Cascade high-temperature heat pump system based on low-gwp mixed working fluid and performance optimization method

Abstract

The application discloses a cascade high-temperature heat pump system based on low-GWP mixed working medium and a performance optimization method, and the system comprises a high-temperature cycle and a low-temperature cycle; the high-temperature cycle adopts a first non-azeotropic mixed working medium (R1233zd(E) / R1234ze(Z)), and the low-temperature cycle adopts a second non-azeotropic mixed working medium (R1234ze(E) / R245fa). When optimization is performed, a thermodynamic model is first constructed based on a Peng-Robinson state equation and a van der Waals co volume mixing rule; then, a Pareto optimal solution set is generated by using a non-dominated sorting genetic algorithm-II, with the maximization of COP, the minimization of compressor pressure ratio and the minimization of system GWP as the targets; finally, the optimal proportion of the working medium is screened out by using a TOPSIS method, and the application is suitable for high-temperature heat pump application scenarios such as industrial waste heat recovery. The cascade high-temperature heat pump system based on low-GWP mixed working medium and the performance optimization method with the above structure and steps aim to solve the technical problem that high efficiency and low environmental impact of the cascade high-temperature heat pump are difficult to balance.

Description

Technical Field

[0001] This invention relates to the field of heat pump technology, and in particular to a cascade high-temperature heat pump system based on a low-GWP mixed working fluid and a method for performance optimization. Background Technology

[0002] Cascade high-temperature heat pumps, with their tiered energy utilization characteristics of high and low temperature cycles, can effectively expand the operating temperature range of heat pumps and achieve efficient recovery of industrial waste heat. They have irreplaceable application value in fields such as industrial waste heat recovery, food processing and drying, and pharmaceutical sterilization. Their core advantages lie in their simple structure, high safety, and strong environmental adaptability, which can meet the high-temperature heating needs in multiple scenarios.

[0003] However, with the gradual implementation of global environmental regulations such as the Kigali Amendment, traditional refrigerants with high global warming potential (GWP) (such as R134a and R245fa) are being gradually restricted or phased out due to their significant impact on climate change. Cascade high-temperature heat pumps face a core technological bottleneck: "it is difficult to balance high efficiency with low environmental impact." On the one hand, although new-generation low-GWP pure working fluids (such as R1234yf and R1234ze(E)) meet environmental standards, when they directly replace traditional working fluids, the system's heating capacity and coefficient of performance (COP) generally decrease, making it difficult to meet the energy efficiency requirements for high-temperature heating. On the other hand, existing research on mixed working fluids focuses on single-cycle optimization and does not conduct precise ratio design for the wide-temperature-range operation characteristics of cascade high-temperature heat pumps. Furthermore, it lacks multi-objective synergistic optimization of COP, compressor pressure ratio, and GWP, leading to problems such as excessively high pressure ratio (causing compressor failure), excessive exhaust temperature (affecting equipment lifespan), and large energy loss (energy waste).

[0004] Furthermore, traditional cascade heat pump system designs often neglect the temperature glide characteristics of non-azeotropic working fluids, leading to poor matching between high- and low-temperature stages, excessively large temperature differences in intermediate heat exchangers, and further exacerbating energy losses. This makes it difficult to fully utilize the cascade energy utilization advantages of the cascade cycle. Therefore, there is an urgent need to develop a system performance optimization scheme that adapts to the operating conditions of cascade high-temperature heat pumps, while also considering low GWP, high COP, and safe operation, in order to overcome the limitations of existing technologies. Summary of the Invention

[0005] The purpose of this invention is to provide a cascade high-temperature heat pump system and its performance optimization method based on a low-GWP mixed working fluid. This invention improves the system's energy efficiency and environmental friendliness through thermodynamic modeling and multi-objective optimization algorithms. It is particularly suitable for non-azeotropic mixed working fluids with low global warming potential (GWP) and can be widely used in industrial and civilian scenarios requiring high-temperature heating, such as industrial waste heat recovery, food processing drying, and pharmaceutical sterilization.

[0006] To achieve the above objectives, the present invention provides a cascade high-temperature heat pump system based on a low-GWP mixed working fluid, comprising a high-temperature stage cycle, a low-temperature stage cycle, and an intermediate heat exchanger connecting the high-temperature stage cycle and the low-temperature stage cycle.

[0007] The high-temperature stage cycle uses a non-azeotropic mixture of R1233zd(E) / R1234ze(Z) working fluid, with a mass ratio of R1233zd(E) to R1234ze(Z) of 0.62:0.38.

[0008] The cryogenic stage cycle uses a non-azeotropic mixture of R1234ze(E) / R245fa working fluid, with a mass ratio of R1234ze(E) to R245fa of 0.45:0.55.

[0009] The intermediate heat exchanger has a heat transfer temperature difference of 5K, enabling energy exchange between the condensation and heat release of the low-temperature working fluid and the evaporation and heat absorption of the high-temperature working fluid.

[0010] Preferably, the high-temperature stage cycle includes a high-temperature side compressor, a high-temperature condenser, and a high-temperature side expansion valve; the low-temperature stage cycle includes a low-temperature side compressor, a low-temperature evaporator, a low-temperature side expansion valve, and a phase separator; the isentropic efficiency of both the high-temperature side compressor and the low-temperature side compressor is 0.75.

[0011] Preferably, the non-azeotropic working fluid used in the high-temperature stage cycle has a GWP ≤ 10, a combustion rate of 2.0-2.3 cm / s, and a safety level of A1 / A2L; the non-azeotropic working fluid used in the low-temperature stage cycle has a GWP ≤ 500, a combustion rate of 2.0-2.5 cm / s, and a safety level of A1 / A2L.

[0012] A performance optimization method for a cascade high-temperature heat pump system based on a low-GWP mixed working fluid, wherein the cascade high-temperature heat pump system includes a high-temperature stage cycle and a low-temperature stage cycle, the high-temperature stage cycle uses a first non-azeotropic mixed working fluid, and the low-temperature stage cycle uses a second non-azeotropic mixed working fluid. The optimization method includes the following steps:

[0013] S1. Constructing a thermodynamic model: Based on the Peng-Robinson equation of state and the van der Waalsco volume mixing rule, a thermodynamic model of the cascade high-temperature heat pump system is established. The thermodynamic model is used to calculate the system's thermodynamic parameters and core performance indicators. The thermodynamic parameters include the working fluid's pressure, temperature, enthalpy, and molar volume. The core performance indicators include the coefficient of performance (COP), compressor pressure ratio, total global warming potential (GWP), and compressor exhaust temperature.

[0014] S2. Set multi-objective optimization and constraints: take maximizing energy parameter COP, minimizing compressor pressure ratio, and minimizing GWP as objective functions, and take the compressor exhaust temperature not exceeding a preset temperature threshold and the compressor pressure ratio not exceeding a preset pressure ratio threshold as constraints, and determine the mass fraction of the first component in the first non-azeotropic working fluid and the mass fraction of the second component in the second non-azeotropic working fluid as optimization variables.

[0015] S3, NSGA-II Algorithm Optimization: Using the NSGA-II algorithm, with the optimization variables as input, the optimization objective value corresponding to each set of optimization variables is calculated based on the thermodynamic model. Iterative optimization is performed through non-dominated sorting, crowding calculation and elite retention strategy to generate the Pareto optimal solution set.

[0016] S4. Optimal Solution Selection: The Pareto optimal solution set is comprehensively evaluated using the TOPSIS method. Based on the preset weight allocation rules, the closeness between each candidate solution and the positive ideal solution is calculated. The candidate solution with the largest closeness is selected as the optimal solution. The optimal solution corresponds to the optimal mass ratio of the first non-azeotropic working fluid and the second non-azeotropic working fluid.

[0017] Preferably, S1 constructs a thermodynamic model, specifically including:

[0018] S1.1 Describe the thermodynamic properties of the mixed working fluid under different temperatures and pressures using the Peng-Robinson equation of state;

[0019] For mixing on both the high-temperature and low-temperature sides, the Peng-Robinson equation of state is expressed as follows:

[0020] (1)

[0021] in, P Pressure, unit: ; R This is the universal gas constant. ; Volume is the molar volume, in units of ; Temperature, unit: K ;

[0022] a represents the gravitational term, and b represents the co-volume term, expressed as follows;

[0023] (2)

[0024] (3)

[0025] (4)

[0026] (5)

[0027] in, The critical pressure is expressed in Pa. The critical temperature is K; It is the eccentricity factor;

[0028] S1.2 For non-azeotropic working fluids, calculate the overall gravitational term using van der Waalsco's volume mixing rule. Concordance volume term It corrects deviations in the equation of state for pure working fluids and adapts to the non-ideal thermodynamic behavior of mixed working fluids.

[0029] Gravitational term Concordance volume term The calculation formula is as follows:

[0030] (6)

[0031] (7)

[0032] (8)

[0033] in, This represents the mole fraction of each component in the mixed working fluid; The coefficient represents the binary interaction coefficient. These are the fitting parameters; and These are the gravitational term and co-volume term for component i, respectively;

[0034] S1.3 Calculate the system's energy performance parameters, including heating capacity, power consumption, and COP;

[0035] High-temperature side heating With power consumption They are represented as follows:

[0036] (9)

[0037] (10)

[0038] The power consumption on the low-temperature side is expressed as:

[0039] (11)

[0040] In the formula: This refers to the circulating flow rate of the working fluid on the high-temperature side. This refers to the enthalpy value at the outlet of the high-temperature side compressor. The enthalpy at the outlet of the high-temperature condenser represents the isentropic throttling process. , This refers to the enthalpy value at the evaporator inlet. This refers to the circulating flow rate of the working fluid on the low-temperature side. This refers to the enthalpy value at the outlet of the low-temperature compressor. This refers to the enthalpy value at the evaporator outlet. The compressor has isentropic efficiency;

[0041] System performance coefficient The calculation formula is:

[0042] (12)

[0043] S1.4. Assess the safety of the working fluid mixture by calculating the combustion rate;

[0044] The formula for calculating the combustion rate of a mixed working fluid is:

[0045] (13)

[0046] in, The combustion rate of the working fluid. Let i be the combustion rate of the i-th pure working fluid. Let i be the mass fraction of the i-th pure working fluid;

[0047] S1.5. Evaluate the environmental performance of the system by calculating GWP;

[0048] The formula for calculating the GWP of a mixed working fluid is:

[0049] (14)

[0050] in, GWP for a certain level of mixed working fluid, Let i be the mass fraction of the i-th working fluid. Let GWP be the value of the i-th working fluid;

[0051] The formula for calculating the total GWP of the system is:

[0052] (15)

[0053] (16)

[0054] in, These are the circulation flow rates on the high-temperature side and the low-temperature side, respectively. This refers to the enthalpy of the working fluid at the outlet of the intermediate heat exchanger on the low-temperature side. This represents the enthalpy difference of the low-temperature working fluid in the intermediate heat exchanger. This refers to the enthalpy of the working fluid at the outlet of the high-temperature side throttle valve. This represents the enthalpy difference of the high-temperature working fluid in the intermediate heat exchanger.

[0055] S1.6. Quantify the irreversible losses of each component of the system through analysis;

[0056] The reference ambient temperature is set to T = 293.15 K, the reference atmospheric pressure is P = 101.325 kPa, and the enthalpy of the working fluid under ambient conditions is... Entropy The value of for any state point j The calculation formula is:

[0057] (17)

[0058] in, The flow path of the working fluid passing through state point j is as follows: Let J be the enthalpy of the working fluid at state point j. Let be the entropy value of the working fluid at state point j;

[0059] Value flowing through the evaporator Represented as:

[0060] (18)

[0061] Value flowing through the condenser Represented as:

[0062] (19)

[0063] in, and These are the condensation temperatures of the working fluid in the evaporator and condenser, respectively. and The heat transfer temperature difference between the condenser and the evaporator is set to 5K;

[0064] The loss of each component in the system is expressed as:

[0065] (20)

[0066] in, For compressor damage, The inlet working fluid temperature of the compressor is 0.5%. The working fluid output value of the compressor. Input power to the compressor;

[0067] (twenty one)

[0068] in, For condenser losses, , These are the inlet and outlet temperatures of the high-temperature working fluid in the condenser, respectively. , These are the values ​​of the fluid inlet and outlet of the condenser on the user side, respectively.

[0069] (twenty two)

[0070] in, For evaporator losses, , These are the temperatures of the low-temperature working fluid entering and exiting the evaporator, respectively. , These are the values ​​of the low-grade heat source fluid entering and exiting the evaporator, respectively.

[0071] (twenty three)

[0072] in, Losses due to intermediate heat exchangers , These are the inlet and outlet temperatures of the high-temperature working fluid in the intermediate heat exchanger, respectively. , These are the temperatures of the low-temperature working fluid entering and exiting the intermediate heat exchanger, respectively.

[0073] (twenty four)

[0074] in, For the loss of the throttle valve, The inlet working fluid temperature of the throttle valve is [value missing]. The value of the working fluid at the outlet of the throttle valve.

[0075] Preferably, in step S2, the range of values ​​for the optimization variables is as follows: the mass fraction of the first component in the first non-azeotropic working fluid is 0.3-0.9, and the mass fraction of the second component in the second non-azeotropic working fluid is 0.2-0.6; wherein, when the mass fraction of the first component is below 0.3, the high-temperature stage circulating pressure ratio exceeds the preset pressure ratio threshold, and when it is above 0.9, the system COP decreases; when the mass fraction of the second component is below 0.2, the total system GWP exceeds 500, and when it is above 0.6, the low-temperature stage circulating volumetric cooling capacity decreases.

[0076] Preferably, in step S3, the parameters of the NSGA-II algorithm are set as follows: population size of 100 individuals, number of iterations of 60 generations, crossover probability of 0.8-0.9, and mutation probability of 0.01-0.03; during the iteration process, when the average COP change of the Pareto optimal solution set for 10 consecutive generations is less than 0.01, the algorithm is determined to have converged.

[0077] Preferably, in step S4, the preset weight allocation rule is as follows: performance coefficient COP weight 0.5, compressor pressure ratio weight 0.2, system total GWP weight 0.2, and compressor exhaust temperature weight 0.1; the positive ideal solution is the set of indicators with maximum COP, minimum pressure ratio, minimum GWP, and minimum exhaust temperature.

[0078] Preferably, the first non-azeotropic working medium is a combination of R1233zd(E) and R1234ze(Z), and the second non-azeotropic working medium is a combination of R1234ze(E) and R245fa; the first component is R1233zd(E), and the second component is R1234ze(E).

[0079] Preferably, the performance indicators corresponding to the optimal solution selected in step S4 are: system COP≥4.1, compressor pressure ratio≤3.3, system total GWP≤220, and compressor discharge temperature≤116℃; the optimal mass ratio of the first non-azeotropic working fluid is R1233zd(E):R1234ze(Z)=0.62:0.38, and the optimal mass ratio of the second non-azeotropic working fluid is R1234ze(E):R245fa=0.45:0.55.

[0080] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0081] 1. Significantly improved environmental performance: The high-temperature stage uses a non-azeotropic mixture of R1233zd (E) / R1234ze (Z) working fluid, and the low-temperature stage uses a non-azeotropic mixture of R1234ze (E) / R245fa working fluid. Each component of both types of working fluid has low GWP characteristics. After optimization of the ratio, the total GWP of the system can meet the requirements of the Kigali Amendment and F-Gas regulations for low environmental impact working fluids, realize low-carbon operation of the heat pump system throughout its entire life cycle, and meet the global green and low-carbon development needs.

[0082] 2. Significantly Optimized Energy Efficiency: The non-azeotropic working fluid inherently possesses temperature glide characteristics, effectively reducing the temperature difference within the heat exchanger and minimizing heat loss during the heat transfer process. The optimal ratio of the working fluid on the high and low temperature sides was obtained using the NSGA-II multi-objective optimization algorithm, resulting in ratios of 0.62:0.38 and 0.45:0.55, respectively. Under these ratios, the system COP reaches 4.12, the pressure ratio decreases to 3.2, and the exhaust temperature is controlled below 115℃, fully meeting safety constraints. Compared to the traditional R245fa / R134a pure working fluid system, the optimized system exhibits a 27.2% increase in COP and a 69.0% reduction in GWP, demonstrating superior overall performance.

[0083] 3. Reliable operational safety performance: Through multi-objective optimization, the compressor pressure ratio and exhaust temperature are strictly constrained. After optimization, the pressure ratio is controlled within the safety threshold to avoid problems such as decreased volumetric efficiency and mechanical fatigue caused by high pressure. The exhaust temperature is lower than the critical value of carbonization of the lubricating medium, ensuring long-term stable operation of the compressor. At the same time, the combustion rate of the mixed working fluid is lower than the safety limit, and the safety level reaches A1 / A2L, meeting the safety requirements of industrial scenarios.

[0084] 4. Strong adaptability to a wide range of operating conditions: The system performance is stable and the COP decay is gradual within a wide range of condensing temperature (70-100℃) and evaporating temperature (20-35℃). When the intermediate temperature fluctuates, the heat loss changes little. It can adapt to the high-temperature heating needs of different heat sources such as industrial waste heat recovery, food processing drying, and pharmaceutical sterilization, thus broadening the application scope of cascade high-temperature heat pumps.

[0085] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0086] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0087] Figure 1 This is a schematic diagram of a cascade high-temperature heat pump system according to an embodiment of the present invention;

[0088] Figure 2 This is a pressure-enthalpy diagram of a cascade high-temperature heat pump system based on a low-GWP mixed working fluid according to an embodiment of the present invention;

[0089] Figure 3 This is a comparison chart of the pressure ratios of different combinations of working fluids in embodiments of the present invention;

[0090] Figure 4 This is a comparison diagram of GPW with different combinations of working fluids according to embodiments of the present invention;

[0091] Figure 5 This is a comparison diagram of the COP of different combinations of working fluids in embodiments of the present invention;

[0092] Figure 6 This is a graph showing the variation of condensation pressure with condensation temperature for different components in an embodiment of the present invention.

[0093] Figure 7 This is a graph showing the variation of high-temperature working fluid condensation pressure with condensation temperature for different components in an embodiment of the present invention.

[0094] Figure 8 This is a graph showing the variation of the condensation pressure of the low-temperature working fluid with condensation temperature for different components in an embodiment of the present invention.

[0095] Figure 9 This is a graph showing the change in calorific value per unit volume of the high-temperature working fluid with condensation temperature for different components in an embodiment of the present invention.

[0096] Figure 10 This is a graph showing the change in calorific value per unit volume of the low-temperature working fluid with condensation temperature for different components in an embodiment of the present invention.

[0097] Figure 11 This is a graph showing the variation of exhaust temperature of the low-temperature working fluid with evaporation temperature for different components in an embodiment of the present invention.

[0098] Figure 12 This is a graph showing the variation of exhaust temperature of the high-temperature working fluid with condensation temperature for different components in an embodiment of the present invention.

[0099] Figure 13 This is a graph showing the change in evaporation pressure of the high-temperature working fluid with evaporation temperature for different components in an embodiment of the present invention. Detailed Implementation

[0100] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0101] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0102] Example

[0103] This embodiment applies the proposed cascade high-temperature heat pump system and performance optimization method based on a low-GWP mixed working fluid to an industrial waste heat recovery scenario with a low heat source temperature of 35°C and a target heating temperature of 100°C.

[0104] I. System Configuration

[0105] like Figure 1As shown, the cascade high-temperature heat pump system based on low-GWP mixed working fluid consists of a high-temperature stage cycle (HTC) and a low-temperature stage cycle (LTC). The two cycles are independent of each other and are connected by an evaporator-condenser. The evaporator-condenser acts as an evaporator in the high-temperature stage cycle and as a condenser in the low-temperature stage cycle. The high-temperature stage working fluid is throttled by a throttling valve and exchanges heat with the low-temperature stage working fluid discharged from the low-temperature compressor in the evaporator-condenser. The low-temperature stage working fluid condenses into a liquid state, and the high-temperature stage working fluid evaporates into a gaseous state. Figure 1 and Figure 2 In the diagram, 1-8 represent refrigerant state points, where 1-2-3-4 belong to the low-temperature stage cycle, and 5-6-7-8 belong to the high-temperature stage cycle. The core system parameters are as follows:

[0106] Working fluid combination: The high-temperature stage uses a non-azeotropic mixture of R1233zd (E) / R1234ze (Z) working fluid, and the low-temperature stage uses a non-azeotropic mixture of R1234ze (E) / R245fa working fluid;

[0107] Operating parameters: Low-temperature side working fluid evaporation temperature 35℃, high-temperature side working fluid condensation temperature 100℃, intermediate heat exchanger heat transfer temperature difference 5K, high and low temperature side compressor isentropic efficiency of 0.75; high-temperature stage mixed working fluid GWP≤10, combustion speed 2.0-2.3cm / s (safety level A1 / A2L), low-temperature stage mixed working fluid GWP≤500, combustion speed 2.0-2.5cm / s (safety level A1 / A2L).

[0108] Constraints: Maximum compressor pressure ratio ≤ 3.5, maximum discharge temperature ≤ 120℃, mass fraction of R1233zd(E) on the high-temperature side 0.3-0.9, mass fraction of R1234ze(E) on the low-temperature side 0.2-0.6.

[0109] The performance optimization method for a cascade high-temperature heat pump system based on a low-GWP mixed working fluid includes the following steps:

[0110] II. Performance Optimization Methods

[0111] The key steps and calculation results of the performance optimization method for cascade high-temperature heat pump systems based on low-GWP mixed working fluids are as follows:

[0112] S1: Thermodynamic Model Construction: The thermodynamic properties of the working fluid are described based on the Peng-Robinson equation of state (Equation 1-5). The parameters of the mixed working fluid are corrected by the van der Waals volume mixing rule (Equation 6-8). The system's heating capacity, power consumption (Equation 9-11), COP (Equation 12), combustion rate (Equation 13), GWP (Equation 14-16), and component losses (Equation 17-24) are calculated in sequence to complete the model construction.

[0113] S2: Multi-objective optimization and constraint setting: With the objectives of maximizing COP, minimizing pressure ratio, and minimizing GWP, the optimization variables are set as the mass fraction of R1233zd (E) on the high temperature side (0.3-0.9) and the mass fraction of R1234ze (E) on the low temperature side (0.2-0.6), with constraints of pressure ratio ≤3.5 and exhaust temperature ≤120℃.

[0114] S3: NSGA-II Algorithm Optimization: Assume a population size of 100, 60 iterations, a crossover probability of 0.85, and a mutation probability of 0.02. Generate the Pareto optimal solution set through non-dominated sorting and elite retention strategy iteration. When the average COP change of the Pareto solution set for 10 consecutive generations is <0.01, the algorithm is considered to have converged.

[0115] S4: Optimal solution selection: The TOPSIS method was used to calculate the closeness, and the weight ratios were set as follows: COP=0.5, pressure ratio=0.2, GWP=0.2, exhaust temperature=0.1. The optimal ratios were selected as follows: high temperature stage R1233zd(E) / R1234ze(Z) (0.62:0.38), low temperature stage: R1234ze(E) / R245fa (0.45:0.55).

[0116] III. Comparative Experiments with Other Mixed Working Media

[0117] To verify the advantages of the working fluid combination and optimization method of the present invention, three sets of comparative working fluid combinations were set up (covering traditional working fluid, environmentally friendly pure working fluid, and non-optimized mixed working fluid), specifically:

[0118] The working fluid combination of the present invention is as follows: Combination 1: high temperature side R1233zd(E) / R1234ze(Z) (0.62:0.38), low temperature side: R1234ze(E) / R245fa (0.45:0.55);

[0119] Traditional working fluid, combination 2: high temperature side R245fa (pure), low temperature side R134a (pure).

[0120] Pure environmentally friendly working fluid, combination 3: high temperature side R1233zd(E) (pure), low temperature side R1234ze(E) (pure)

[0121] Non-optimized mixed working fluid combination, combination 4: high temperature side R1234ze(Z) / R245fa (0.6:0.4), low temperature side R1234ze(E) / R600a (0.5:0.5).

[0122] 1. Analysis of pressure ratio, GWP, and COP

[0123] The above combination was applied to a cascade heat pump under the same operating conditions (evaporation temperature 35℃, condensation temperature 100℃). Using MATLAB, the Refprop generator was called to generate the changes in COP, pressure ratio, and GWP based on the proportions and properties of each working fluid. The specific pressure ratio of each component was also calculated. Figure 3 As shown, GWP changes are as follows Figure 4 As shown.

[0124] Combination 2 uses a pure working fluid of R245fa and R134a, with a pressure ratio as high as 3.8, far exceeding the reasonable threshold for stable operation of the equipment. This causes the compressor to face excessively high discharge pressure during operation, which can easily lead to problems such as increased equipment vibration and leakage of sealing components. Long-term continuous operation will significantly increase the risk of mechanical fatigue failure, posing a serious challenge to the reliability of the system. At the same time, the GWP value of this combination reaches 1048.0, which is far from the current F-Gas regulations' stringent low-carbon requirements for heat pump working fluids (GWP must be ≤150), and has an essential defect in environmental compliance, making it difficult to adapt to the development needs of green energy equipment under the "dual carbon" target.

[0125] Combination 3 uses a pure working fluid combination of R1233zd(E) and R1234ze(E). Although its pressure ratio (2.8) and GWP (1.0) show relative advantages and demonstrate certain low-carbon potential, it lacks temperature glide capability due to the inherent characteristics of a single working fluid. During the operation of a cascade heat pump, the condensing and evaporating temperatures of the variable-temperature heat source are in a dynamic state. A single working fluid cannot effectively adapt to this dynamic heat source, and "local overcooling or overheating" is very likely to occur, making it difficult to ensure stable heating of the system over a wide operating range. Moreover, the excessively low pressure ratio deviates from the optimal range of cycle efficiency, which significantly restricts the volumetric efficiency of the compressor, greatly limiting further improvement of cycle energy efficiency and failing to meet the actual demand of the heat pump system for high-efficiency heating.

[0126] Combination 4 uses a mixed working fluid scheme of R1234ze(Z), R245fa, R1234ze(E) and R600a, with a pressure ratio of 3.5 and a GWP of 218.93. Although the pressure ratio barely meets the program's threshold limit and has a certain theoretical basis for adaptation, the working fluid ratio has not been iteratively corrected by precise optimization methods such as the NSGA-II algorithm. As a result, the temperature glide characteristics and the adaptability to the variable temperature heat source are poor, leading to irreversible losses in the heat transfer process that are 8%-12% higher than those of the optimized combination. In addition, the introduction of the flammable working fluid R600a on the low-temperature side requires the addition of safety redundancy designs such as leak detection and explosion-proof pressure drop compensation to meet the requirements of safe operation. This undoubtedly increases the flow resistance of the system and further drags down the cycle efficiency, resulting in a significant reduction in the energy efficiency performance of this combination in practical applications.

[0127] In contrast, the optimized mixed working fluid scheme of Combination 1 in this application controls the pressure ratio at 3.2 and the GWP at 160.08. Utilizing the synergistic mechanism of "temperature glide adaptation + precise algorithm control," on the one hand, the 3-5℃ temperature glide characteristic naturally possessed by the non-azeotropic working fluid enables precise matching with the variable-temperature heat source, effectively reducing irreversible losses during heat transfer; on the other hand, through the NSGA-II algorithm, iterative optimization of the working fluid ratio on the high-temperature side (0.62:0.38) and the low-temperature side (0.45:0.55), as well as the intermediate heat exchange temperature difference (2-3℃), etc., ensures equipment safety (the pressure ratio is at a balance between the equipment's safe load ≤3.5 and the optimal cycle efficiency range of 3.0-3.5, avoiding high-pressure risks to the compressor), while greatly improving the synergistic optimization level of volumetric efficiency and compression work. This achieves a multi-objective balance of safe equipment operation, compliance with environmental standards, and optimal energy efficiency, deeply aligning with the energy development needs guided by the "dual carbon" goal.

[0128] The results of the comparative study on the coefficient of performance (COP) of the four cascade heat pump working fluid combinations under the same operating conditions are as follows: Figure 5 As shown, combination 1 (the optimized non-azeotropic working fluid mixture) exhibits the highest COP value, while the COP of combinations 2, 3, and 4 are reduced by 27.2%, 15.0%, and 7.8%, respectively, showing a decreasing energy efficiency trend of "optimized working fluid > non-optimized working fluid > environmentally friendly pure working fluid > traditional pure working fluid". The core reason for this phenomenon is that combination 1, through the good matching between the 3–5℃ temperature glide of the non-azeotropic working fluid and the variable temperature heat source, and the NSGA-II algorithm for the synergistic optimization of the ratio and cycle parameters, reduces the logarithmic mean temperature difference (LMTD) of heat transfer to 2–3℃ and reduces compression work by 5%–7%, thereby minimizing irreversible losses in heat transfer and flow processes. In contrast, the pure working fluid combinations (combinations 2 and 3) have a fixed phase change temperature and an inherent heat exchange temperature difference of 5–8°C with the variable-temperature heat source, resulting in a significant increase in irreversible losses. Although combination 4 is a mixed working fluid, the ratio has not been fully optimized, causing a mismatch between the temperature glide and the heat source. In addition, the safety redundancy design brought about by the introduction of R600a on the low-temperature side has a negative impact on energy efficiency. Therefore, its irreversible losses are still higher than those of combination 1.

[0129] 2. Multi-objective optimization analysis of different mixed working fluids

[0130] A cascade heat pump consists of a high-temperature cycle and a low-temperature cycle coupled through an intermediate heat exchanger: the refrigerant on the low-temperature side condenses and releases heat in the intermediate heat exchanger, and this heat is absorbed by the refrigerant on the high-temperature side. Changes in the condensation temperature not only directly affect the operating pressure and heat exchange efficiency of the high-temperature side, but also are transferred to the low-temperature side through the intermediate heat exchange process, thus affecting its evaporation temperature and pressure.

[0131] First, the impact of condensation temperature variation on the overall system performance index COP was evaluated. Within the condensation temperature range of 70–100℃, the COP curves for the four working fluid combinations as a function of condensation temperature are shown below. Figure 6 As shown.

[0132] As the condensation temperature increases, the system COP generally shows a downward trend. This is because the increased condensation temperature leads to a larger temperature difference between the working fluid and the heat sink, increasing the power consumption during compression and reducing the heating effect, which conforms to the second law of thermodynamics. The magnitude and rate of COP decrease vary significantly among different working fluid combinations. For example, combination 1 has a higher COP than combination 2 at all condensation temperatures, indicating that it has a better energy conversion efficiency. This is due to its thermodynamic properties (such as critical temperature and phase change characteristics) being more compatible with the cascade system, reducing irreversible losses during compression and heat exchange.

[0133] Next, the impact of condensing temperature on parameters such as heating capacity per unit volume, condensing pressure, and exhaust temperature was evaluated. These parameters are closely related to the physical properties of the working fluid itself, and the performance of the working fluid on both the high and low temperature sides needs to be examined separately. Therefore, this embodiment analyzed eight combinations of the above four combinations, four groups of working fluids each on the high and low temperature sides. The eight combinations are as follows:

[0134]

[0135] Through high-temperature side condensation pressure data set ( Figure 7 It can be seen that within the condensing temperature range of 80-110℃, the condensing pressure of combination 1 (R1233zd(E) / R1234ze(Z)=0.62:0.38) is consistently lower than that of other working fluid combinations on the high-temperature side (combinations 3, 5, and 7), especially maintaining a reasonable pressure level under the high condensing temperature condition of 110℃. This makes it compatible with the pressure range of mainstream high-temperature heat pump compressors, effectively reducing equipment operating energy consumption and design costs. Further analysis of the high-temperature side unit volume heating capacity data group (…) Figure 9 Under the same condensing temperature conditions, combination 1 shows a significantly improved heating capacity per unit volume, outperforming combination 3 (R245fa pure working fluid) and combination 7 (R1234ze (Z) / R245fa=0.6:0.4) across the entire operating range of 80-110℃, and only slightly lower than combination 5 (R1233zd (E) pure working fluid), but with a more balanced overall thermodynamic performance. (From the high-temperature side exhaust temperature data group...) Figure 12 Analysis shows that the exhaust temperature of combination 1 is consistently lower than that of combination 3 and combination 7 in the range of 80-110℃, and is far from the safe operating threshold of the compressor, providing sufficient safety margin for the long-term stable operation of the system.

[0136] Low-temperature side unit volume heat production data set ( Figure 10The data shows that within the evaporation temperature range of 15-50℃, the volumetric heating capacity of combination 2 (R1234ze (E) / R245fa=0.45:0.55) continuously improves, significantly outperforming the traditional pure working fluid combination 4 (R134a), and its heating capacity is close to that of combination 8 (R1234ze (E) / R600a=0.5:0.5), while avoiding the combustion and explosion safety risks associated with combination 8 due to the presence of R600a. Based on the low-temperature side exhaust temperature data group (… Figure 11 The exhaust temperature of combination 2 is lower than that of combination 4 and combination 8 in the entire operating range of 15-50℃, and its advantage is more prominent under low evaporation temperature conditions, which helps to reduce the operating load of the compressor and improve the reliability of equipment operation.

[0137] The core synergistic advantage is reflected in the high-temperature side evaporation pressure data set ( Figure 13 ) and low-temperature side condensing pressure data set ( Figure 8 In this system, at the optimal design temperature of 45℃ for the intermediate heat exchanger, the evaporation pressure of combination 1 and the condensation pressure of combination 2 are highly compatible, with a very small pressure difference, which is far superior to the matching effect of other working fluid combinations. This allows the heat transfer temperature difference of the intermediate heat exchanger to be controlled within the optimal range, significantly reducing irreversible heat transfer losses and improving the system's circulation efficiency.

[0138] In summary, the non-azeotropic working fluid combination of combination 1 and combination 2 exhibits excellent thermodynamic performance in terms of high-temperature side condensing pressure, heating capacity per unit volume, and exhaust temperature data, as well as low-temperature side heating capacity per unit volume and exhaust temperature data. Furthermore, through precise matching of the high-temperature side evaporation pressure and low-temperature side condensing pressure data, the system achieves synergistic optimization. It comprehensively possesses the core characteristics of high-efficiency heating, safety and stability, and strong system adaptability, providing an ideal working fluid solution for cascade heat pump systems.

[0139] The remaining technical features in the above embodiments can be flexibly selected by those skilled in the art to meet different specific practical needs according to actual circumstances. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims. In the above description, numerous specific details have been set forth to provide a thorough understanding of the present invention. However, it will be apparent to those skilled in the art that these specific details are not necessary to implement the present invention. In other instances, to avoid obscuring the present invention, well-known techniques, such as specific construction details, operating conditions, and other technical conditions, have not been specifically described.

[0140] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A performance optimization method for a cascade high-temperature heat pump system based on a low-GWP mixed working fluid, characterized in that, The cascade high-temperature heat pump system includes a high-temperature stage cycle and a low-temperature stage cycle, as well as an intermediate heat exchanger connecting the high-temperature stage cycle and the low-temperature stage cycle. The high-temperature stage cycle uses a first non-azeotropic working fluid, and the low-temperature stage cycle uses a second non-azeotropic working fluid. The optimization method includes the following steps: S1. Constructing a thermodynamic model: Based on the Peng-Robinson equation of state and the van der Waalsco volume mixing rule, a thermodynamic model of the cascade high-temperature heat pump system is established, and the thermodynamic parameters and core performance indicators of the thermodynamic model are calculated. The thermodynamic parameters include the pressure, temperature, enthalpy, and molar volume of the working fluid, and the core performance indicators include the coefficient of performance (COP), compressor pressure ratio, total global warming potential (GWP) of the system, and compressor exhaust temperature. S2. Set multi-objective optimization and constraints: With the performance parameters COP maximized, compressor pressure ratio minimized, and GWP minimized as objective functions, and the compressor exhaust temperature not exceeding a preset temperature threshold and the compressor pressure ratio not exceeding a preset pressure ratio threshold as constraints, determine the mass fraction of the first component in the first non-azeotropic working fluid and the mass fraction of the second component in the second non-azeotropic working fluid as optimization variables; the first non-azeotropic working fluid is a combination of R1233zd(E) and R1234ze(Z), and the second non-azeotropic working fluid is a combination of R1234ze(E) and R245fa; the first component is R1233zd(E), and the second component is R1234ze(E); S3, NSGA-II Algorithm Optimization: Using the NSGA-II algorithm, with the optimization variables as input, the optimization objective value corresponding to each set of optimization variables is calculated based on the thermodynamic model. Iterative optimization is performed through non-dominated sorting, crowding calculation and elite retention strategy to generate the Pareto optimal solution set. S4. Optimal Solution Selection: The Pareto optimal solution set is comprehensively evaluated using the TOPSIS method. Based on the preset weight allocation rules, the closeness between each candidate solution and the positive ideal solution is calculated. The candidate solution with the largest closeness is selected as the optimal solution. The optimal solution corresponds to the optimal mass ratio of the first non-azeotropic working fluid and the second non-azeotropic working fluid.

2. The performance optimization method for a cascade high-temperature heat pump system based on a low-GWP mixed working fluid according to claim 1, characterized in that: In step S2, the range of values ​​for the optimization variables is: the mass fraction of the first component in the first non-azeotropic working fluid is 0.3-0.9, and the mass fraction of the second component in the second non-azeotropic working fluid is 0.2-0.

6.

3. The performance optimization method for a cascade high-temperature heat pump system based on a low-GWP mixed working fluid according to claim 2, characterized in that: In step S3, the parameters of the NSGA-II algorithm are set as follows: population size of 100 individuals, number of iterations of 60 generations, crossover probability of 0.8-0.9, and mutation probability of 0.01-0.

03. During the iteration process, when the average COP change of the Pareto optimal solution set for 10 consecutive generations is less than 0.01, the algorithm is considered to have converged.

4. The performance optimization method for a cascade high-temperature heat pump system based on a low-GWP mixed working fluid according to claim 3, characterized in that: In step S4, the preset weight allocation rule is as follows: performance coefficient COP weight 0.5, compressor pressure ratio weight 0.2, system total GWP weight 0.2, and compressor exhaust temperature weight 0.1; the positive ideal solution is the set of indicators with maximum COP, minimum pressure ratio, minimum GWP, and minimum exhaust temperature.

5. The performance optimization method for a cascade high-temperature heat pump system based on a low-GWP mixed working fluid according to claim 4, characterized in that: The performance indicators corresponding to the optimal solution selected in step S4 are: system COP≥4.1, compressor pressure ratio≤3.3, system total GWP≤220, and compressor discharge temperature≤116℃; the optimal mass ratio of the first non-azeotropic working fluid is R1233zd(E):R1234ze(Z)=0.62:0.38, and the optimal mass ratio of the second non-azeotropic working fluid is R1234ze(E):R245fa=0.45:0.55.

Images