Joint simulation method of air-supply enthalpy-increase cascade type steam heat pump based on model predictive control

Abstract

The invention discloses a model predictive control-based joint simulation method for a gas-supplementing and enthalpy-increasing cascade steam heat pump, and belongs to the technical field of gas-supplementing and enthalpy-increasing cascade steam heat pumps. The method comprises the following steps: S1, establishing a dynamic model of each component of the gas-supplementing enthalpy-increasing cascade steam heat pump; s2, connecting all parts according to a unified interface to form a system overall dynamic model, and performing dynamic simulation; s3, the dynamic simulation data of the air-supplementing and enthalpy-increasing cascade type steam heat pump system is applied, and multi-output and multi-input state space model identification is carried out; s4, using the identified state space model as a prediction model, and developing a model prediction controller MPC; the behavior of the system in a period of time in the future is predicted, the optimal control input is solved through an optimization method, and real-time and accurate control over the system is achieved. According to the invention, when the system deals with external load change and working condition change, the operation safety of the system is maintained while rapid and accurate load tracking and temperature control are realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of air-injection enthalpy-increasing cascade steam heat pumps, and in particular relates to a joint simulation method of air-injection enthalpy-increasing cascade steam heat pumps based on model predictive control. Background Art

[0002] The VI-CSHP (Ventilation-Injection Cascade Steam Heat Pump) is an energy-boosting device that transfers heat from a low-temperature heat source to a high-temperature heat source by consuming a small amount of external energy. Compared to other types of heat pumps, the VI-CSHP boasts advantages such as wide temperature range adaptability, high energy conversion efficiency, and robustness against fluctuating operating conditions. It is widely considered a highly promising heat pump technology. Based on these advantages, the VI-CSHP has been applied in various practical engineering fields, such as the chemical industry, residential heating, and food processing.

[0003] Since the VI-CSHP system is a typical thermoelectric strongly coupled nonlinear system, it involves complex processes such as fluid flow, heat transfer, electrochemical reactions, and reforming reactions. This results in significant dynamic characteristics in the operation of the VI-CSHP system, with problems such as significant overshoot, dynamic response hysteresis, and insufficient anti-interference ability, making it difficult to meet the requirements of high-precision control. When the external load changes, if the dynamic response of the internal steam temperature and the flash tank hot water temperature lags behind the power response, the VI-CSHP performance and life will be reduced, or even fail. Therefore, in actual operation, the VI-CSHP system needs to respond quickly to external load changes while maintaining safe operation. This means that the safe and stable application of the VI-CSHP system not only requires a high-precision, easily scalable and portable numerical simulation model of the heat pump system, but also requires the design of a set of efficient and economical control methods.

[0004] For the VI-CSHP system, a strongly coupled thermoelectric system, the strong coupling characteristics of the internal parameters of the system further aggravate the control difficulty, and there is an urgent need to explore advanced control strategies that combine dynamic optimization and robust adaptability. Summary of the Invention

[0005] To address the challenges of existing technologies, this paper provides a co-simulation method for a cascade steam heat pump with air injection and enthalpy increase, based on model predictive control. By establishing a unified, high-precision VI-CSHP system across multiple domains and designing an efficient intelligent control method for the system, this co-simulation method is applied to control the VI-CSHP steam temperature and the flash tank hot water temperature. This ensures that the system maintains operational safety while achieving rapid and accurate load tracking and temperature control in response to changes in external loads and operating conditions.

[0006] To solve the above technical problems, the present invention provides the following technical solution: a joint simulation method of a cascade steam heat pump with air injection and enthalpy increase based on model predictive control, comprising the following steps:

[0007] S1. Based on the heat transfer mechanism, establish the dynamic model of each component of the cascade steam heat pump with air injection and enthalpy increase;

[0008] S2. Connect all components according to the unified interface to form the overall dynamic model of the system and perform dynamic simulation;

[0009] S3. Apply dynamic simulation data of the air-injection enthalpy-increasing cascade steam heat pump system to perform multi-output and multi-input state space model identification;

[0010] S4. Use the identified state-space model as a prediction model to develop a model predictive controller (MPC). Based on the simplified and reduced-order state-space model of the system, predict the system's behavior over a period of time in the future, and solve the optimal control input through optimization methods. The MPC controller periodically performs prediction, optimization, and execution of control actions to achieve real-time and precise control of the system.

[0011] Furthermore, the aforementioned step S1 includes the following sub-steps:

[0012] S11. Establish the condenser, condenser-evaporator and evaporator models as follows:

[0013]

[0014] Where ρ is density, u is specific internal energy, v is flow velocity, k is heat transfer coefficient, c is p is the specific heat capacity, T a 、T w and T b are the temperatures of the water side, heat exchange wall and refrigerant side respectively, and A is the cross-sectional area;

[0015] S12, establish a flash tank model,

[0016] Dynamic modeling of gas phase water and liquid phase water is performed separately:

[0017] The gas phase mass balance equation in the flash tank is as follows:

[0018]

[0019] Where m g is the steam quality in the flash tank, M evap is the mass flow rate of water vapor naturally evaporated in the tank, M cond is the mass flow rate of water vapor naturally condensed in the tank, M g,out is the outlet steam mass flow rate, M g,fis the mass flow rate of the water vapor portion during the flash evaporation process;

[0020] The energy balance equation of the gas phase in the flash tank is as follows:

[0021]

[0022] Where k gl is the heat transfer coefficient between water vapor and liquid water in the flash tank, A gl is the heat exchange area between water vapor and liquid water in the flash tank, h g,sat and h l,sat are the enthalpies of saturated water vapor and saturated water in the flash tank,

[0023] The mass balance equation of the liquid phase in the flash tank is as follows:

[0024]

[0025] Where m l is the mass of hot water in the flash tank, M f,in,c is the hot water flow rate at the condenser inlet and outlet, M l,f is the mass flow rate of the unflashed water at the condenser outlet, M w is the water replenishment flow;

[0026] The energy balance equation of the liquid phase in the flash tank is as follows:

[0027]

[0028] Where M cond is the mass flow rate of water vapor naturally condensed in the tank, h g,sat and h l,sat are the enthalpy of saturated water vapor and saturated water in the flash tank, M evap is the mass flow rate of water vapor naturally evaporated in the tank;

[0029] S13. Build a compressor and expansion valve model. The compressor power is expressed as:

[0030] W com =m1(h 1' -h1)+m2(h2-h 1” ) (9)

[0031]

[0032] Where h1 is the specific enthalpy of the compressor suction port, h 1' is the specific enthalpy at the end of the first stage compression, h 1” is the specific enthalpy before the second stage compression, h2 is the specific enthalpy before the second stage compression, h 1',is is the specific enthalpy at the end of the first stage of compression under isentropic conditions, η sis the isentropic efficiency;

[0033]

[0034] Where h 2,is is the specific enthalpy when the second stage compression is an isentropic process.

[0035] Furthermore, in the aforementioned step S2, the overall system dynamic model includes:

[0036] Evaporator, low-temperature compressor, condenser-evaporator, first low-temperature expansion valve, low-temperature flash unit, second low-temperature expansion valve, high-temperature compressor, condenser, first high-temperature expansion valve, high-temperature flash unit, second high-temperature expansion valve, water pump;

[0037] The low-temperature compressor, the first channel of the condenser evaporator, the first low-temperature expansion valve, the low-temperature flash unit, the second low-temperature expansion valve and the first channel of the evaporator are sequentially connected through a refrigerant pipeline to form a low-temperature refrigerant circulation loop;

[0038] The high-temperature compressor, the first channel of the condenser, the first high-temperature expansion valve, the high-temperature flasher, the second high-temperature expansion valve and the second channel of the condenser evaporator are sequentially connected through a refrigerant pipeline to form a high-temperature refrigerant circulation loop;

[0039] In the low-temperature refrigerant circulation loop, the outlet of the low-temperature compressor is connected to the inlet of the first channel of the condenser evaporator through a refrigerant pipeline, the outlet of the first channel of the condenser evaporator is connected to the inlet of the first low-temperature expansion valve through a refrigerant pipeline, the outlet of the first low-temperature expansion valve is connected to the inlet of the low-temperature flasher through a refrigerant pipeline, the gas outlet of the low-temperature flasher is connected to the gas supply inlet of the low-temperature compressor through a refrigerant pipeline, the liquid outlet of the low-temperature flasher is connected to the inlet of the second low-temperature expansion valve through a refrigerant pipeline, the outlet of the second low-temperature expansion valve is connected to the inlet of the first channel of the evaporator through a refrigerant pipeline, and the outlet of the first channel of the evaporator is connected to the inlet of the low-temperature compressor through a refrigerant pipeline;

[0040] In the high-temperature refrigerant circulation loop, the outlet of the high-temperature compressor is connected to the inlet of the first channel of the condenser through a refrigerant pipeline, the outlet of the first channel of the condenser is connected to the inlet of the first high-temperature expansion valve through a refrigerant pipeline, the outlet of the first high-temperature expansion valve is connected to the inlet of the high-temperature flasher through a refrigerant pipeline, the gas outlet of the high-temperature flasher is connected to the air supply inlet of the high-temperature compressor through a refrigerant pipeline, the liquid outlet of the high-temperature flasher is connected to the inlet of the second high-temperature expansion valve through a refrigerant pipeline, the outlet of the second high-temperature expansion valve is connected to the inlet of the second channel of the condenser evaporator through a refrigerant pipeline, and the outlet of the second channel of the condenser evaporator is connected to the inlet of the high-temperature compressor through a refrigerant pipeline.

[0041] Furthermore, the aforementioned step S3 includes the following sub-steps:

[0042] S31, the controlled variables are the hot water temperature and steam temperature of the flash tank, and the system control variables are the flash tank outlet valve opening and steam flow rate;

[0043] S32. Design a two-input, two-output state-space model to simulate the input-output characteristics of the system. The model is expressed as follows:

[0044]

[0045] Where x m is the state variable, A m , B m , C m With D m To identify the model coefficient matrix, the input u contains the flash tank outlet valve opening and steam flow rate in sequence, and the output y contains the flash tank hot water temperature and steam temperature in sequence.

[0046] Furthermore, the aforementioned step S4 includes the following sub-steps:

[0047] S41. Change the prediction model to incremental type, that is, use differential form to represent each variable and expand it.

[0048]

[0049] Where x(t)=[Δx m (t)y(t)], and predict the output of the system in the future time domain according to the augmented state space equation:

[0050] Y=FX(k i )+ΦΔU

[0051]

[0052] in,

[0053] ΔU=[Δu(k i ) T Δu(k i +1) T Δu(k i +2) T ...Δu(k i +N c -1) T ] T ,

[0054] ΔUY=[y(k i +1|k i ) T y(k i +2|ki ) T y(k i +3|k i ) T ...y(k i +N p ∣k i ) T ] T , N p For prediction

[0055] Time domain, N c To control the time domain;

[0056] S42, the rolling optimization of the controller MPC is to continuously solve the cost function within the scope of the model constraints to obtain the optimal control sequence of the system. Based on the optimization goal, the cost function of MPC and the related constraints are as follows:

[0057]

[0058] Among them, Y r (k) is the preset value of the system, Φ y , Φ u , Φ w is the weight matrix of tracking index, control index and electrical efficiency, ΔU max , ΔU min , U max and U min They are the maximum and minimum values ​​of each control quantity, control quantity increment, and output;

[0059] S43. During actual operation of the controller MPC, the influence of external interference and model mismatch is eliminated through feedback correction, and the system state variables are updated based on the error between the output result of the controlled mechanism model and the predicted value of the prediction model.

[0060] Furthermore, in the aforementioned step S1, a dynamic model of each component of the air-compensation and enthalpy-increasing cascade steam heat pump is established; in step S3, dynamic simulation data of the air-compensation and enthalpy-increasing cascade steam heat pump system is used to perform multi-output and multi-input state-space model identification; in step S4, the identified state-space model is used as a prediction model to develop a model predictive controller (MPC); step S4 also includes establishing a SIMULINK / Modelica joint simulation platform to perform model predictive control on the air-compensation and enthalpy-increasing cascade steam heat pump system, including the following sub-steps:

[0061] S401. Export the dynamic mechanism model established based on Modelica as an FMU file that complies with the FMI standard. S402. Import the above FMU file into SIMULINK, connect the control variable of the FMU file with the optimal control instruction of the MPC controller; and connect the controlled variable of the FMU file with the observer to form a joint simulation system.

[0062] S403. After the simulation starts, the FMU file calls the built-in solver of the FMU to obtain the system controlled quantity and pass it to the observer.

[0063] S404, the observer calculates the state variables of the prediction model according to the current control instructions and the system controlled quantity. Update and correct, and pass it to MPC.

[0064] S405, MPC performs rolling optimization based on the control objectives and explicit constraints to solve the current optimal control instructions and transmits them to the FMU to complete a control process;

[0065] S406: Return to step S401 and continue until the control process ends.

[0066] Furthermore, the aforementioned joint simulation method of the air-injection and enthalpy-increasing cascade steam heat pump based on model predictive control also includes S5, establishing a SIMULINK / Modelica joint simulation platform, performing model predictive control on the air-injection and enthalpy-increasing cascade steam heat pump system, performing simulation calculations under four different operating conditions of set value disturbance, external disturbance, internal disturbance and model parameter perturbation, and comparatively analyzing the MPC controller and the traditional PID controller.

[0067] Compared with the prior art, the beneficial technical effects of the present invention using the above technical solution are as follows:

[0068] This invention provides a co-simulation design method for modeling and controlling a cascade steam heat pump system with air-injection and enthalpy-increasing. A dynamic model of the system was established, and model identification and controller design were performed. This method addresses the issues of untimely load tracking and poor temperature control during load fluctuations. The co-simulation method achieves efficient control of the dynamic system, enabling rapid and accurate load tracking and temperature control while extending system life and improving operational stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] FIG1(a) is a schematic diagram of the system structure of the present invention, and FIG1(b) is a diagram of the overall dynamic model of the system.

[0070] Figure 2 It is a schematic diagram of the dual-loop PID controller structure.

[0071] Figure 3 This is the block diagram of the predictive control structure of the VI-CSHP system.

[0072] Figure 4(a) is a graph showing the change in the set value of the hot water temperature in the flash tank.

[0073] Figure 4(b) is a graph showing the change in the flash tank steam temperature set point.

[0074] Figure 5(a) is a comparison of the control effects of the controlled hot water temperature under different strategies.

[0075] Figure 5(b) is a comparison of the control effects of the controlled steam temperature under different strategies.

[0076] Figure 6(a) is a comparison of the control effects of the control quantity flash tank outlet valve opening under different strategies.

[0077] Figure 6(b) is a comparison of the control effects of the controlled steam flow under different strategies.

[0078] Figure 7 This is the predictive control structure diagram under steam temperature step disturbance (external disturbance).

[0079] Figure 8(a) is a comparison of the hot water temperature in the flash tank under MPC and PID control under external disturbance.

[0080] Figure 8(b) is a comparison of steam temperature under MPC and PID control under external disturbance.

[0081] Figure 8(c) is a comparison of the flash tank outlet valve opening under MPC and PID control under external disturbance.

[0082] Figure 8(d) is a comparison of steam flow rates under MPC and PID control under external disturbance.

[0083] Figure 9 This is the predictive control structure diagram under the step disturbance of the flash tank outlet valve opening (internal disturbance).

[0084] Figure 10(a) is a comparison of the hot water temperature in the flash tank under MPC and PID control under internal disturbance.

[0085] Figure 10(b) is a comparison of steam temperature under MPC and PID control under internal disturbance.

[0086] Figure 10(c) is a comparison of the flash tank outlet valve opening under MPC and PID control under internal disturbance.

[0087] Figure 10(d) is a comparison of steam flow rates under MPC and PID control under internal disturbance.

[0088] In the figure, 1-evaporator, 2-low-temperature compressor, 3-condenser evaporator, 4-first low-temperature expansion valve, 5-low-temperature flash unit, 6-second low-temperature expansion valve, 7-high-temperature compressor, 8-condenser, 9-first high-temperature expansion valve, 10-high-temperature flash unit, 11-second high-temperature expansion valve, 12-water pump. DETAILED DESCRIPTION

[0089] In order to better understand the technical content of the present invention, specific embodiments are given and described below with reference to the accompanying drawings.

[0090] Various aspects of the present invention are described herein with reference to the accompanying drawings, which show a number of illustrative embodiments. The embodiments of the present invention are not limited to those described in the accompanying drawings. It should be understood that the present invention can be implemented by any of the various concepts and embodiments described above, as well as the concepts and implementations described in detail below, because the concepts and embodiments disclosed herein are not limited to any particular implementation. In addition, some aspects disclosed herein may be used alone or in any appropriate combination with other aspects disclosed herein.

[0091] The present invention provides a joint simulation method for a cascade steam heat pump with air supplementation and enthalpy increase based on model predictive control, which is characterized by comprising the following steps:

[0092] S1. Based on the heat transfer mechanism, the multi-domain unified modeling language Modelica is used to establish the dynamic model of each component of the air-injection enthalpy-increasing cascade steam heat pump;

[0093] S2. Connect all components according to the unified interface to form the overall dynamic model of the system and perform dynamic simulation;

[0094] S3. Apply dynamic simulation data of the air-injection enthalpy-increasing cascade steam heat pump system to perform multi-output and multi-input state space model identification in SIMULINK;

[0095] S4. Use the identified state-space model as a prediction model and develop a model predictive controller (MPC) in SIMULINK. Based on the simplified and reduced-order state-space model of the system, predict the system's behavior over a period of time in the future, and solve the optimal control input through optimization methods. The MPC controller periodically performs prediction, optimization, and execution of control actions to achieve real-time and precise control of the system.

[0096] Furthermore, step S1 includes the following sub-steps:

[0097] S11. Establish the condenser, condenser-evaporator and evaporator models as follows:

[0098]

[0099] Where ρ is density, kg / m3 ; u is specific internal energy, kJ / (kg·K); v is flow velocity, m / s; k is heat transfer coefficient, kJ / (m 2 ·K);c p is the specific heat capacity, kJ / (kg·K); T a 、T w and T b are the temperatures of the water side, heat exchange wall and refrigerant side, respectively, ℃; A is the cross-sectional area; m 2 .

[0100] S12, establish a flash tank model,

[0101] The system uses a flash tank to store water and generate steam. In order to study the characteristics of the steam at the flash tank outlet, dynamic modeling is performed for the gas phase water and the liquid phase water respectively:

[0102] The gas phase mass balance equation in the flash tank is as follows:

[0103]

[0104] Where m g is the steam mass in the flash tank, kg; M evap is the mass flow rate of water vapor naturally evaporated in the tank, kg; M cond is the mass flow rate of water vapor naturally condensed in the tank, kg; M g,out is the outlet steam mass flow rate, kg; M g,f is the mass flow rate of water vapor during the flash evaporation process, kg / s.

[0105] The energy balance equation of the gas phase in the flash tank is as follows:

[0106]

[0107] Where k gl is the heat transfer coefficient between water vapor and liquid water in the flash tank, W / (m 2 K); A gl is the heat exchange area between water vapor and liquid water in the flash tank, m 2 ;h g,sat and h l,sat are the enthalpies of saturated water vapor and saturated water in the flash tank, kJ / kg respectively.

[0108] The mass balance equation of the liquid phase in the flash tank is as follows:

[0109]

[0110] Where m l is the mass of hot water in the flash tank, kg / s; M f,in,c is the hot water flow rate at the inlet and outlet of the condenser, kg / s; Ml,f is the mass flow rate of the unflashed water at the condenser outlet, kg / s; M w is the water replenishment flow rate, kg / s.

[0111] The energy balance equation of the liquid phase in the flash tank is as follows:

[0112]

[0113] Where M cond is the mass flow rate of water vapor naturally condensed in the tank, h g,sat and h l,sat are the enthalpy of saturated water vapor and saturated water in the flash tank, M evap is the mass flow rate of water vapor naturally evaporated in the tank;

[0114] S13. Build a compressor and expansion valve model. The compressor power is expressed as:

[0115] W com =m1(h 1' -h1)+m2(h2-h 1” ) (9)

[0116]

[0117] Where h1 is the specific enthalpy of the compressor suction port, kJ / kg; h 1' is the specific enthalpy at the end of the first stage compression, kJ / kg; h 1” is the specific enthalpy before the second stage compression, kJ / kg; h2 is the specific enthalpy before the second stage compression, kJ / kg; h 1',is is the specific enthalpy at the end of the first stage of compression under isentropic conditions, kJ / kg; η s is the isentropic efficiency;

[0118]

[0119] Where h 2,is is the specific enthalpy when the second stage compression is an isentropic process, kJ / kg.

[0120] Referring to Figures 1(a) and (b), the overall dynamic model of the system includes:

[0121] Evaporator 1, low-temperature compressor 2, condenser evaporator 3, first low-temperature expansion valve 4, low-temperature flash unit 5, second low-temperature expansion valve 6, 7-high-temperature compressor 7, condenser 8, first high-temperature expansion valve 9, 10-high-temperature flash unit 10, 11-second high-temperature expansion valve 11, water pump 12;

[0122] Among them, the low-temperature compressor 2, the first channel of the condenser evaporator 3, the first low-temperature expansion valve 4, the low-temperature flash 5, the second low-temperature expansion valve 6 and the first channel of the evaporator 1 are connected in sequence through the refrigerant pipeline to form a low-temperature refrigerant circulation loop;

[0123] The high-temperature compressor 7, the first channel of the condenser 8, the first high-temperature expansion valve 9, the high-temperature flasher 10, the second high-temperature expansion valve 11 and the second channel of the condenser evaporator 3 are sequentially connected through a refrigerant pipeline to form a high-temperature refrigerant circulation loop;

[0124] In the low-temperature refrigerant circulation loop, the outlet of the low-temperature compressor 2 is connected to the inlet of the first channel of the condenser evaporator 3 through a refrigerant pipeline, the outlet of the first channel of the condenser evaporator 3 is connected to the inlet of the first low-temperature expansion valve 4 through a refrigerant pipeline, the outlet of the first low-temperature expansion valve 4 is connected to the inlet of the low-temperature flasher 5 through a refrigerant pipeline, the gas outlet of the low-temperature flasher 5 is connected to the gas supply inlet of the low-temperature compressor 2 through a refrigerant pipeline, the liquid outlet of the low-temperature flasher 5 is connected to the inlet of the second low-temperature expansion valve 6 through a refrigerant pipeline, the outlet of the second low-temperature expansion valve 6 is connected to the inlet of the first channel of the evaporator 1 through a refrigerant pipeline, and the outlet of the first channel of the evaporator 1 is connected to the inlet of the low-temperature compressor 2 through a refrigerant pipeline;

[0125] In the high-temperature refrigerant circulation loop, the outlet of the high-temperature compressor 7 is connected to the inlet of the first channel of the condenser 8 through a refrigerant pipeline, the outlet of the first channel of the condenser 8 is connected to the inlet of the first high-temperature expansion valve 9 through a refrigerant pipeline, the outlet of the first high-temperature expansion valve 9 is connected to the inlet of the high-temperature flasher 10 through a refrigerant pipeline, the gas outlet of the high-temperature flasher 10 is connected to the air supply inlet of the high-temperature compressor 7 through a refrigerant pipeline, the liquid outlet of the high-temperature flasher 10 is connected to the inlet of the second high-temperature expansion valve 11 through a refrigerant pipeline, the outlet of the second high-temperature expansion valve 11 is connected to the inlet of the second channel of the condenser evaporator 3 through a refrigerant pipeline, and the outlet of the second channel of the condenser evaporator 3 is connected to the inlet of the high-temperature compressor 7 through a refrigerant pipeline.

[0126] Furthermore, step S3 includes the following sub-steps:

[0127] S31. Based on the system's application requirements and safety constraints, the control objective of this fuel cell system is to accurately and rapidly track external loads while ensuring system thermal safety. Therefore, the controlled variables are the flash tank hot water temperature and steam temperature. To achieve this control objective, the system control variables are the flash tank outlet valve opening and steam flow rate.

[0128] S32. Design a two-input, two-output state-space model to simulate the input-output characteristics of the system. The model is expressed as follows:

[0129]

[0130] Where x m is the state variable, A m , B m , C m With D m To identify the model coefficient matrix, the input u contains the flash tank outlet valve opening and steam flow rate in sequence, and the output y contains the flash tank hot water temperature and steam temperature in sequence.

[0131] Furthermore, step S4 includes the following sub-steps:

[0132] S41. Change the prediction model to incremental type, that is, use differential form to represent each variable and expand it.

[0133]

[0134] Where x(t)=[Δx m (t)y(t)], and predict the output of the system in the future time domain according to the augmented state space equation:

[0135] Y=FX(k i )+ΦΔU

[0136]

[0137] in,

[0138] ΔU=[Δu(k i ) T Δu(k i +1) T Δu(k i +2) T ...Δu(k i +N c -1) T ] T ,

[0139] ΔUY=[y(k i +1|k i ) T y(k i +2|k i ) T y(k i +3|k i ) T ...y(k i +N p ∣k i ) T ] T , N p For prediction

[0140] Time domain, N c To control the time domain;

[0141] S42, the rolling optimization of the controller MPC is to continuously solve the cost function within the scope of the model constraints to obtain the optimal control sequence of the system. Based on the optimization goal, the cost function of MPC and the related constraints are as follows:

[0142]

[0143] Among them, Y r (k) is the preset value of the system, Φ y , Φ u , Φ w is the weight matrix of tracking index, control index and electrical efficiency, ΔU max , ΔU min , U max and U min They are the maximum and minimum values ​​of each control quantity, control quantity increment, and output;

[0144] S43. During actual operation of the controller MPC, the influence of external interference and model mismatch is eliminated through feedback correction, and the system state variables are updated based on the error between the output result of the controlled mechanism model and the predicted value of the prediction model.

[0145] Furthermore, the VI-CSHP system dynamic model and intelligent control algorithm were designed in Modelica and SIMULINK, respectively. Therefore, it was necessary to establish a SIMULINK / Modelica joint simulation platform to perform model predictive control on the air-injection enthalpy-increasing cascade steam heat pump system. The specific steps include:

[0146] S401. Export the dynamic mechanism model established based on Modelica as a Functional Mock-up Unit (FMU) file that complies with the Functional Mock-up Interface (FMI) standard.

[0147] S402 , import the above FMU file into SIMULINK, connect the control variable of the FMU file with the optimal control instruction of the MPC controller; connect the controlled variable of the FMU file with the observer to form a joint simulation system.

[0148] S403. After the simulation starts, the FMU file calls the built-in solver of the FMU to obtain the system controlled quantity and pass it to the observer.

[0149] S404, the observer calculates the state variables of the prediction model according to the current control instructions and the system controlled quantity. Update and correct, and pass it to MPC.

[0150] S405. Based on the control objectives and explicit constraints, MPC performs rolling optimization to solve the current optimal control instruction and transmits it to the FMU to complete a control process.

[0151] Furthermore, step S5 includes the following sub-steps:

[0152] S51: For the design of conventional PID controller, based on the identification results of the differential evolution algorithm, the transfer function model of the VI-CSHP system presents a dual-input dual-output architecture, in which the input parameters are the flash tank outlet valve opening and the steam flow rate, and the output parameters are the flash tank hot water temperature and the steam temperature. Compared with the single-variable system, there is a coupling relationship between the two sets of output variables and the input variables of this system, which brings challenges to the design of the controller. If a single PID controller is used to achieve the control target, it will not only increase the design complexity of the control system, but also have an adverse effect on subsequent maintenance. In view of this, the present invention adopts a conventional distributed PID control method to artificially split the multivariable system into two single-variable subsystems, and use a single-loop PID controller to control each subsystem separately. A dual-loop PID controller is built on the Simulink platform, and its overall structure is as follows: Figure 2 shown.

[0153] The upper control loop stabilizes the hot water temperature by adjusting the flash tank outlet valve opening, while the lower control loop adjusts the steam compressor flow rate to ensure that the high-temperature steam parameters generated by the cascade heat pump accurately match process requirements. This dual-loop control strategy effectively ensures the dynamic response and steady-state accuracy of key process parameters.

[0154] S52: For the simulation under given value disturbance, the given value includes the hot water temperature and steam temperature of the flash tank. The MPC controller determines the optimal control law through the optimization algorithm based on the deviation between the set value and the actual output of the controlled object, and then regulates the flash tank outlet valve opening and steam flow to form a closed-loop control circuit, such as Figure 3 shown.

[0155] After the system stabilizes, the flash tank hot water temperature setpoint increases by 5°C at 1000 s, decreases by 5°C at 2500 s, decreases by 5°C at 4000 s, and increases by 5°C at 5500 s. Figure 4 shows the step-by-step changes in the setpoints. Figure 4(a) shows the change in the flash tank hot water temperature setpoint. Figure 4(b) shows the change in the flash tank steam temperature setpoint.

[0156] After using the MPC controller and PID controller, the control effects of the controlled variable were compared, as shown in Figures 5(a) and 5(b). Based on simulation data analysis, when the flash tank hot water temperature setpoint was disturbed during the 1000-2500 s period, the MPC controller based on the state-space model exhibited lower overshoot characteristics compared to the traditional PID controller, allowing the system to converge to the steady-state operating point more quickly. Furthermore, the MPC control had a smaller coupling effect on the steam temperature, allowing the steam temperature to quickly recover to the target setpoint. When the steam temperature setpoint was disturbed during the 4000-5500 s period, the MPC control again demonstrated superior performance, effectively suppressing overshoot and significantly shortening the time it took for the system to reach steady state. During this process, the flash tank hot water temperature also maintained good stability, with its overshoot significantly reduced and able to quickly recover to the predetermined operating point, fully verifying the effectiveness and robustness of the MPC control.

[0157] After using the MPC controller and PID controller, the control effects of the control quantities are compared, as shown in Figures 6(a) and 6(b). From the analysis results of the above simulation figures, it can be seen that when the given values ​​of the flash tank hot water temperature or steam temperature are disturbed, the MPC controller built based on the state space model shows significant advantages compared with the traditional PID controller. Under the action of this MPC controller, the response speed of the two control quantities, the flash tank outlet valve opening and steam flow, is greatly improved, and the change range is small. This feature ensures the stability and robustness of the unit during operation.

[0158] S52: For the simulation of control systems under external disturbances, during the operation stage of complex thermal systems, due to the existence of various uncertain disturbances, the controlled quantity is prone to fluctuations or deviations, thereby inducing external disturbances. For the VI-CSHP system, such external disturbances will directly threaten the stable operation of the control unit, resulting in the degradation of control performance and endangering the stability of system operation. In order to verify the anti-interference ability of the proposed MPC controller, at t=3500s, the disturbance situation of increasing the controlled quantity steam temperature by 10% from 120℃ is taken as an example to construct a typical external disturbance test scenario, and compared and analyzed with the traditional PID control strategy. The external disturbance suppression predictive control architecture of the VI-CSHP system is as follows: Figure 7 shown.

[0159] When the system faces a temperature step disturbance, the steam temperature suddenly jumps by 10% from the stable operating point. Under this condition, a comparative analysis is conducted on the control results of the MPC controller and the traditional PID controller. The results are as follows Figure 8(a) to Figure 8(d)As shown in the figure. The results show that when a positive step disturbance occurs in the external steam temperature, the system maintains the target set value constant. The adjustment mechanism based on model predictive control is immediately activated, driving the valve opening and steam flow parameters to increase rapidly, so that the controlled temperature parameters accurately return to the preset benchmark. Compared with the traditional PID control strategy, the fluctuation amplitude of the control variable under the MPC framework is significantly reduced and the dynamic response is faster, while the PID adjustment path shows obvious overshoot characteristics and the adjustment rate lags. Therefore, the MPC controller proposed in this paper effectively guarantees the stable operation requirements of the VI-CSHP system under external disturbance conditions.

[0160] S53: For the simulation of the control system under internal disturbance, during the operation of the control system, the control quantity will fluctuate or deviate due to the influence of various factors, which is the formation of internal disturbance. For the VI-CSHP system, the internal disturbance will interfere with the stable operation of the controller, which will not only weaken the control efficiency, but also affect the overall stability of the system. In actual engineering applications, internal disturbance is always a key influencing factor that cannot be ignored in thermal systems. In order to verify the anti-internal disturbance performance of the model predictive control system designed in this paper, when t=3500s, the disturbance condition of a 10% step opening of the flash tank outlet valve is taken as an example, and a comparative analysis is carried out with the conventional PID controller. The state space model predictive control structure under the step disturbance (internal disturbance) of the flash tank outlet valve opening of the VI-CSHP system is as follows: Figure 9 shown.

[0161] When the VI-CSHP system faced a step disturbance in the flash tank outlet valve opening, the valve opening suddenly jumped 10% from the stable operating point. Under this condition, a comparative analysis of the control performance of the model MPC controller and a traditional PID controller was conducted, with the results shown in Figure 10.

[0162] from Figure 10(a) to Figure 10(d) It can be seen that when a step disturbance occurs in the opening of the flash tank outlet regulating valve, the system exhibits significant multivariable coupling characteristics: the hot water temperature and steam temperature of the flash tank show a synchronous decay trend, while the steam flow rate produces a positive step response. In response to this strong interference condition, the closed-loop control architecture based on set value tracking dynamically adjusts the flash tank outlet valve opening instruction, so that the key controlled variables can quickly converge to the steady-state operating point, and the transition time is short. This strong robustness feature stems from MPC's ability to accurately compensate for the system's inertia link and its explicit processing mechanism for actuator constraints, which fully verifies its engineering applicability in resisting endogenous disturbances under complex working conditions of VI-CSHP systems.

[0163] Through example analysis, it can be seen that the involved MPC controller can realize VI-CSHP and achieve fast load tracking while meeting the temperature safety constraints, which is a significant improvement compared with the traditional PID controller.

[0164] While the present invention has been described above with reference to preferred embodiments, this is not intended to limit the present invention. Persons skilled in the art will readily appreciate that various modifications and variations can be made without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention shall be determined by the appended claims.

Claims

1. A joint simulation method for a cascade steam heat pump with air injection and enthalpy increase based on model predictive control, characterized in that: The following steps are involved: S1. Based on the heat transfer mechanism, establish the dynamic model of each component of the cascade steam heat pump with air injection and enthalpy increase; S2. Connect all components according to the unified interface to form the overall dynamic model of the system and perform dynamic simulation; S3. Apply dynamic simulation data of the air-injection enthalpy-increasing cascade steam heat pump system to perform multi-output and multi-input state space model identification; S4. Use the identified state-space model as a prediction model to develop a model predictive controller (MPC). Based on the simplified and reduced-order state-space model of the system, predict the system's behavior over a period of time in the future, and solve the optimal control input through optimization methods. The MPC controller periodically performs prediction, optimization, and execution of control actions to achieve real-time and precise control of the system.

2. The joint simulation method of a cascade steam heat pump with air supplement and enthalpy increase based on model predictive control according to claim 1, characterized in that: Step S1 includes the following sub-steps: S11. Establish the condenser, condenser-evaporator and evaporator models as follows: Where ρ is density, u is specific internal energy, v is flow velocity, k is heat transfer coefficient, c is p is the specific heat capacity, T a 、T w and T b are the temperatures of the water side, heat exchange wall and refrigerant side respectively, and A is the cross-sectional area; S12, establish a flash tank model, Dynamic modeling of gas phase water and liquid phase water is performed separately: The gas phase mass balance equation in the flash tank is as follows: Where m g is the steam quality in the flash tank, M evap is the mass flow rate of water vapor naturally evaporated in the tank, M cond is the mass flow rate of water vapor naturally condensed in the tank, M g,out is the outlet steam mass flow rate, M g,f is the mass flow rate of the water vapor portion during the flash evaporation process; The energy balance equation of the gas phase in the flash tank is as follows: Where k gl is the heat transfer coefficient between water vapor and liquid water in the flash tank, A gl is the heat exchange area between water vapor and liquid water in the flash tank, h g,sat and h l,sat are the enthalpies of saturated water vapor and saturated water in the flash tank, The mass balance equation of the liquid phase in the flash tank is as follows: Where m l is the mass of hot water in the flash tank, M f,in,c is the hot water flow rate at the condenser inlet and outlet, M l,f is the mass flow rate of the unflashed water at the condenser outlet, M w is the water replenishment flow; The energy balance equation of the liquid phase in the flash tank is as follows: Where M cond is the mass flow rate of water vapor naturally condensed in the tank, h g,sat and h l,sat are the enthalpy of saturated water vapor and saturated water in the flash tank, M evap is the mass flow rate of water vapor naturally evaporated in the tank; S13. Build a compressor and expansion valve model. The compressor power is expressed as: W com =m1(h 1' -h1)+m2(h2-h 1” ) (9) Where h1 is the specific enthalpy of the compressor suction port, h 1' is the specific enthalpy at the end of the first stage compression, h 1” is the specific enthalpy before the second stage compression, h2 is the specific enthalpy before the second stage compression, h 1',is is the specific enthalpy at the end of the first stage of compression under isentropic conditions, η s is the isentropic efficiency; Where h 2,is is the specific enthalpy when the second stage compression is an isentropic process.

3. The joint simulation method of a cascade steam heat pump with air supplement and enthalpy increase based on model predictive control according to claim 1, characterized in that: In step S2, the overall dynamic model of the system includes: Evaporator (1), low-temperature compressor (2), condenser evaporator (3), first low-temperature expansion valve (4), low-temperature flash unit (5), second low-temperature expansion valve (6), high-temperature compressor (7), condenser (8), first high-temperature expansion valve (9), high-temperature flash unit (10), second high-temperature expansion valve (11), water pump (12); The low-temperature compressor (2), the first channel of the condenser evaporator (3), the first low-temperature expansion valve (4), the low-temperature flasher (5), the second low-temperature expansion valve (6) and the first channel of the evaporator (1) are sequentially connected through a refrigerant pipeline to form a low-temperature refrigerant circulation loop; The high-temperature compressor (7), the first channel of the condenser (8), the first high-temperature expansion valve (9), the high-temperature flasher (10), the second high-temperature expansion valve (11) and the second channel of the condenser evaporator (3) are sequentially connected through a refrigerant pipeline to form a high-temperature refrigerant circulation loop; In a low-temperature refrigerant circulation loop, the outlet of the low-temperature compressor (2) is connected to the inlet of the first channel of the condenser evaporator (3) through a refrigerant pipeline, the outlet of the first channel of the condenser evaporator (3) is connected to the inlet of the first low-temperature expansion valve (4) through a refrigerant pipeline, the outlet of the first low-temperature expansion valve (4) is connected to the inlet of the low-temperature flasher (5) through a refrigerant pipeline, the gas outlet of the low-temperature flasher (5) is connected to the gas supply inlet of the low-temperature compressor (2) through a refrigerant pipeline, the liquid outlet of the low-temperature flasher (5) is connected to the inlet of the second low-temperature expansion valve (6) through a refrigerant pipeline, the outlet of the second low-temperature expansion valve (6) is connected to the inlet of the first channel of the evaporator (1) through a refrigerant pipeline, and the outlet of the first channel of the evaporator (1) is connected to the inlet of the low-temperature compressor (2) through a refrigerant pipeline; In the high-temperature refrigerant circulation loop, the outlet of the high-temperature compressor (7) is connected to the inlet of the first channel of the condenser (8) through a refrigerant pipeline, the outlet of the first channel of the condenser (8) is connected to the inlet of the first high-temperature expansion valve (9) through a refrigerant pipeline, the outlet of the first high-temperature expansion valve (9) is connected to the inlet of the high-temperature flasher (10) through a refrigerant pipeline, the gas outlet of the high-temperature flasher (10) is connected to the air supply inlet of the high-temperature compressor (7) through a refrigerant pipeline, the liquid outlet of the high-temperature flasher (10) is connected to the inlet of the second high-temperature expansion valve (11) through a refrigerant pipeline, the outlet of the second high-temperature expansion valve (11) is connected to the inlet of the second channel of the condenser evaporator (3) through a refrigerant pipeline, and the outlet of the second channel of the condenser evaporator (3) is connected to the inlet of the high-temperature compressor (7) through a refrigerant pipeline.

4. The joint simulation method of a cascade steam heat pump with air supplement and enthalpy increase based on model predictive control according to claim 1, characterized in that: Step S3 includes the following sub-steps: S31, the controlled variables are the hot water temperature and steam temperature of the flash tank, and the system control variables are the flash tank outlet valve opening and steam flow rate; S32. Design a two-input, two-output state-space model to simulate the input-output characteristics of the system. The model is expressed as follows: Where x m is the state variable, A m , B m , C m With D m To identify the model coefficient matrix, the input u contains the flash tank outlet valve opening and steam flow rate in sequence, and the output y contains the flash tank hot water temperature and steam temperature in sequence.

5. The joint simulation method of a cascade steam heat pump with air supplement and enthalpy increase based on model predictive control according to claim 1, characterized in that: Step S4 includes the following sub-steps: S41. Change the prediction model to incremental type, that is, use differential form to represent each variable and expand it. Where x(t)=[Δx m (t)y(t)], and predict the output of the system in the future time domain according to the augmented state space equation: in, ΔU=[Δu(k i ) T Δu(k i +1) T Δu(k i +2) T ...Δu(k i +N c -1) T ] T , ΔUY=[y(k i +1|k i ) T y(k i +2|k i ) T y(k i +3|k i ) T …y(k i +N p ∣k i ) T ] T , N p is the prediction time domain, N c To control the time domain; S42, the rolling optimization of the controller MPC is to continuously solve the cost function within the scope of the model constraints to obtain the optimal control sequence of the system. Based on the optimization goal, the cost function of MPC and the related constraints are as follows: Among them, Y r (k) is the preset value of the system, Φ y , Φ u , Φ w is the weight matrix of tracking index, control index and electrical efficiency, ΔU max , ΔU min , U max and U min They are the maximum and minimum values ​​of each control quantity, control quantity increment, and output; S43. During actual operation of the controller MPC, the influence of external interference and model mismatch is eliminated through feedback correction, and the system state variables are updated based on the error between the output result of the controlled mechanism model and the predicted value of the prediction model.

6. The joint simulation method of a cascade steam heat pump with air supplement and enthalpy increase based on model predictive control according to claim 1, characterized in that: In step S1, a dynamic model of each component of the air-injection enthalpy-increasing cascade steam heat pump is established; in step S3, dynamic simulation data of the air-injection enthalpy-increasing cascade steam heat pump system is used to perform multi-output and multi-input state-space model identification; in step S4, the identified state-space model is used as a prediction model to develop a model predictive controller (MPC); step S4 also includes establishing a SIMULINK / Modelica co-simulation platform to perform model predictive control on the air-injection enthalpy-increasing cascade steam heat pump system, including the following sub-steps: S401. Export the dynamic mechanism model established based on Modelica into an FMU file that complies with the FMI standard. S402 , import the above FMU file into SIMULINK, connect the control variable of the FMU file with the optimal control instruction of the MPC controller; connect the controlled variable of the FMU file with the observer to form a joint simulation system. S403. After the simulation starts, the FMU file calls the built-in solver of the FMU to obtain the system controlled quantity and pass it to the observer. S404, the observer calculates the state variables of the prediction model according to the current control instructions and the system controlled quantity. Update and correct, and pass it to MPC. S405, MPC performs rolling optimization based on the control objectives and explicit constraints to solve the current optimal control instructions and transmits them to the FMU to complete a control process; S406: Return to step S401 and continue until the control process ends.

7. The joint simulation method of a cascade steam heat pump with air supplement and enthalpy increase based on model predictive control according to claim 1, characterized in that: It also includes S5, establishing a SIMULINK / Modelica joint simulation platform, and performing model predictive control on the air-injection enthalpy-increasing cascade steam heat pump system. Simulation calculations are performed under four different operating conditions: set value disturbance, external disturbance, internal disturbance, and model parameter perturbation, and a comparative analysis is performed between the MPC controller and the traditional PID controller.

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