Multi-objective hierarchical control method for a three-stage cascade heat pump system

Abstract

The present application relates to the technical field of heat pump system control, and is a kind of multi-objective hierarchical control method of three-stage cascade heat pump system, comprising: hierarchical optimization of control target is carried out using dictionary sequence optimization framework, and priority is divided into P0 layer, P1 layer and P2 layer;P0 layer, P1 layer and P2 layer are solved respectively;A double-time-scale hierarchical control framework is used to construct a steady-state planning optimization layer and a dynamic tracking control layer respectively;The evaporation temperature of the intermediate cycle in the cascade system and the evaporation temperature of the high-temperature cycle are taken as the intermediate temperature, the intermediate temperature state is observed, and a warning mechanism is established.The present application realizes low valley energy storage and high peak energy release through multi-objective hierarchical control, and through the double-time-scale hierarchical control framework, the steady-state layer makes planning optimization, and the dynamic layer makes rapid constraint satisfaction, meeting the real-time calculation requirements of PLC.

Description

Technical Field

[0001] This invention relates to the field of heat pump system control technology, and in particular to a multi-objective hierarchical control method for a three-stage cascade heat pump system. Background Technology

[0002] Three-stage cascade heat pump systems are widely used in industries such as food, beverage, and pharmaceuticals. These systems employ three different refrigerants to form three independent cycles: a low-temperature stage, an intermediate stage, and a high-temperature stage. Heat is transferred through cascaded interstage condensers and evaporators, simultaneously meeting multiple process requirements. For example, in a combined cooling and heating (CCHP) scenario, the low-temperature stage produces process cooling at -5°C to -7°C (e.g., alcohol-water), while the intermediate and high-temperature stages cascade to produce hot water at 80~120°C. The system simultaneously meets both process cooling and cleaning / disinfection needs, with significantly higher energy efficiency than traditional chillers and gas boilers. However, the control of cascade systems faces the following core challenges: (1) The disconnect between hardware cognition and control methods Existing combined cooling and heating heat pump systems, such as the invention patent application "Combined Cooling and Heating Heat Pump System and its Integrated Cascade Condenser-Evaporator," have recognized the physical nature of the intermediate temperature being naturally determined by the system's thermal balance and having an extremely narrow independently controllable range. However, this hardware understanding has not yet been translated into system control method design. Current control methods still treat the intermediate temperature as a setpoint, tracking target, or optimization variable, and have not established an observation, early warning, and tiered protection mechanism based on this physical understanding.

[0003] (2) Multiple objectives are coupled and have huge differences in priority. Cascade systems need to simultaneously meet multiple process requirements: the dominant process output at the cryogenic stage (rigid constraints, process safety), the secondary process output at the high-temperature stage (soft constraints, allowing short-term deviations), and minimizing the total system operating cost (economic objective). The priorities of these three process requirements differ significantly; insufficient dominant output can lead to product quality issues or even production stoppages, while short-term deviations in secondary outputs can be buffered by energy storage. Traditional MPC (Multi-Process Control) methods weighted summation of these three objectives cannot guarantee the absolute priority of rigid constraints.

[0004] (3) The independent controllable range of intermediate temperature is extremely narrow. The intermediate temperature of a cascade system is implicitly determined by the thermodynamic balance equation. Once the hardware configuration is set, the intermediate temperature is essentially whatever value is achieved, and frequency adjustment during operation can only be fine-tuned within ±10% (approximately ±2~3℃). Existing control methods generally use the intermediate temperature as the setpoint to track the target, attempting to correct the intermediate temperature through PID or MPC. This is ineffective control of a parameter with an extremely narrow controllable range, wasting computing power and potentially causing system oscillations.

[0005] Wang et al. (2020) proposed using ESC to optimize the intermediate temperature of a cascade system in real time to maximize COP. However, the fundamental problem with this method is that the independently controllable range of the intermediate temperature is only ±2~3℃, and the process of continuously applying perturbations to find the optimal point by ESC itself introduces additional energy consumption and oscillations; moreover, this optimal point drifts with load changes, requiring complex online optimization to track a changing target, resulting in a complex control structure and poor robustness. This invention, recognizing the extremely narrow independently controllable range of the intermediate temperature, abandons the pursuit of such meaningless tracking and instead focuses on early warning protection, simplifying the control structure and eliminating tracking errors.

[0006] If the intermediate temperature prediction and control method based on data-driven models (such as BP neural networks) is transplanted to cascade systems, it will also face the problem of lack of physical foundation: the model is entirely based on data-driven and does not embed the thermal balance constraints of the cascade system. When the operating conditions deviate from the training distribution, the control will fail. In addition, the intermediate temperature is also treated as an independent controllable variable, which leads to a bias in the cognitive premise.

[0007] (4) Economic dispatch demand under time-of-use pricing Industrial electricity prices are typically based on peak-valley time-of-use pricing, such as 1.0 yuan / kWh during peak hours, 0.6 yuan / kWh during off-peak hours, and 0.3 yuan / kWh during off-peak hours. If a cascaded power system operates at a constant load, it will incur high electricity costs during peak periods. However, existing control methods do not consider the timing of electricity prices and cannot achieve economical dispatching of energy storage during off-peak hours and energy release during peak hours.

[0008] (5) The engineering reality of asynchronous heating and cooling loads In industrial settings, the loads of different processes often change asynchronously, such as high cooling loads in summer and high heating loads in winter. Existing control methods do not have coordination strategies designed for this asynchronous characteristic, leading to a sharp drop in system efficiency under off-design conditions, or even shutdown due to constraint conflicts.

[0009] Based on the technical deficiencies in the existing technologies, there is a need to provide a control method that can solve the problems of multi-objective priority differentiation, intermediate temperature perception bias, time-of-use pricing economic dispatch, and load asynchrony coordination faced by cascade systems. Summary of the Invention

[0010] To address the aforementioned technical problems, this invention provides a multi-objective hierarchical control method for a three-stage cascade heat pump system. This invention primarily utilizes a hierarchical control method based on a lexicographical order optimization architecture; it overcomes the physical cognitive bias of existing control methods that treat intermediate temperature as an independent control objective, correctly recognizing the extremely narrow controllable range of intermediate temperature through state observation and early warning mechanisms; it solves the problem of high operating costs caused by existing control methods failing to consider load timing differences, achieving energy storage during off-peak hours and energy release during peak hours through multi-objective hierarchical control. Through a dual-timescale hierarchical control architecture, the steady-state layer performs planning optimization, while the dynamic layer performs rapid constraint satisfaction, meeting the real-time calculation requirements of the PLC.

[0011] The technical means employed in this invention are as follows: A multi-objective hierarchical control method for a three-stage cascade heat pump system includes: The control objective is hierarchically optimized using a lexicographical optimization architecture, with priorities divided into P0, P1, and P2 layers. Solutions are then applied to each of the P0, P1, and P2 layers. A dual-time-scale hierarchical control architecture is used to construct a steady-state programming optimization layer and a dynamic tracking control layer. The evaporation temperatures of the intermediate stage cycle and the high-temperature stage cycle in the cascade system are used as intermediate temperatures. The state of these intermediate temperatures is observed, and an early warning mechanism is established. Control commands are output to adjust the operating frequency of each stage compressor and the charging and discharging power of the energy storage tank, thereby achieving real-time physical control of the heat pump system.

[0012] Furthermore, the P0 layer is an absolute hard constraint with the highest priority. Based on the current dominant process load demand, it directly calculates and locks the frequency setpoint of the corresponding compressor stage to ensure that the output absolutely matches the demand. The dominant process load refers to the load with the greatest impact on process safety and the strongest rigidity in the cascade system. If the P0 layer has no feasible solution, the output dominant load cannot meet the alarm and triggers the safety protection.

[0013] Furthermore, the P1 layer is a soft constraint, which is of secondary priority, and the secondary process output is maintained within the set value range; the secondary process output refers to the output in the cascade system that has little impact on process safety and allows for short-term deviations; the P1 layer is solved within the feasible region of the P0 layer, allowing for moderate deviations under extreme operating conditions.

[0014] Furthermore, the P2 layer is the objective for optimizing operating costs and has the lowest priority; within the feasible regions of P0 and P1, it minimizes the system operating cost in the prediction time domain.

[0015] in, for The system operating cost at any given time, which includes at least operating electricity costs, overall energy consumption, and carbon emissions. The penalty weight is the rate of change of frequency. This represents the change in compressor frequency at time k relative to the previous time. This represents the number of sampling steps in the prediction time domain. This represents the cumulative value of the system's operating cost within the predicted time domain;

[0016] The P2 layer only searches for the lowest operating cost running point within the feasible region where the P0 and P1 layers converge, and does not repeatedly apply weighted penalties to the secondary output.

[0017] Furthermore, when solving for the P0 layer, the frequency of the corresponding stage compressor is directly calculated and locked based on the dominant process load requirements. ; Within the feasible region of the P0 layer, the P1 layer is solved, and the secondary process output tracking error is minimized. The frequency of the remaining compressor stages is adjusted accordingly. If there is no feasible solution for the P1 layer, the secondary output is allowed to deviate from the set value range but not exceed the relaxation threshold. When the deviation exceeds the allowable deviation, a secondary output deviation warning is triggered. Solve the P2 layer within the feasible regions of the P0 and P1 layers, optimizing the frequency of the remaining stage compressors and the charging and discharging power of the energy storage tank with the goal of minimizing the total operating cost.

[0018] Furthermore, the steady-state planning optimization layer, based on the steady-state thermal balance model and load forecasting, solves for the optimal energy storage scheduling plan and the reference values ​​of secondary compressor frequencies within the forecast time domain. It employs a steady-state linear model and solves it using linear programming, outputting the reference values ​​of secondary compressor frequencies for each time period. Third-stage compressor frequency reference value And the energy storage tank charging and discharging plan.

[0019] Furthermore, the dynamic tracking control layer can quickly respond to load fluctuations and constraint satisfaction, and track the benchmark value given by the steady-state planning optimization layer; it adopts a locally linearized state-space model and uses dimensionality-reduced quadratic programming for solution, with the main optimization variables being the secondary and tertiary compressor frequencies, and outputs the frequency setpoints of each compressor stage.

[0020] Furthermore, the early warning mechanism includes a first-level early warning, a second-level protection, and a third-level shutdown. The first-level early warning indicates that when the intermediate temperature deviates from the design balance value by more than ±5℃, an operating status deviation warning is triggered, prompting the operator to check the load matching and equipment status, without triggering control adjustments. The second-level protection indicates that when the intermediate temperature deviates from the design balance value by more than ±10℃, a load reduction protection is triggered, automatically reducing the maximum operating frequency of the secondary and third-stage compressors by 20% to prevent the compressor discharge temperature from being too high or the pressure ratio from exceeding the limit, while simultaneously sending an alarm to the operator. The third-level shutdown indicates that when the intermediate temperature deviates from the design balance value by more than ±15℃, a safety shutdown protection is triggered, shutting down the compressors step by step to prevent equipment damage.

[0021] Compared with the prior art, the present invention has the following advantages: This invention employs a lexicographical optimization architecture. The P0 layer directly locks the corresponding compressor frequency based on the dominant load demand, prioritizing ensuring the dominant output is not lower than the demand under any operating condition. The P2 layer optimizes purely operational costs and does not include secondary output tracking terms, achieving true separation of the three layers. Actual measurements show a dominant load satisfaction rate of ≥99.5%, while the satisfaction rate of traditional weighted MPC significantly decreases when constraints conflict.

[0022] In this invention, the dominant frequency is directly determined by the P0 layer and does not participate in the optimization of the P1 and P2 layers, fundamentally eliminating the possibility of sacrificing the dominant output for optimization costs. The physical basis of frequency locking in the P0 layer is the monotonic thermodynamic relationship between the compressor frequency and output in the cascade system, which is a physical inevitability based on irreversibility. The frequencies of the remaining stages are tracked for secondary outputs in the P1 layer and optimized for operational costs in the P2 layer, reducing the control dimension from high-dimensional to low-dimensional, resulting in simple and reliable engineering implementation.

[0023] This invention positions the intermediate temperature as a state observation value rather than a control target, establishing a deviation early warning mechanism without tracking the setpoint. This is based on a correct understanding of the physical nature of cascaded systems. The intermediate temperature is determined by hardware configuration and thermodynamic balance, and its independently controllable range is only ±2~3℃. Forcibly using it as a control target would be an excessive constraint on the system's degrees of freedom. Regarding the ESC intermediate temperature optimization method and data-driven predictive control method proposed by Wang et al. (2020), this invention points out their common drawback: treating the intermediate temperature as an independently controllable variable introduces additional energy consumption and oscillations in the process of continuously applying disturbances to find the optimal intermediate temperature, and the optimal point drifts with the load, leading to a complex control structure; the data-driven model lacks a thermodynamic and physical foundation, and control fails when the operating conditions deviate from the training distribution. This invention abandons attempts to control the intermediate temperature, instead adopting an observation-based early warning approach, a correct choice based on the physical nature of the system, simplifying the control structure and eliminating tracking errors.

[0024] This invention incorporates load forecasting and energy storage status into the MPC optimization objective. By using a peak-shaving and valley-filling strategy where thermal storage tanks store energy during periods of low operating costs and release energy during periods of high costs, the operating cost is reduced by 15-25% compared to constant load operation.

[0025] This invention adopts a layered architecture consisting of a steady-state programming optimization layer and a dynamic tracking control layer. The dynamic layer reduces the high-dimensional QP to a low-dimensional one through sensitivity dimensionality reduction, with a solution time of <15ms. It can run in real time on Siemens S7-1500 series PLCs, meeting the millisecond-level control cycle requirements of industrial sites.

[0026] The strict priority of lexicographical order optimization used in this invention ensures that even under extreme conditions, such as a sudden drop of 15°C in heat source temperature or a sudden increase of 50% in dominant load, the most rigid dominant load constraint is still satisfied first, and the system will not shut down due to constraint conflicts. Compared to the 95% availability of traditional weighted MPC systems, the availability of this invention is increased to over 99.5%. Attached Figure Description

[0027] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 This is a diagram of the multi-objective hierarchical control system architecture of the three-stage cascade heat pump system in this invention.

[0029] Figure 2 This is a flowchart of the lexicographical order optimization solution in this invention.

[0030] Figure 3 This is a logic diagram for intermediate temperature state observation and early warning in this invention.

[0031] Figure 4 This is a schematic diagram of time-of-use electricity pricing economic dispatch in this invention.

[0032] Figure 5 This is an information interaction diagram of the dual-time-scale hierarchical control in this invention.

[0033] Figure 6 This is a schematic diagram comparing the method of the present invention with a comparative example in an embodiment of the present invention. Detailed Implementation

[0034] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0035] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0036] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0037] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following drawings denote similar items; therefore, once an item is defined in one drawing, it need not be further discussed in subsequent drawings.

[0038] like Figure 1 As shown, the present invention provides a multi-objective hierarchical control method for a three-stage cascade heat pump system, including: hierarchical optimization of control objectives using a lexicographic optimization architecture, dividing priorities into P0, P1 and P2 layers; lexicographic optimization refers to a method of sorting multiple optimization objectives according to strict priority, and considering the optimization of low-priority objectives only after the high-priority objectives are fully optimized, which is different from weighted summation multi-objective optimization.

[0039] In a preferred embodiment of this invention, the P0 layer is an absolute hard constraint with the highest priority. Based on the current dominant process load demand, it directly calculates and locks the frequency setpoint of the corresponding compressor stage to ensure absolute output matching of requirements. The dominant process load refers to the load with the greatest impact on process safety and the strongest rigidity in a cascade system. If the P0 layer has no feasible solution, meaning the corresponding compressor stage cannot meet the dominant load demand even at full frequency, an alarm for unmet dominant load is output, triggering safety protection. For example, in a combined cooling and heating system scenario, the cooling load is the dominant process load; in a pure refrigeration scenario, the cooling load is the dominant process load; and in a pure heat pump scenario, the heat load is the dominant process load.

[0040] An absolute hard constraint represents a constraint that cannot be violated under any operating condition. If there is no feasible solution, the optimization problem is unsolvable, and the system triggers a protection mechanism. In this invention, the P0 layer represents the absolute satisfaction of the dominant process load.

[0041] The physical mechanism of direct frequency locking at the P0 level is as follows: in a cascade system, the frequency of each compressor stage has a monotonically increasing relationship with the output (cooling or heating) of the corresponding stage, and the dominant load must be prioritized. Locking the dominant stage frequency directly to the demand-corresponding value, rather than participating in the optimization solution, is a physical necessity based on the irreversibility of thermodynamics. If the dominant stage frequency participates in optimization, the optimizer may reduce the dominant stage frequency to lower operating costs, leading to insufficient dominant output and irreversible process losses, such as the entire batch of products being scrapped due to excessive fermenter temperature. P0 level frequency locking removes this stage from the optimization variables, fundamentally eliminating this possibility.

[0042] In a preferred embodiment of this invention, the P1 layer is a soft constraint, representing a secondary priority, with the secondary process output maintained within a set value range. The secondary process output refers to the output in the cascade system that has a minimal impact on process safety and allows for short-term deviations; for example, in a combined cooling and heating system scenario, the high-temperature hot water temperature is the secondary process output. The P1 layer is solved within the feasible region of the P0 layer, allowing for moderate deviations under extreme conditions.

[0043] Soft constraints are constraints that allow for moderate deviations under extreme conditions. Deviations incur penalties but do not render the optimization problem unsolvable.

[0044] In a specific implementation, as a preferred embodiment of the present invention, the P2 layer is the target for optimizing operating costs and has the lowest priority; within the feasible regions of P0 and P1, the system operating cost in the prediction time domain is minimized:

[0045] in, for The system operating cost at any given time, which includes at least operating electricity costs, overall energy consumption, and carbon emissions. The penalty weight is the rate of change of frequency. This represents the change in compressor frequency at time k relative to the previous time. This represents the number of sampling steps in the prediction time domain. This represents the cumulative value of the system's operating cost within the predicted time domain;

[0046] The P2 layer only searches for the lowest operating cost running point within the feasible region where the P0 and P1 layers converge, and does not repeatedly apply weighted penalties to the secondary output.

[0047] Priority Levels (P0 / P1 / P2): This invention employs a lexicographical optimization architecture, dividing the control objectives into three levels based on strict priority, where P represents the priority level. P0 represents the highest priority absolute hard constraint, P1 represents the next highest priority soft constraint, and P2 represents the lowest priority optimization objective. The optimizer solves the problem layer by layer in the order of P0, P1, and P2. High-priority constraints cannot be violated, and low-priority objectives are optimized within the feasible regions of high-priority objectives.

[0048] The solutions are obtained for layers P0, P1, and P2 respectively. In a preferred embodiment of the present invention, when solving for layer P0, the frequency of the corresponding stage compressor is directly calculated and locked based on the dominant process load requirements. .

[0049] Solve the P1 layer within the feasible region of the P0 layer, and adjust the frequency of the remaining compressor stages with the goal of minimizing the secondary process output tracking error; if the P1 layer has no feasible solution, that is, the P0 layer constraint is too tight and cannot simultaneously satisfy the secondary output, allow the secondary output to deviate from the set value range but not exceed the relaxation threshold, and trigger the secondary output deviation warning when the deviation exceeds the allowable deviation.

[0050] Solve the P2 layer within the feasible regions of the P0 and P1 layers, with the goal of minimizing the total operating cost, and optimize the frequency of the remaining stage compressors and the charging and discharging power of the energy storage tank.

[0051] A dual-time-scale hierarchical control architecture is adopted to construct a steady-state planning optimization layer and a dynamic tracking control layer, respectively. In a preferred embodiment of the invention, the steady-state planning optimization layer, based on a steady-state thermal balance model and load forecasting, solves for the optimal energy storage scheduling plan and the reference values ​​of secondary compressor frequencies within the forecast time domain (24 hours). A steady-state linear model is used to solve the problem through linear programming, outputting the reference values ​​of secondary compressor frequencies for each time period. Third-stage compressor frequency reference value And the energy storage tank charging and discharging plan. The operating cycle is 5-10 minutes.

[0052] In a preferred embodiment of this invention, the dynamic tracking control layer can quickly respond to load fluctuations and constraint fulfillment, tracking the baseline value given by the steady-state planning optimization layer. A locally linearized state-space model is used, solved using dimensionality-reduced quadratic programming, with the primary optimization variables being the frequencies of the secondary and tertiary compressors, outputting the frequency setpoints for each compressor stage. The operating cycle is 1-10 seconds.

[0053] Sensitivity analysis of the control variables using steady-state COP was conducted, and the two variables with the highest sensitivity (secondary and tertiary compressor frequencies) were selected as the principal optimization variables. The remaining variables followed the established association rules. The high-dimensional QP was reduced to 2-dimensional, with a solution time of <15ms.

[0054] The two layers of information exchange are as follows: the steady-state planning and optimization layer serves as the reference frequency output by the upper layer, and the energy storage plan serves as the reference trajectory for the lower dynamic tracking and control layer. The actual operating status output by the lower layer is fed back to the upper layer for model updates.

[0055] The dual-time-scale hierarchical control mechanism decomposes the control task into two layers of control at different time scales: the upper layer performs slow planning, and the lower layer performs fast tracking. This invention's dual-time-scale control is geared towards cascade heat pump process control (second- to minute-level), which differs from the energy dispatching of integrated electric-thermal energy systems (hour-level).

[0056] The dual-timescale architecture of this invention is geared towards process control of cascade heat pumps, with the compressor frequency as the decision variable (continuously adjustable at the second level) and the control cycle at the second level, requiring real-time operation on a PLC. In contrast, the day-ahead and intraday scheduling of integrated electrothermal energy systems (Ma et al., 2023; Yao et al., 2018) is geared towards economic scheduling of energy systems, with equipment start-up / shutdown status and hourly power allocation as the decision variables, and a control cycle of 15 minutes to 1 hour, without involving dynamic constraints on compressor frequency or second-level real-time requirements. These two technologies belong to different technical fields and should not be confused.

[0057] The evaporation temperatures of the intermediate stage cycle and the high-temperature stage cycle in the cascade system are used as intermediate temperatures. These intermediate temperatures are naturally determined by the system's thermodynamic balance, and their independent controllable range is extremely narrow (±2~3℃), making them unsuitable as control targets. The intermediate temperature state is observed, and an early warning mechanism is established. Control commands are output to adjust the operating frequency of each stage compressor and the charging / discharging power of the energy storage tank, achieving real-time physical control of the heat pump system. The state observation values ​​are only used to monitor the system's operating status and are not measurement parameters used for closed-loop control. The intermediate temperature in this invention is a state observation value.

[0058] In a preferred embodiment of this invention, the early warning mechanism includes a first-level early warning, a second-level protection, and a third-level shutdown. The design equilibrium intermediate temperature is the expected value determined during the system design phase through compressor displacement matching and heat exchanger area configuration. The actual operating intermediate temperature fluctuates within a small range around this value.

[0059] The first-level early warning indicates that when the intermediate temperature deviates from the design balance value by more than ±5℃, an operational status deviation warning is triggered, prompting the operator to check the load matching and equipment status, without triggering control adjustments.

[0060] The secondary protection means that when the intermediate temperature deviates from the design balance value by more than ±10℃, the load reduction protection is triggered, automatically reducing the maximum operating frequency of the secondary and tertiary compressors by 20% to prevent the compressor discharge temperature from being too high or the pressure ratio from exceeding the limit, and at the same time sending an alarm to the operator.

[0061] The three-level shutdown means that when the intermediate temperature deviates from the design balance value by more than ±15℃, the safety shutdown protection is triggered, and the compressor is shut down step by step to prevent equipment damage.

[0062] This invention does not track the intermediate temperature setpoint or perform PID control, nor does it use the intermediate temperature as the control target or optimization variable for MPC. Wang et al. (2020) proposed using ESC to optimize the intermediate temperature of the cascade system in real time to maximize COP. However, this invention, based on thermodynamic analysis, points out that the intermediate temperature is determined by the following formula:

[0063] In the formula, This indicates the intermediate temperature of the cascade system, namely the evaporation temperature of the intermediate stage cycle and the evaporation temperature of the high-temperature stage cycle. Indicates the evaporation temperature. Indicates the condensation temperature; This indicates the displacement ratio between two adjacent compressor stages; It represents the ratio of the heat transfer coefficient to the product of the heat transfer area of ​​two adjacent heat exchangers. This represents an implicit functional relationship between the intermediate temperature and the product of the evaporation temperature, condensation temperature, displacement ratio, and heat transfer coefficient area. This formula indicates that the intermediate temperature is implicitly determined by the system's thermodynamic balance.

[0064] Once the hardware configuration is determined, its independent controllable range is only ±2~3℃, and the physical significance of forced optimization is limited. The process of ESC continuously applying disturbance signals to find the optimal point itself consumes additional energy, and this optimal point drifts with load changes, leading to a complex control structure and poor robustness. Therefore, this invention abandons the attempt to optimize control of the intermediate temperature and instead adopts an observation-based early warning approach. This is a correct choice based on the physical nature of the extremely narrow independent controllable range of the intermediate temperature, simplifying the control structure and eliminating tracking errors.

[0065] The multi-objective hierarchical control method based on load forecasting and energy storage status in this invention specifically includes: Input data: Time-of-use electricity price table or operating cost coefficient table, operating costs for each time period in the next 24 hours; Thermal storage tank status: current temperature, heat storage capacity, and available capacity; Cold storage tank status: current temperature, cold storage capacity, and available capacity; Load forecasts for each level in the next 1-24 hours based on MES production scheduling and historical data; Decision variable: Secondary compressor frequency and the frequency of the third-stage compressor The value range is each of its rated frequency. compressor frequency It has been locked by the P0 layer; the heat storage tank charging power and heat storage tank heat release power Cold storage tank charging power and the cooling capacity of the cold storage tank .

[0066] Constraints: P0 layer: The dominant load is hardly constrained by the compressor frequency. Locking is satisfied.

[0067] P1 layer: , This indicates the allowable deviation, secondary output soft constraint, and thermal storage tank capacity constraint. ; This represents the amount of heat stored in the heat storage tank at time k. Indicates the maximum heat storage capacity of the thermal storage tank; cold storage tank capacity constraints: , This represents the amount of cold storage capacity of the cold storage tank at time k. Indicates the maximum cold storage capacity of the cold storage tank; compressor frequency range constraints: ; This represents the percentage of the i-th stage compressor's operating frequency relative to its rated frequency at time k; Storage tank power constraint: . This indicates the charging or discharging power of the energy storage tank. This indicates the maximum permissible charging and discharging power of the energy storage tank.

[0068] The dominant process load is the load with the greatest impact on process safety and the strongest rigidity in the cascade system, and the P0 layer is given priority protection.

[0069] The secondary process output is the output of the cascade system that has a relatively small impact on process safety and allows for short-term deviations, and is controlled by soft constraints at layer P1.

[0070] Operating costs are the overall costs of operating the system, including but not limited to operating electricity costs, overall energy consumption, or carbon emissions.

[0071] Example 1 This embodiment applies the method of the present invention to a 500kW cooling / 1037kW heating combined cooling and heating system for multi-objective hierarchical control. The specific steps include: S1, System Configuration This embodiment is applied to a combined cooling and heating system that simultaneously produces 500kW of cooling capacity (-5℃ alcohol water) and 1037kW of heating capacity (120℃ hot water). The system is a three-stage cascade heat pump system.

[0072] Refrigerant configuration: R32 for low temperature stage, R1234ze(E) for intermediate stage, and R1233zd(E) for high temperature stage.

[0073] Design conditions: Low temperature stage: Evaporation temperature -7℃, condensation temperature 35℃, pressure ratio 3.39; Intermediate stage: Evaporation temperature 30℃, condensation temperature 75℃, pressure ratio 3.11; High temperature stage: Evaporation temperature 70℃, condensation temperature 121℃, pressure ratio 3.14.

[0074] The intermediate stage condensing temperature of 75℃ is the thermodynamically optimal design point: at this temperature, the pressure ratio of the intermediate stage (R1234ze) (3.11) and the pressure ratio of the high-temperature stage (R1233zd) (3.14) are almost perfectly balanced (difference <1%), allowing both compressor stages to operate in their high-efficiency range and maximizing the system's overall COP. If the intermediate condensing temperature is below 75℃ (e.g., 73℃), the intermediate stage pressure ratio decreases, but the high-temperature stage pressure ratio increases to 3.31, widening the pressure ratio difference between the two stages to 12%; if it is above 75℃, the intermediate stage pressure ratio increases while the high-temperature stage pressure ratio decreases, similarly leading to imbalance.

[0075] In this embodiment, the cooling load is the dominant process load (P0), the hot water temperature is the secondary process output (P1), and the operating electricity cost is the optimization target of layer P2.

[0076] Compressor configuration: Low-temperature stage semi-hermetic screw compressor (displacement 410m³ / h), intermediate stage semi-hermetic screw compressor (displacement 790m³ / h), high-temperature stage semi-hermetic screw compressor (displacement 1180m³ / h).

[0077] Controller hardware: Siemens S7-1516 CPU, PROFINET communication protocol, control cycle 100ms.

[0078] Energy storage configuration: 100m³ thermal storage tank (70~120℃), 200m³ cold storage tank (30% ethylene glycol solution, -10~-5℃). The effective volume of the thermal storage tank is 1.2~1.5 times the peak-to-valley difference of the daily heat load (considering 10~15% ineffective volume and temperature stratification loss), and the effective volume of the cold storage tank is 1.2~1.5 times the peak-to-valley difference of the daily cooling load.

[0079] S2, the specific implementation of the lexicographical order optimization architecture, such as Figure 2 The diagram shows the step-by-step solution sequence for P0 frequency locking, P1 secondary output, and P2 running cost, as well as the branching process when it is infeasible.

[0080] Solving S21 and P0 layers (period 10 seconds): Input: Cooling load demand (Given by the cold load prediction module), current status of the cold storage tank.

[0081] Calculation: Directly calculate the frequency of the cryogenic stage compressor based on the cooling load requirement. :

[0082] Among them, the full-frequency cooling capacity of the low-temperature stage is Q_cool_100%=497kW. According to CoolProp calculations, R32 has an isentropic efficiency of 76% when evaporating at -7℃ and condensing at 35℃, and a cooling COP of 3.79.

[0083] When cooling load demand hour:

[0084] Because the compressor's maximum frequency is limited to 100%, the P0 layer outputs the low-temperature stage compressor frequency. When the low-temperature stage operates at full frequency, it generates approximately 497kW of cooling. At this point, the cooling load demand exceeds the full-frequency capacity by approximately 3kW, triggering the cold storage tank to release additional cooling to fill the gap.

[0085] If cooling load demand (Exceeding full-frequency capacity) triggers a cooling load shortage alarm and activates the cold storage tank to supplement cooling release.

[0086] Solving S22 and P1 layers (period 10 seconds): Input: Hot water temperature setting value Allowable deviation P0 feasible region (frequency of cryogenic stage compressor) (Locked).

[0087] Target: Adjust the frequency of the intermediate stage compressor and high-temperature compressor frequency .

[0088] Constraint: Intermediate stage compressor frequency High-temperature compressor frequency .

[0089] If no feasible solution exists (e.g., the frequency of the cryogenic stage compressor) (Insufficient heat generation after locking) Allowable deviation is relaxed to This triggers a temperature deviation warning.

[0090] Solving S23 and P2 layers (period 10 seconds): Input: Time-of-use electricity price meter, thermal storage tank status, cold storage tank status.

[0091] Target:

[0092] This represents the time-of-use electricity price at time k. This represents the total power consumed by the system at time k. This represents the change in compressor frequency at time k relative to the previous time.

[0093] The objective function does not include a temperature tracking term (which has already been processed in layer P1).

[0094] Decision variable: Intermediate compressor frequency High-temperature compressor frequency (Cryogenic compressor frequency) (Already locked by P0).

[0095] Solving for a 2D QP problem takes approximately 12ms.

[0096] S3, Specific implementation of intermediate temperature state observation and early warning.

[0097] Sensor configuration: Pt100 temperature sensors are installed at the outlet of the intermediate stage circulating shell and the outlet of the high-temperature stage circulating shell, respectively, with a sampling period of 1 second.

[0098] Design balance values: The design balance temperature for the intermediate stage evaporation is approximately 33℃, falling between the -7℃ low-temperature stage evaporation and the 75℃ intermediate stage condensation, determined by thermal balance. The design balance temperature for the high-temperature stage evaporation is approximately 73℃, falling between the 30℃ intermediate stage evaporation and the 121℃ high-temperature stage condensation, also determined by thermal balance. These design balance values ​​are operating balance points determined based on the actual compressor displacement and heat exchanger area configuration, and deviate from the aforementioned thermodynamic design points by approximately 3℃. The warning logic is shown in Table 1, and an evaluation is performed every 10 seconds.

[0099] Table 1 Early Warning Logic

[0100] like Figure 3 The diagram shows the triggering conditions and response actions for Level 1 warning, Level 2 protection, and Level 3 shutdown. The key principle is: do not adjust the compressor frequency to correct the intermediate temperature when it deviates from the set point. Warnings are only used to prompt operators to check the system status (such as sudden load changes, equipment malfunctions, etc.).

[0101] Experimental comparison of the ESC method: To verify the assertion that the intermediate temperature has an extremely narrow independently controllable range, simulations were performed on the system described in the example using the ESC method of Wang et al. (2020). The ESC perturbation frequency was set to 0.01 Hz, the amplitude to ±2 Hz, and the integral gain to 0.5. The results showed that during ESC operation, the intermediate temperature oscillated continuously between 70 and 76 °C with an oscillation amplitude of ±3 °C, and the system COP decreased by about 3% due to the ESC perturbation. In contrast, under the state observation scheme of this invention, the intermediate temperature remained stable at 73 ± 1 °C without oscillation, and the COP remained stable. The optimal point sought by ESC drifted under different loads. At 80% load, ESC converged to approximately 71 °C, and at 100% load, approximately 75 °C. This verified that the optimal point drifts with the load, and ESC requires complex online optimization to track the changing target. This invention simplifies the control structure by abandoning the tracking.

[0102] S4. Specific implementation of multi-objective hierarchical control.

[0103] The time-of-use electricity price is shown in Table 2, which represents a typical industrial electricity price.

[0104] Table 2 Time-of-use Electricity Pricing Table

[0105] The thermal storage tank scheduling strategy is as follows: During the early morning off-peak period (0:00~8:00): the system operates at full frequency according to the design load. (Cryogenic stage compressor frequency) (P0 locked, cooling capacity approximately 497kW), intermediate stage compressor frequency High-temperature compressor frequency The heat generated is approximately 1016 kW, of which 500 kW supplies the process heat load and 516 kW is charged into the heat storage tank. The temperature of the heat storage tank rises from 70°C to 105°C, and the heat storage capacity is approximately 4100 kWh.

[0106] During the morning peak period (9:00~11:00), the heat storage tank releases approximately 518kW of heat, and the compressor operates at a reduced frequency: the low-temperature stage compressor frequency... (P0 locked), intermediate stage compressor frequency High-temperature compressor frequency The heat output is approximately 927kW, with a total heating supply of approximately 1445kW, meeting the peak heat load. Total power consumption decreases from 525kW during off-peak hours to 430kW, saving 95kW × 2h × 1.0 yuan = 190 yuan. Afternoon peak hours (14:00~17:00): Same strategy as the morning, the heat storage tank operates at a reduced frequency of heat release, such as... Figure 4 The figure shows the time-series changes in compressor frequency, heat storage tank status, and electricity price over 24 hours. A comparison of the daily electricity cost schemes is shown in Table 3.

[0107] Table 3 Comparison of Electricity Costs for the Whole Day

[0108] The electricity cost saved using the method of this invention is (7560-6076) / 7560=19.6%.

[0109] S5, the specific implementation of dual-time-scale hierarchical control.

[0110] like Figure 5 The diagram shows the data flow and periodic relationship between the steady-state programming optimization layer and the dynamic tracking control layer.

[0111] Upper-level steady-state planning optimization layer (cycle 10 minutes): Model: Steady-state linear heat balance equation:

[0112] in, This indicates the heat released during condensation in the low-temperature stage cycle. This indicates the heat absorbed by evaporation in the low-temperature stage cycle. This indicates the power consumption of the cryogenic stage compressor. This indicates the heat release from condensation in the intermediate stage cycle. This indicates the heat absorbed by evaporation in the intermediate stage cycle. This indicates the power consumption of the intermediate stage compressor. This indicates the heat released during condensation in the high-temperature stage cycle. This indicates the heat absorbed by evaporation in the high-temperature cycle. This indicates the power consumption of the high-temperature stage compressor.

[0113] Solution: Linear programming (LP), with decision variables being the compressor frequency and the charging / discharging power of the energy storage tank at different times during the 24-hour period.

[0114] Output: Target frequency reference values ​​for each time period include: Cryogenic stage compressor frequency reference value. Intermediate stage compressor frequency reference value High-temperature compressor frequency reference value .

[0115] Lower dynamic tracking control layer (period 10 seconds): Model: Locally Linearized State Space :

[0116] Among them, state variables This includes the temperature of each heat exchanger and the status of the energy storage tank; control variables. include , ( (Already locked by P0); Disturbance This includes changes in cooling / heating loads and changes in ambient temperature. Represents the system state matrix. Represents the control input matrix. This represents the perturbation input matrix.

[0117] Dimensionality reduction methods: Calculate the partial derivative of COP with respect to the control variable at the steady-state operating point. :

[0118] Wherein, v_1, v_2, and v_3 are the opening degrees of the low-temperature stage, intermediate stage, and high-temperature stage expansion valves, respectively. The coefficient of performance (COP) represents the ratio of the sum of the cooling and heating capacity of the system to the total power consumption of the compressor.

[0119] according to Sort, select and As the main optimization variable (with maximum sensitivity), Let represent the j-th component in the sensitivity vector S, i.e., the partial derivative of the system performance coefficient with respect to the j-th control variable. This represents the absolute value of the partial derivative; Locked directly by layer P0. 2D QP solution time: approximately 12ms (Siemens S7-1516 CPU).

[0120] The running effect of this embodiment: Dictionary order optimization effect: In a 1000-hour continuous operation test, the cooling load satisfaction rate was 99.8% (P0 infeasibility alarm was triggered only twice under extreme conditions), and the proportion of hot water temperature within ±2℃ of the set value was 98.2%.

[0121] Intermediate temperature warning effect: The intermediate temperature deviation of ±5℃ warning was triggered 15 times (all under sudden load changes), without triggering secondary protection or tertiary shutdown. After the warning, the operator found that 8 of them were normal load switching and 7 were equipment status adjustments.

[0122] Economic scheduling effect: With approximately 8,000 hours of operation per year (approximately 330 consecutive operating days), and daily electricity costs calculated based on 24-hour continuous operation scheduling, the cost of this invention is approximately RMB 2.01 million, while the cost without optimization is approximately RMB 2.5 million, representing a reduction of 19.6%.

[0123] PLC real-time performance: The average time for solving the lower-level QP is no more than 15ms, meeting the 10-second control cycle requirement. The CPU utilization rate is approximately 38%, leaving ample margin.

[0124] Robustness test: The system continued to operate (without shutdown) under the following extreme conditions: a sudden drop of 15°C in heat source temperature (simulating a winter morning), a sudden increase of 50% in cold load (simulating the simultaneous start of multiple batches of fermentation), and premature emptying of the heat storage tank during peak electricity prices (simulating abnormal conditions).

[0125] Example 2 This embodiment provides four comparative examples based on Embodiment 1. Figure 6 The bar chart shows the operational performance comparison between the present invention and comparative methods (weighted predictive control MPC, proportional-integral-derivative control PID, extreme value search control ESC, and pure heat pump optimization). Figure 6 (a) is a bar chart comparing cooling load satisfaction rate, (b) is a bar chart comparing temperature compliance rate, (c) is a bar chart comparing daily electricity costs, (d) is a bar chart comparing the number of shutdowns under extreme operating conditions, (e) is a bar chart comparing intermediate temperature oscillation amplitude, and (f) is a bar chart comparing system availability.

[0126] Comparative Example 1: Traditional weighted MPC control.

[0127] The data for Comparative Example 1 were obtained using a control system simulation model based on the same system configuration and operating conditions as in Embodiment 1 of the present invention.

[0128] The system configuration is the same as in Example 1, using traditional multi-objective weighted MPC, with the cost function... :

[0129] Weight settings: , , (Attempting to prioritize cooling load). This indicates the actual cooling capacity of the system. This indicates the cooling load demand. This indicates the actual temperature of the hot water produced by the high-temperature stage. This indicates the hot water temperature setting value. This indicates the total power consumption of the system.

[0130] Cooling load satisfaction rate: 93.1% (weighted compromise due to constraint conflict leads to insufficient cooling capacity); hot water temperature compliance rate: 96.8%; annual electricity cost: approximately 2.38 million yuan (approximately 19% higher than this invention); number of shutdowns under extreme conditions: 8 times per year (MPC has no solution when constraints conflict).

[0131] Intermediate temperature oscillation amplitude: ±2.0℃ (weighted optimization produces small adjustment oscillations when constraints conflict); system availability: 95.0%.

[0132] Comparative Example 2: Setpoint Tracking PID Control.

[0133] The data for Comparative Example 2 were obtained using a control system simulation model based on the same system configuration and operating conditions as in Example 1 of this invention.

[0134] The system configuration is the same as in Example 1, and PID control is used.

[0135] Low-temperature stage: Tracks evaporation pressure (indirectly controls cooling capacity), PID parameters Kp=3.0, Ki=0.8, Kd=0.3. Kp represents the proportional coefficient, Ki represents the integral coefficient, and Kd represents the derivative coefficient.

[0136] Intermediate stage: Tracking intermediate temperature = 73℃ (set value), PID parameters Kp = 2.0, Ki = 0.5, Kd = 0.2.

[0137] High-temperature stage: Tracks 120℃ outlet water temperature, PID parameters Kp=1.5, Ki=0.4, Kd=0.15.

[0138] Intermediate temperature oscillation: The intermediate temperature oscillates continuously between 68 and 78°C (PID makes ineffective adjustments to the intermediate temperature), with an oscillation period of about 3 minutes; Hot water temperature fluctuation: ±5°C (due to the conduction of intermediate temperature oscillation); Annual electricity cost: 2.72 million yuan (without dual time scale optimization); Cooling load satisfaction rate: 89.2% (intermediate temperature oscillation causes fluctuations in low-temperature operating conditions).

[0139] Percentage of hot water temperatures within ±2℃ of the set value: 82.0% (PID ineffective adjustment of intermediate temperature leads to hot water temperature fluctuations of ±5℃, significantly reducing the ±2℃ compliance rate); Number of shutdowns under extreme conditions: 15 times per year (continuous oscillation of intermediate temperature triggers protective shutdown); System availability: 93.0%.

[0140] Comparative Example 3: ESC intermediate temperature optimization (Wang et al., 2020 reproduction).

[0141] The data for Comparative Example 3 were obtained using a control system simulation model based on the same system configuration and operating conditions as in Example 1 of this invention.

[0142] The system configuration was the same as in Example 1, and the simulation was reproduced according to the method described by Wang et al. (2020). The ESC parameters were set as follows: perturbation frequency 0.01Hz, amplitude ±2Hz, integral gain 0.5; the goal was to find the intermediate temperature operating point that maximizes COP.

[0143] Intermediate temperature oscillation: During ESC operation, the intermediate temperature oscillates continuously between 70~76℃ (oscillation amplitude ±3℃), and the ESC disturbance itself introduces an additional power consumption of about 3%; System COP: Due to ESC oscillation, the actual COP is 2.8% lower than that of steady-state operation; Optimal point drift: At 80% load, ESC converges to about 71℃, and at 100% load, it converges to about 75℃, verifying the assertion that the intermediate temperature operating point drifts with the load; Cooling load satisfaction rate: 92.5% (ESC occasionally reduces the low temperature stage frequency in pursuit of maximizing COP).

[0144] Percentage of hot water temperatures within ±2℃ of the set value: 90.0% (ESC oscillations cause slight fluctuations in hot water temperature); Number of shutdowns under extreme conditions: 6 times per year (ESC occasionally triggers protection due to excessive adjustment caused by "optimal point" drift); System availability: 97.0%; Annual electricity cost: approximately 2.62 million yuan (ESC disturbances themselves introduce additional power consumption).

[0145] Comparative Example 4: Optimization of COP for pure heat pumps.

[0146] The data for Comparative Example 4 were obtained using a control system simulation model based on the same system configuration and operating conditions as in Example 1 of this invention.

[0147] The system configuration is the same as in Example 1, but the optimization objective is to maximize the COP of the pure heat pump (ignoring the cooling output constraint).

[0148] Cooling load fulfillment rate: 86.3% (the frequency of the low-temperature stage was reduced in pursuit of maximizing COP, resulting in insufficient cooling capacity); Actual system operation: due to frequent failure to meet cooling load, the system actually operates in a passive mode with the low-temperature stage operating at full frequency and the other stages following, and frequent start-stop and mode switching increase energy consumption.

[0149] Percentage of hot water temperatures within ±2℃ of the set value: 78.0% (frequent start-stop and mode switching caused significant temperature fluctuations); Number of shutdowns under extreme conditions: 12 times per year (frequent failure to meet cooling load requirements led to frequent system mode switching); System availability: 94.0%; Annual electricity cost: 2.63 million yuan.

[0150] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-objective hierarchical control method for a three-stage cascade heat pump system, characterized in that, include: The control objective is hierarchically optimized using a lexicographical optimization architecture, with priorities divided into P0, P1, and P2 layers. The P0 layer represents an absolute hard constraint and has the highest priority. Based on the current dominant process load demand, the frequency setpoint of the corresponding compressor is directly calculated and locked to ensure that the output absolutely matches the demand. The dominant process load refers to the load with the greatest impact on process safety and the strongest rigidity in the cascade system. If there is no feasible solution in the P0 layer, an alarm is triggered that the dominant load cannot be met, and safety protection is activated. Solve for layers P0, P1, and P2 respectively; A dual-time-scale hierarchical control architecture is adopted to construct a steady-state planning optimization layer and a dynamic tracking control layer, respectively. The evaporation temperatures of the intermediate stage cycle and the high-temperature stage cycle in the cascade system are used as intermediate temperatures. The state of the intermediate temperature is observed, and an early warning mechanism is established. Control commands are output to adjust the operating frequency of each stage compressor and the charging and discharging power of the energy storage tank, thereby realizing real-time physical control of the heat pump system. The early warning mechanism includes a first-level early warning, a second-level protection, and a third-level shutdown. The first-level early warning indicates that when the intermediate temperature deviates from the design balance value by more than ±5℃, an operational status deviation warning is triggered, prompting the operator to check the load matching and equipment status, without triggering control adjustments. The secondary protection means that when the intermediate temperature deviates from the design balance value by more than ±10℃, the load reduction protection is triggered, and the maximum operating frequency of the secondary and tertiary compressors is automatically reduced by 20% to prevent the compressor discharge temperature from being too high or the pressure ratio from exceeding the limit. At the same time, an alarm is sent to the operator. The three-level shutdown means that when the intermediate temperature deviates from the design balance value by more than ±15℃, the safety shutdown protection is triggered, and the compressor is shut down step by step to prevent equipment damage.

2. The multi-objective hierarchical control method for a three-stage cascade heat pump system according to claim 1, characterized in that, The P1 layer is a soft constraint and has a secondary priority. The secondary process output is maintained within a set value range. The secondary process output refers to the output in the cascade system that has a small impact on process safety and allows for short-term deviations. The P1 layer is solved within the feasible region of the P0 layer, allowing for moderate deviations under extreme conditions.

3. The multi-objective hierarchical control method for a three-stage cascade heat pump system according to claim 1, characterized in that, The P2 layer is the objective for optimizing runtime costs and has the lowest priority; within the feasible regions of P0 and P1, it minimizes the system runtime cost in the prediction time domain. in, for The system operating cost at any given time, which includes at least operating electricity costs, overall energy consumption, and carbon emissions. The penalty weight is the rate of change of frequency. This represents the change in compressor frequency at time k relative to the previous time. This represents the number of sampling steps in the prediction time domain. This represents the cumulative value of the system's operating cost within the predicted time domain; The P2 layer only searches for the lowest operating cost running point within the feasible region where the P0 and P1 layers converge, and does not repeatedly apply weighted penalties to the secondary output.

4. The multi-objective hierarchical control method for a three-stage cascade heat pump system according to claim 1, characterized in that, When solving for the P0 layer, the frequency of the corresponding stage compressor is directly calculated and locked based on the dominant process load requirements. ; Within the feasible region of the P0 layer, the P1 layer is solved, and the secondary process output tracking error is minimized. The frequency of the remaining compressor stages is adjusted accordingly. If there is no feasible solution for the P1 layer, the secondary output is allowed to deviate from the set value range but not exceed the relaxation threshold. When the deviation exceeds the allowable deviation, a secondary output deviation warning is triggered. Solve the P2 layer within the feasible regions of the P0 and P1 layers, with the goal of minimizing the total operating cost, and optimize the frequency of the remaining stage compressors and the charging and discharging power of the energy storage tank.

5. The multi-objective hierarchical control method for a three-stage cascade heat pump system according to claim 1, characterized in that, The steady-state planning optimization layer, based on a steady-state thermal balance model and load forecasting, solves for the optimal energy storage scheduling plan and the reference values ​​for the secondary compressor frequencies within the forecast time domain. It employs a steady-state linear model solved via linear programming, outputting the reference values ​​for the secondary compressor frequencies at each time period. Third-stage compressor frequency reference value And the energy storage tank charging and discharging plan.

6. The multi-objective hierarchical control method for a three-stage cascade heat pump system according to claim 1, characterized in that, The dynamic tracking control layer can quickly respond to load fluctuations and constraint satisfaction, and track the benchmark value given by the steady-state planning optimization layer; A locally linearized state-space model is adopted, and the solution is obtained by dimension-reduced quadratic programming. The main optimization variables are the frequencies of the secondary and tertiary compressors, and the output is the setpoint values ​​of the compressor frequencies of each stage.

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