectively, are expressed in units of... .

[0061] Before mixing with the refrigerant after primary compression at the intermediate gas injection port of compressor 1, the two-phase unsaturated refrigerant absorbs heat from the secondary compression stage of the compressor while passing through the heat absorption line, achieving partial or complete vaporization. To facilitate understanding of the principle behind the reduction in compressor discharge temperature during the gas injection process and the entropy production analysis of the compression process in subsequent analyses, this process is equivalent to the two-phase unsaturated refrigerant exchanging heat with the high-temperature gas generated during the secondary compression stage of compressor 1, thus continuing to release latent heat. The partially or completely vaporized refrigerant, after passing through the heat absorption line, is injected through the intermediate gas injection port of compressor 1 and mixed with the refrigerant after primary compression. The mixed refrigerant is then heated by the intermediate pressure... As the gas continues to be compressed by the secondary compressor, the pressure gradually increases, and the gas temperature rises accordingly. This is called the initial stage of the second-stage compression process.

[0062] In the initial stage of the second-stage compression process, the refrigerant exchanges heat with the two-phase unsaturated refrigerant passing through the heat absorption line. Since the temperature of the two-phase unsaturated refrigerant is almost constant at its saturation temperature, the refrigerant releases heat and cools down during the second-stage compression process; the two-phase unsaturated refrigerant in the make-up gas branch absorbs heat and vaporizes, thus increasing its dryness. , And the enthalpy increases. At this time, the refrigerant temperature in the second-stage compression process is... Down to , Approximately equal to the saturation temperature of the refrigerant under intermediate pressure, this heat exchange process achieves self-cooling during the secondary compression process, effectively absorbing the heat of compression and reducing the cavity temperature, thus creating better initial thermodynamic conditions for the secondary compression stage.

[0063] The refrigerant after primary compression and the refrigerant that has partially or completely vaporized after passing through the heat absorption pipe are in thermal contact, but have not yet mixed into a single flow, forming a separate two-flow heat exchange control volume. Based on energy conservation, the heat exchange capacity is: (7) in, The heat transfer capacity of the two-flow heat exchanger control volume, in units of , This refers to the enthalpy of the refrigerant in the initial stage of the two-stage compression process, expressed in units of... , The enthalpy of the refrigerant during the second-stage compression process after cooling through the heat absorption pipe is expressed in units of... , The enthalpy of the refrigerant after it has partially or completely vaporized through the heat absorption pipe, expressed in units of... .

[0064] During the above process, the gas supply branch is at an intermediate pressure. Before the unsaturated makeup gas enters the compressor's intermediate makeup gas inlet and mixes completely with the refrigerant at the first-stage compressor outlet, it exchanges heat with the high-temperature gas generated in the initial stage of the second-stage compression in the heat absorption line. This heat exchange process occurs before the two streams have undergone mass mixing, exhibiting typical two-stream heat exchange behavior. The outcome depends on the matching relationship between the amount of heat released by the high-temperature gas in the initial stage of the second-stage compression and the vaporization potential of the makeup gas itself in the heat absorption line. Since the initial state of the makeup gas is a two-phase or near-saturated liquid at intermediate pressure, its heat absorption process preferentially utilizes phase change vaporization rather than temperature increase. Therefore, after the heat exchange, the makeup gas refrigerant in the makeup gas branch may exhibit two different thermodynamic states: one is partial vaporization with some liquid remaining, existing in a two-phase mixed state; the other is complete vaporization after absorbing sufficient heat, or even entering a slightly superheated state while continuing to absorb heat. These will be explained separately below.

[0065] Scenario 1: When the refrigerant in the gas supply branch partially vaporizes after passing through the heat absorption pipe, i.e. Therefore, (8) (9) Solve simultaneously with energy equation (7) and At this time, the actual refrigerant inlet temperature of the compressor's gas supply branch is The values ​​can be found in a table based on the refrigerant pressure and enthalpy.

[0066] Scenario 2: When the refrigerant in the gas supply branch completely vaporizes after passing through the heat absorption pipe, i.e. If the vaporized refrigerant has not yet been superheated, there is , If there is still residual heat after the refrigerant has completely vaporized, it will cause the refrigerant to overheat and the corresponding... Lower, at this time Based on the current gas supply pressure and gas supply enthalpy, the entropy value of the current refrigerant state can be calculated.

[0067] At this point, the entropy production generated by "the refrigerant after primary compression and the refrigerant that has partially or completely vaporized after passing through the heat absorption pipes coming into thermal contact, but not yet mixed into a single flow" forming a separate two-flow heat exchange control volume for, (10) in, This is the refrigerant entropy value in the initial stage of secondary compression, in units of... , The refrigerant entropy value after heat exchange in the two-stream heat exchange control volume during the second stage compression, in units of... .

[0068] If the refrigerant in the make-up gas branch partially vaporizes after passing through the heat absorption line, it may also be in the two-phase region after mixing with the refrigerant after the first stage compression. In this case, the pressure of the mixed refrigerant should still be considered. enthalpy value The entropy value is obtained by looking up the table. The compressor entropy production during the refrigerant mixing process can be obtained. for: (11) in, This represents the net heat exchange between the mixing section control volume and the external environment, expressed in units of... , The temperature of the outer surface of the control section housing in the mixing section, in units of .

[0069] In the two-stage compression process of compressor 1, the temperature of the refrigerant in the initial stage of the two-stage compression rises from the temperature after mixing with the makeup gas to... The entropy production of the process is, (12) in, This represents the net heat exchange between the initial stage of the secondary compression and the external environment, expressed in units of... , Temperature of the outer surface of the primary stage compressor housing, in units of .

[0070] After being cooled by vaporization heat exchange, the refrigerant continues to be compressed to exhaust pressure through the latter stage of secondary compression. The temperature rose again to Because the phase change in the previous stage absorbs heat, the initial gas temperature decreases significantly, and the final exhaust temperature... The exhaust temperature is significantly lower than that in traditional enthalpy-increasing systems. This "heating-cooling-heating" composite compression path achieves active regulation of compression heat without the need for independent jet ports, thus suppressing exhaust temperature and improving system energy efficiency and operational stability.

[0071] At this time, the secondary compression outlet (i.e. Figure 2 The refrigerant pressure (located at the position of the number 4) is enthalpy value The refrigerant temperature in the later stage of compression is... Rise to The entropy production of the process is, (13) in, The entropy value of the refrigerant at the outlet of the second-stage compressor, in units of... , This represents the net heat exchange between the intermediate stage of the secondary compression and the external environment, expressed in units of... , Temperature of the outer surface of the casing in the intermediate stage of the secondary compression, in units of... .

[0072] The total entropy production during the compression process is obtained by simultaneously solving equations (4), (10), (11), (12), and (13), where the mass entropy flows at the internal boundaries cancel each other out. (14) in, As a common simplification practice in engineering, all heat dissipation is converted into an equivalent total heat dissipation. And take an equivalent boundary temperature (Average temperature of the entire casing).

[0073] As a preferred option for the compression process, the target makeup gas dryness is determined based on the different operating ambient temperatures of the unit. The optimal dryness range for the refrigerant used for gas replenishment is: .

[0074] With the system COP maximization and the total entropy production of the compression process as objective functions, the opening degree of the electronic expansion valve (first expansion valve 3 and second expansion valve 5) and the flow rate of the condenser side water pump 22 in the main loop and the gas replenishment branch are dynamically adjusted by combining optimization algorithms, thereby adjusting the optimal gas replenishment state point (optimal dryness range) and relative gas replenishment amount under partial gas replenishment conditions.

[0075] During the optimization process, safety constraints such as upper and lower limits of refrigerant superheat / subcooling, upper and lower limits of make-up gas dryness, and upper limit of compressor efficiency are applied to prevent liquid slugging and overheating risks. The optimization results are fed back to the system operation to optimize the system's operating status.

[0076] Specifically, multi-objective optimization problems require simultaneously satisfying multiple different and often conflicting objectives, which have different performance evaluation methods. It is worth noting that multi-objective optimization problems typically present an infinite set of possible solutions, representing optimal trade-offs in the objective function space. However, due to the conflicts between different objective functions, it is difficult to find a set of decision variable values ​​that simultaneously minimizes or maximizes all components of all functions.

[0077] Based on the results, an optimization algorithm is used to dynamically adjust the opening of the electronic expansion valve in the main loop and the gas injection branch, as well as the flow parameters of the condenser-side water pump 22. This adjusts the optimal gas injection state point (optimal dryness range) and relative gas injection volume under partial gas injection conditions, optimizes the compressor's operating state, and further improves system energy efficiency. Constraints are set during the optimization process, including upper and lower limits for secondary suction dryness, superheat / subcooling, intermediate pressure, and compressor efficiency, to prevent liquid slugging and overheating risks. Through a dynamic iterative process of "optimization-feedback-re-optimization," the algorithm can correct the electronic expansion valve opening and water pump flow in real time, ensuring that the system consistently approaches the multi-objective optimal balance range of energy efficiency and entropy production under various operating conditions. This achieves synergistic optimization operation that maximizes energy efficiency and minimizes irreversible losses.

[0078] Based on the above operations, the objective function in this system analysis is to maximize the system's performance coefficient COP and the total entropy production of the compression process. The minimum combination is determined and compared with a heat pump system without gas replenishment. Therefore, the objective function in this system analysis can be expressed by the formula: (15) (16) in, The entropy production generated by first-level compression, in units of ; The entropy production is generated by the release of latent heat from the two-phase unsaturated refrigerant in the make-up gas branch, with units of [unit missing]. ; The entropy production generated during the mixing phase, in units of ; and The entropy production resulting from secondary compression, in units of ; This refers to the input power of the primary compressor, measured in units of... ; The heat output of the condenser, in units of .

[0079] like Figures 3-5 As shown, the total entropy production during the system compression process is... The online estimation of the system performance coefficient COP serves as the comprehensive optimization objective function, establishing a multi-objective optimization model centered on improving energy efficiency and reducing irreversible losses. For example... Figure 3 As shown, COP is related to the total entropy production of the compression process. The changes are determined by the key thermodynamic state parameters of the cycle process, including the dryness of the make-up gas. Intermediate air replenishment pressure Suction superheat, liquid subcooling, and compressor efficiency are used as decision variables. To achieve dynamic control of these state variables, the opening degree of the first expansion valve 3 is selected. Second expansion valve 5 opening degree With condensate side water pump 22 flow rate As a control measure, the optimization objective is solved under hard / soft constraints to obtain the optimal combination of the gas injection state (optimal dryness range, relative gas injection rate) and heat exchange matching. Different variables may exist in a multi-objective optimization problem. To obtain an ideal multi-objective optimization solution set, a set of important parameters should be selected as decision variables. The multi-objective optimization process for gas injection enthalpy-increasing heat pump performance is as follows: Figure 4 As shown.

[0080] To address the aforementioned nonlinear and multi-objective coupling characteristics, NSGA-II is employed for solution. This algorithm, through population selection, crossover, and mutation operations, gradually approximates the optimal solution set during evolutionary iteration, effectively searching for the Pareto Front of the system. By employing a mechanism of "non-dominated sorting + crowding calculation + elite retention," it can uniformly search for the optimal solution set in the complex objective space, avoiding getting trapped in local optima. At this front, each solution represents the optimal combination of system COP and total entropy production under different trade-offs.

[0081] First, an initial population is randomly generated within the variable space, with each individual representing a different combination of control parameters. The corresponding parameters are then calculated using a thermodynamic model. , The values ​​are normalized and sorted according to non-dominated relationships. Pareto levels are defined using this non-dominated sorting, and non-deteriorating optimal solutions are selected. The crowding distance between individuals is calculated to maintain a uniform distribution of the solution set. Selection, crossover, and mutation operations are used to generate a new generation of the population, retaining the best individuals (elite strategy). This evolutionary iteration is repeated until convergence. Iteration stops when the algorithm reaches the maximum number of iterations or when the change in the Pareto front is less than a set threshold. The final first front solution set (Front 1) is the Pareto optimal front of the system.

[0082] Specifically, the following multi-objective optimization model is established. (17) (18) Among them, the opening degree of the first expansion valve 3 Used to adjust the liquid supply of evaporator 4 and the system superheat. The opening degree of the second expansion valve 5 Used to adjust the relative air supply volume and intermediate air supply pressure. Flow rate of condensate pump 22 It is used to affect the pressure of condenser 2 and the heat exchange temperature difference of economizer 6, thereby changing the dryness of the make-up gas and the intermediate pressure.

[0083] The constraints are as follows: , , , , , in, To replenish air dryness, This is the intermediate pressure, in units of , This is the condensation pressure, in units of... , Evaporation pressure, unit: , Evaporator superheat, unit: , This refers to the condenser subcooling, measured in units of... , For compressor efficiency.

[0084] Next, target normalization is performed to eliminate dimensional differences. (19) in, For the first The original values ​​of each target. , The maximum and minimum values ​​of the target during the sample or iteration process. After normalization, all target values ​​are in the range [0, 1].

[0085] After normalization, the comprehensive evaluation function is: (20) in, As a comprehensive evaluation indicator, , The weights are determined through Pareto front analysis. Prioritize energy efficiency When irreversibility / stability takes precedence, take , The normalized system performance coefficient COP, This represents the total entropy production of the normalized compression process.

[0086] like Figure 5 The diagram illustrates the workflow of NSGA-II. First, the population is initialized with the generation number Gen=1. A quadratic regression function obtained from response surface analysis is calculated, followed by non-dominated ranking and crowding calculation. Random crossover and mutation generate new offspring. NSGA-II adds the calculation of elitist strategies and crowding distance, reducing computational complexity and allowing it to better adapt to population diversity under low population fitness conditions. This method is highly practical and exhibits uniform and good convergence. Finally, the generation number and loop checks are checked, and the above process is repeated until the evolutionary requirements are met, yielding the Pareto optimal solution set.

[0087] NSGA-II guarantees global optimum through non-dominated sorting, elitist strategy, and crowding calculation, avoiding premature convergence leading to local optima. Furthermore, NSGA-II generates new offspring through crowding calculation, random crossover, and mutation, which helps maintain population diversity and ensures the independence of different factors. The most prominent advantage of genetic algorithms is their strong global search capability and better convergence. Currently, NSGA-II, based on genetic algorithms, is one of the most practical multi-objective evolutionary algorithms for thermal system optimization problems, possessing advantages such as strong robustness and fast population distance estimation.

[0088] The non-dominated sorting genetic algorithm (NSGA-II) was used for multi-objective optimization. The maximum number of iterations in NSGA-II was set to 200, the population size was 100, the crossover ratio was 0.8, the mutation ratio was 0.1, and the mutation rate was 0.2. The Pareto optimal front was obtained after iterative calculation in Matlab.

[0089] Analysis of the Pareto solution set yields the following: High COP region – system energy efficiency is high, but entropy production is slightly higher; Low-entropy production areas – the system suffers less irreversible loss, but energy efficiency is slightly reduced; The compromise zone – where system energy efficiency and losses reach their optimal balance.

[0090] Selecting energy efficiency priority schemes from Pareto solutions ( =0.5, =0.5), balancing COP improvement with irreversible system losses.

[0091] It should be noted that the parts not described in detail in this solution are all prior art. The above embodiments are only used to illustrate the present invention, but the present invention is not limited to the above embodiments. Any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A gas-replenishing enthalpy-increasing heat pump system, characterized in that: It includes a compressor (1), a condenser (2), a first expansion valve (3), an evaporator (4), and a second expansion valve (5). The compressor (1) is a two-stage gas-fueling and enthalpy-increasing compressor. The outlet of the compressor (1) is connected to the condenser (2), the first expansion valve (3), and the evaporator (4) in sequence through pipelines, and returns from the evaporator (4) to the inlet of the compressor (1) to form the main circuit. The system is also provided with a gas supply branch. The inlet end of the gas supply branch is connected to the pipeline between the condenser (2) and the first expansion valve (3), and the outlet end is connected to the intermediate gas supply port of the compressor (1). The second expansion valve (5) is located at the inlet end of the gas supply branch.

2. The gas-replenishing enthalpy-increasing heat pump system as described in claim 1, characterized in that: The gas replenishment branch also includes a heat absorption pipe installed on the casing of the compressor (1). The outlet end of the gas replenishment branch is connected to the middle gas replenishment port of the compressor (1) through the heat absorption pipe. This is used to allow the refrigerant in the gas replenishment branch to enter the compressor (1) through the heat absorption pipe, thereby achieving a cooling effect on the compressor (1) and recovering heat energy.

3. The gas-replenishing enthalpy-increasing heat pump system as described in claim 1, characterized in that: An economizer (6) is provided between the main circuit and the gas supply branch. One end of the economizer (6) is connected to the main circuit, and the other end is connected to the second expansion valve (5) and the heat absorption pipe on the gas supply branch. It is used to utilize the heat of the main circuit to partially vaporize the refrigerant in the gas supply branch.

4. A multi-objective optimization method for entropy production in a gas-fuel-injection enthalpy-increasing heat pump system, based on the heat pump system as described in any one of claims 1 to 3, characterized in that: Includes the following steps, S1. Set up a heat pump system test bench and collect core thermodynamic parameters under stable operating conditions; S2. Establish the system entropy production model and the system performance coefficient calculation model, and use the parameters collected in S1 to correct the model; S3. Determine the control variables and security constraints with the goal of minimizing entropy production and maximizing system performance coefficients; S4. Data normalization processing and construction of a comprehensive evaluation function; S5. Use a non-dominated sorting genetic algorithm to iteratively find the optimal solution and output the Pareto optimal frontier. S6. Select control parameters according to actual needs, feed them back to the system for dynamic operation, and verify the adaptability under changing operating conditions.

5. The multi-objective optimization method for entropy production of a gas-injection enthalpy-increasing heat pump system as described in claim 4, characterized in that: In step S1, the condenser (2) and evaporator (4) on the test bench both use water bath heat exchange. A condensing side water tank (21) and a condensing side water pump (22) are provided on one side of the condenser (2). The condensing side water pump (22) is used to drive the heat exchange medium in the condensing side water tank (21) to exchange heat with the condenser (2).

6. The multi-objective optimization method for entropy production of a gas-replenishing enthalpy-increasing heat pump system as described in claim 4, characterized in that: In step S2, the system entropy production model includes a two-stage compressor (1) entropy production model for the first-stage compression process, an entropy production model for the gas injection evaporation process, an entropy production model for the gas injection mixing process, and an entropy production model for the second-stage compression process. The entropy production of each stage is calculated using the thermodynamic parameters of each stage and then summed to obtain the total entropy production of the system. During model correction, the error between the entropy production and system performance coefficients calculated by the model and the measured values ​​derived from the collected parameters in step S1 does not exceed the preset range.

7. The multi-objective optimization method for entropy production of a gas-injection enthalpy-increasing heat pump system as described in claim 5, characterized in that: In step S3, the controlled variables include the opening degree of the first expansion valve (3), the opening degree of the second expansion valve (5), and the flow rate of the condensate side water pump (22). Safety constraints include refrigerant dryness constraints at the gas inlet, superheat constraints at the compressor (1) suction, subcooling constraints at the condenser (2) outlet, intermediate gas injection pressure constraints, and compressor (1) efficiency constraints, which are used to avoid the risk of liquid slugging or overheating in the system.

8. The multi-objective optimization method for entropy production of a gas-replenishing enthalpy-increasing heat pump system as described in claim 4, characterized in that: In step S4, the data normalization process targets the total entropy production of the compression process and the system performance coefficients. The normalized data is uniformly mapped to the same standard interval. The comprehensive evaluation function is used to balance the two objectives of minimizing entropy production and maximizing system performance coefficients, and the priority of the two objectives is adjusted by setting weight coefficients.

9. The multi-objective optimization method for entropy production of a gas-replenishing enthalpy-increasing heat pump system as described in claim 4, characterized in that: In step S5, the non-dominated sorting genetic algorithm uses the NSGA-II algorithm, and outputs the Pareto optimal front when the iteration termination condition is reached.

10. The multi-objective optimization method for entropy production of a gas-replenishing enthalpy-increasing heat pump system as described in claim 4, characterized in that: In step S6, the selection of the optimal control parameters is based on a preset weight bias. The preset weights include stability weight and energy efficiency weight, and the sum of stability weight and energy efficiency weight is fixed. By adjusting the values ​​of stability weight and energy efficiency weight, one can switch between energy efficiency priority mode, stability priority mode, or a balanced mode of both.

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