Energy-storage backup combined scheduling method for adiabatic compressed air energy storage

Abstract

The application discloses an energy-backup combined dispatching method for adiabatic compressed air energy storage, and belongs to the field of power system dispatching. The method is directed to a power system containing large-scale A-CAES, and a corresponding energy-backup combined dispatching strategy is provided. The dispatching strategy can fully play a key role of the A-CAES in positive and negative backup supply, and significantly reduce the regulation pressure of a thermal power unit. Meanwhile, relying on backup continuity constraints, backup dead zones are completely compensated, and the risk of backup calling failure is eliminated from the decision-making level. For the dual nonlinear constraints of the time-coupling type and the time-independent type of the dispatching model, MTFIM is adopted to realize fast and accurate solution of the dispatching problem, and the dual nonlinear problems caused by the time-coupling type energy safety constraint and the time-independent type backup safety constraint of the A-CAES are accurately processed, instead of simply ignoring or approximately simplifying the nonlinear terms, so that safe and high-precision solution of the dispatching model is realized.

Description

Technical Field

[0001] This invention belongs to the field of power system dispatching, and more specifically, relates to an energy-reserve joint dispatching method for adiabatic compressed air energy storage. Background Technology

[0002] In the daily operation of power systems, power sources such as thermal power units are typically required to reserve power regulation margins to cope with the uncertainties in load and renewable energy power. This is called spinning reserve, which should be able to cover the prediction errors of load and renewable energy power. Reserves to cope with positive and negative errors are called positive reserves and negative reserves, respectively. With the large-scale grid connection of wind power, power uncertainty has become increasingly prominent, leading to a tightening of the supply and demand relationship for spinning reserve. When reserve demand is high, relying solely on thermal power units for reserves will significantly increase the daily operating costs of the power system. In addition, to quickly fill the reserve gap, some thermal power units may be forced to start to accelerate the overall reserve response speed, which will compress the available output space of wind power and cause wind curtailment. In extreme cases, the power system may not be able to simultaneously meet the constraints of spinning reserve and power balance, leading to dispatch failure. Summary of the Invention

[0003] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides an energy-backup joint scheduling method for adiabatic compressed air energy storage, which fully leverages the key role of A-CAES in positive and negative backup supply, thereby reducing the regulation pressure on thermal power units.

[0004] To achieve the above objectives, according to a first aspect of the present invention, an energy-backup joint scheduling method for adiabatic compressed air energy storage is provided, comprising: With the goal of minimizing the total operating cost of the power system, a day-ahead energy-reserve joint dispatch model of the power system containing A-CAES is established, and the model is solved under preset constraints to obtain the optimal dispatch scheme of the generating units and the A-CAES in the power system. The power system also includes thermal power units and wind farms; the preset constraints include A-CAES energy constraints, A-CAES reserve constraints, reserve response constraints, reserve continuity constraints, thermal power unit constraints, wind power constraints, and power system constraints.

[0005] According to a second aspect of the present invention, an electronic device is provided, comprising: a computer-readable storage medium and a processor; The computer-readable storage medium is used to store executable instructions; The processor is configured to read executable instructions stored in the computer-readable storage medium and execute the method as described in the first aspect.

[0006] According to a third aspect of the invention, a computer-readable storage medium is provided, the computer-readable storage medium storing computer instructions for causing a processor to perform the method as described in the first aspect.

[0007] According to a fourth aspect of the invention, a computer program product is provided, comprising a computer program or instructions that, when executed by a processor, implement the method described in the first aspect.

[0008] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects: The method provided in this invention proposes a corresponding energy-reserve joint dispatch strategy for power systems containing large-scale A-CAES (Automatic Energy-Reserve Scheduling System), which constructs a reserve model for A-CAES. To address the dual nonlinear constraints of the dispatch model—both time-coupled and time-independent—MTFIM (Mechanical Management Function) is employed to achieve a fast and accurate solution to the dispatch problem. Compared with existing technologies, the main advantages of this invention are as follows: (1) The proposed scheduling strategy can give full play to the key role of A-CAES in positive and negative reserve supply, and significantly reduce the regulation pressure of thermal power units. At the same time, relying on the reserve continuity constraint, the reserve dead zone is fully compensated, and the risk of reserve call failure is eliminated from the decision-making level.

[0009] (2) MTFIM can accurately handle the dual nonlinear problems caused by the time-coupled energy security constraints and the time-independent backup security constraints of A-CAES, rather than simply ignoring or approximating the nonlinear terms, thereby achieving safe and high-precision solution of the scheduling model. Attached Figure Description

[0010] Figure 1 This is a structural diagram of A-CAES.

[0011] Figure 2 The isentropic compression efficiency and expansion efficiency curves of step A in the energy-backup joint scheduling method for adiabatic compressed air energy storage provided in the embodiments of the present invention.

[0012] Figure 3 A diagram showing the range of callable compressed power for the A-CAES energy-backup joint scheduling method for adiabatic compressed air energy storage provided in this embodiment of the invention.

[0013] Figure 4 The four-quadrant backup feasible region diagram of the energy-backup joint scheduling method for adiabatic compressed air energy storage provided in the embodiments of the present invention.

[0014] Figure 5A schematic diagram of the solution process for the day-ahead energy-reserve joint dispatch model of the power system containing A-CAES provided in the embodiments of the present invention (MP and SP represent the main problem and sub-problem, respectively).

[0015] Figure 6 This is a system topology diagram for step B of embodiment 1 of the present invention.

[0016] Figure 7 In the diagrams (a) to (d), the wind power output diagrams for wind farms 1 to 4 in step 1 of Embodiment 1 of the present invention are respectively. Figure 7 In the figure, (e) and (f) are the predicted curves of load power and ambient temperature, respectively.

[0017] Figure 8 In the diagrams (a) and (b), the A-CAES power diagrams for Case 1 and Case 2 of Embodiment 1 of the present invention are shown respectively.

[0018] Figure 9 In the diagrams (a) to (c), the pressure of the A-CAES gas storage chamber, the mass of the hot water tank, and the air flow rate of the expansion subsystem are respectively for Case 1 and Case 2 of Embodiment 1 of the present invention.

[0019] Figure 10 (a) and (b) in the figure are the front view diagrams of Case 1 and Case 2 of Embodiment 1 of the present invention, respectively.

[0020] Figure 11 In the diagrams (a) and (b), the negative backup diagrams for Case 1 and Case 2 of Embodiment 1 of the present invention are shown respectively.

[0021] Figure 12 In the diagrams (a) to (c), respectively, for Case 1 and Case 2 of Embodiment 1 of the present invention, the pressure of the gas storage chamber, the mass of the hot water tank, and the air flow rate of the expansion subsystem are provided by GPI, S2G, and C2G in A-CAES after standby. Figure 12 In the diagrams (d) to (e), the pressure of the gas storage chamber and the mass of the hot water tank after standby are provided by CPI, S2C and G2C in A-CAES, respectively, according to Case 1 and Case 2 of Embodiment 1 of the present invention. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0023] Large-scale adiabatic compressed air energy storage (A-CAES) has advantages such as rapid response, short switching time, and wide power regulation range, and is considered a promising backup power source. Introducing the backup regulation mechanism of A-CAES into the day-ahead dispatch of the power system is expected to alleviate the contradiction of relying solely on thermal power units for backup.

[0024] Based on this, embodiments of the present invention provide an energy-reserve joint scheduling method for adiabatic compressed air energy storage, comprising: With the goal of minimizing the total operating cost of the power system, a day-ahead energy-reserve joint dispatch model of the power system containing A-CAES is established, and the model is solved under preset constraints to obtain the optimal dispatch scheme of the generating units and the A-CAES in the power system. The power system also includes thermal power units and wind farms; the preset constraints include A-CAES energy constraints, A-CAES reserve constraints, reserve response constraints, reserve continuity constraints, thermal power unit constraints, wind power constraints, and power system constraints.

[0025] Specifically, the method provided by the present invention includes the following steps: Step A: Construct an A-CAES thermodynamic model that considers the variation characteristics of key parameters such as temperature, pressure, and efficiency, and integrates parallel compression and constant sliding pressure expansion designs.

[0026] Step B: Construct a day-ahead energy-reserve joint dispatch model for the power system containing A-CAES.

[0027] Step C: Propose a solution method for the nonlinear scheduling model described in Step B.

[0028] In step A, the A-CAES structure is first described as follows: A-CAES structure diagram is as follows: Figure 1 As shown, variables are marked in red; italic subscripts... i , j , k These are the compression level number, expansion level number, and compressed line number, respectively. This refers to the compression power of a single line. Power generation for A-CAES; , , These represent the number of compression levels, expansion levels, and number of compressed lines, respectively. , These are environmental pressure and temperature, respectively. , These are the isentropic compression and expansion efficiencies, respectively. , These are compression ratio and expansion ratio, respectively. , These are the inlet working fluid (i.e., air) temperatures for the compressor and expander, respectively. , These are the efficiency coefficient and pressure loss rate of the heat exchanger, respectively. , , , , These are the working fluid mass, pressure, inlet temperature, internal temperature, and wall temperature of the gas storage chamber, respectively. The outlet temperature of the heat transfer fluid (i.e., hot water) in the heat exchanger of the compression subsystem; , These are the working fluid flow rates of the compression and expansion subsystems, respectively. , These are the water temperatures of the hot water tank and the cold water tank, respectively. For the quality of the hot water tank.

[0029] In step A, the A-CAES thermodynamic model for the compression condition is as follows: During compression, the operation of each row of compressors is independent, and A-CAES can select one or more rows of compressors to operate according to the scheduling plan. A-CAES consumes electrical energy to compress atmospheric air into high-pressure air and stores it in the air storage chamber. Simultaneously, ambient temperature circulating water is pumped from the cold water tank and convects with the high-temperature compressed air in the heat exchanger, achieving interstage cooling of the air. The circulating water absorbs the heat of compression and flows back to the hot water tank. After compression, electrical energy is converted into the potential energy of the compressed air and the thermal energy of the circulating water.

[0030] (1) Compression power

[0031] In the formula, The specific heat capacity of air at constant pressure; This is the specific heat ratio of air.

[0032] (2) Final stage compression ratio During compression, as the pressure in the gas storage chamber increases, the compression ratio of each stage increases to varying degrees, mainly concentrated in the final stage compression ratio. Therefore, we can assume that the final stage compression ratio is a variable, while the compression ratios of other stages are constants.

[0033]

[0034] (3) Isentropic compression efficiency The isentropic compression efficiency can be fitted as a function of the compression power, which exhibits... Figure 2 The changing trend of the blue line.

[0035] (4) Inlet working fluid temperature of the compressor

[0036] (5) Inlet working fluid temperature of the gas storage chamber

[0037] (6) Temperature of the heat transfer medium at the outlet of the heat exchanger

[0038] (7) Temperature of hot water tank

[0039] In the formula, the subscript " t " is a time index; The duration between adjacent moments; This is the specific heat capacity of water.

[0040] (8) Quality of hot water tank

[0041] (9) Gas storage chamber pressure

[0042] In the formula, R is the gas constant of air; This refers to the volume of the gas storage chamber; α and β These are the natural convection heat transfer coefficient and the forced convection heat transfer coefficient between the air and the walls inside the gas storage chamber, respectively.

[0043] (10) Gas storage chamber quality

[0044] (11) Temperature of the gas storage chamber

[0045] In step A, the A-CAES thermodynamic model for the power generation condition is as follows: During power generation, the A-CAES releases high-pressure air from the storage chamber to drive the expander, which in turn powers the generator. Simultaneously, high-temperature circulating water is pumped from the hot water tank and convects with the compressed air in the heat exchanger, achieving interstage reheating of the air to improve its work capacity. If the pressure in the storage chamber is not lower than the rated inlet pressure of the first-stage expander, the A-CAES operates in constant-pressure expansion mode, stabilizing the inlet pressure of the first-stage expander at the rated value by controlling the throttle valve. Conversely, if the pressure is lower, the A-CAES operates in sliding-pressure expansion mode, where the inlet pressure of the first-stage expander equals the pressure in the storage chamber. After power generation, the potential energy of the compressed air and the thermal energy of the circulating water are converted into electrical energy.

[0046] (1) Power generation

[0047] (2) Final stage expansion ratio In constant-pressure expansion mode, the expansion ratio of each stage remains at its rated value. In sliding-pressure expansion mode, as the pressure in the gas storage chamber decreases, the expansion ratio of each stage decreases to varying degrees, mainly concentrated in the final stage expansion ratio. Therefore, it can be assumed that the final stage expansion ratio is a variable, while the expansion ratios of other stages are constants.

[0048]

[0049] (3) Isentropic expansion efficiency The isentropic expansion efficiency can be fitted as a function of power generation, exhibiting... Figure 2 The changing trend of the green line.

[0050] (4) Inlet working fluid temperature of the expander

[0051] (5) Temperature of hot water tank

[0052] (6) Quality of hot water tank

[0053] (7) Gas storage chamber pressure

[0054] (8) Gas storage chamber quality

[0055] (9) Temperature of the gas storage chamber

[0056] In step A, the A-CAES thermodynamic model for the standby condition is as follows: In standby mode, the mass of the gas storage chamber, the temperature and mass of the hot water tank of the A-CAES remain unchanged. However, due to heat exchange between the gas inside the storage chamber and the walls, the pressure and temperature of the storage chamber change.

[0057] (1) Temperature of hot water tank

[0058] (2) Quality of hot water tank

[0059] (3) Gas storage chamber quality

[0060] (4) Gas storage chamber pressure

[0061] (5) Temperature of the gas storage chamber

[0062] In step B, the types of backups that A-CAES can provide and the influencing factors are as follows: A-CAES can provide positive and negative backups in compression, power generation, and standby conditions, as shown in Table 1.

[0063] Table 1

[0064] In each abbreviation, C represents compression, G represents generation, S represents shutdown, P represents power, I represents increase, D represents decrease, and 2 represents conversion. For example, CPD indicates providing positive reserve by reducing power through compression, and G2C indicates providing negative reserve by switching from generation mode to compression mode.

[0065] The standby capability of A-CAES is mainly affected by the following factors.

[0066] (1) Boundaries of power, gas storage chamber pressure, hot water tank mass, and working fluid flow rate of expansion subsystem When A-CAES provides backup by adjusting power or switching from other operating conditions to compression or generation operating conditions, it must be ensured that the above variables do not exceed their limits, as shown in Table 2.

[0067] Table 2

[0068] In Table 2, , These are the maximum and minimum values ​​of single-row compression power, respectively. , These represent the maximum and minimum power generation capacity of the power station, respectively. , These are the maximum and minimum pressure values ​​of the gas storage chamber, respectively. , These represent the maximum and minimum values ​​of the hot water tank's mass, respectively. This represents the upper limit of the airflow rate for the expansion subsystem.

[0069] (2) Climb rate and standby response time Due to limitations in ramp rate and mode switching time, A-CAES cannot complete power regulation and mode switching instantaneously. Typically, A-CAES can switch from full generation to full compression within 5 minutes and return to full generation within 15 minutes. If the power system imposes stringent requirements on backup response time (e.g., 5 minutes), A-CAES may not be able to flexibly provide backup within its power range. However, in practice, power systems generally require full backup response within 15 minutes. Based on this reality, the backup regulation capability of A-CAES will not be limited by the aforementioned ramp rate and backup response time.

[0070] In step B, the spare dead zone of A-CAES is as follows: Because the minimum compression and generation capacity of A-CAES are greater than 0, when the power system calls upon the backup provided by A-CAES through operating condition switching, the required backup power may fall exactly between the minimum power and 0, leading to backup call failure. This power range, although within the backup capacity of A-CAES, cannot be utilized and is called the backup dead zone. For example, if the power system's positive backup demand is 100MW, and A-CAES provides this backup through S2G, its minimum generation capacity is 70MW. If the actual power imbalance is 80MW, A-CAES can start and generate 80MW to compensate; however, when the imbalance is 60MW, A-CAES cannot call upon the backup to restore power balance. In this case, the backup dead zone of A-CAES is (0, 70)MW, and the available backup range is [70, 100]MW. To address the risk of backup response failure, it is essential to ensure that the continuously adjustable backup provided by thermal power units can fully compensate for this backup dead zone.

[0071] Parallel compression can reduce the standby dead zone. For a rated compression power of... Minimum load rate The schedulable power range of A-CAES under single-line, double-line, and triple-line compression designs is as follows: Figure 3 As shown.

[0072] From the diagram, we can conclude that for a given... For A-CAES with a parallel structure, the spare dead zone width on the compression side is ( ):

[0073] In practical engineering, large-scale A-CAES compressors can achieve... Based on this, the backup dead zone is only composed of... The composition, the width is Therefore, parallel compression reduces the dead zone width from... Shrink to This reduces the reserve compensation burden on thermal power units. In this invention, the A-CAES compression side uses a minimum load rate of 0.5. Furthermore, due to the power range being extended to [ , The backup based on CPD and CPI is more flexible.

[0074] In step B, the four-quadrant alternative feasible regions of A-CAES are as follows: Figure 4 This demonstrates the four-quadrant reserve feasibility domain of A-CAES, representing the reserve range provided through 10 methods at different power levels. For example, when A-CAES operates at its rated generating power (the top vertex on the vertical axis), positive reserve cannot be provided via GPI, but negative reserve can be provided via GPD, G2C, or G2S. The first two methods are continuously adjustable, with feasible ranges of [0, ..., ... ]and[ , The third method has a fixed reserve value of [missing value]. .

[0075] In step B, the energy-reserve joint dispatch model for the power system containing A-CAES is as follows: (1) Objective function

[0076]

[0077]

[0078]

[0079]

[0080] In the formula, italic subscripts g , h , t These are the numbers for thermal power units, wind farms, and dispatch time points, respectively. , , These are the operating, standby, and start-up / shutdown costs of thermal power units, respectively. The cost of curtailing wind power; , These are the primary and constant coefficients of the operating cost of thermal power units, respectively. , These are the positive and negative standby cost coefficients for thermal power units, respectively. The cost of a single start-up and shutdown of a thermal power unit; This represents the cost coefficient for wind curtailment penalties. For the operating status of the thermal power unit, take 0 when the unit is stopped and 1 when the unit is started. This refers to the power output of the thermal power unit. , These are the positive and negative backups for the thermal power unit, respectively. , These are the predicted power output and dispatched power output of the wind farm, respectively.

[0081] (2) Energy constraints of A-CAES This section is used to constrain the charging and discharging plan of A-CAES, including the analytical expressions of key state variables and operational boundary constraints. The former has been introduced in step A, and the latter is as follows: ① Operational state constraints

[0082] In the formula, , These represent the compression and power generation states of A-CAES, respectively. When in compression mode, they are 1 and 0, respectively, and when in power generation mode, they are 0 and 1, respectively.

[0083] ② Power Constraint like Figure 2 As shown by the blue line, It typically exhibits a monotonically increasing property. Therefore, given... Under these conditions, the fewer lines of compressed data running online, the higher the overall compression efficiency. Furthermore, It also has an upward convexity. Therefore, in Given a fixed number of online rows, when The overall compression efficiency reaches its maximum when all lines are evenly distributed across the network. These two principles together define the power distribution strategy for each compressed line in A-CAES.

[0084]

[0085]

[0086]

[0087] In the formula, This represents the total compression power of A-CAES; The above power allocation principle applies.

[0088] ③ Pressure constraints in the gas storage chamber and mass constraints of the hot water tank The pressure in the gas storage chamber and the mass of the hot water tank must not exceed their safety limits. Furthermore, to ensure that the power plan of the A-CAES on the current scheduling day does not affect its flexible operation on the following day, the initial pressure in the gas storage chamber on the following day must not be lower than the initial pressure on the current scheduling day, and the initial mass of the hot water tank must not be lower than the initial mass on the current scheduling day.

[0089]

[0090]

[0091]

[0092]

[0093] In the formula, T This represents the number of time points scheduled in the previous day; , These are the initial values ​​for the pressure in the gas storage chamber and the mass of the hot water tank, respectively.

[0094] ④ Airflow constraints of the expansion subsystem

[0095] In the formula, This is the upper limit of the airflow rate for the expansion subsystem; M It is a sufficiently large positive number.

[0096] (3) Alternate constraints of A-CAES This section is used to constrain the backup plan for A-CAES.

[0097] ① Provides positive backup (C2S, C2G, CPD) under compression conditions

[0098]

[0099]

[0100]

[0101]

[0102]

[0103]

[0104] In the formula, The positive backup provided by A-CAES in compression, power generation and standby conditions are C, G and S respectively; To provide positive standby status for A-CAES through operating condition switching, X can take the values ​​C2S, C2G, and S2G. When positive standby is provided through mode X, this variable takes the value 1; otherwise, it takes the value 0. , The changes in gas storage chamber pressure and hot water tank mass caused by the backup of A-CAES are respectively provided. X can be CPI, C2G, GPI, G2C, S2C, or S2G. The working fluid flow rate of the expansion subsystem provided as a backup for A-CAES, X can be C2G, GPI, or S2G. That is, , , , , , These represent the changes in gas storage chamber pressure caused by providing backup for A-CAES in CPI, GPI, S2G, C2G, G2C, and S2C modes, respectively. , , , , , The changes in the mass of the hot water tank caused by providing backup for A-CAES under CPI, GPI, S2G, C2G, G2C, and S2C modes, respectively. , , The working fluid flow rate of the backup post-expansion subsystem is provided for A-CAES under GPI, C2G, and S2G operating conditions, respectively.

[0105] ② Provides negative reserve (CPI) under compression conditions.

[0106]

[0107]

[0108] In the formula, The negative backup provided by A-CAES in compression, power generation, and standby conditions are C, G, and S, respectively.

[0109] ③ Provide positive reserve (GPI) during power generation.

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[0112]

[0113] ④ Provide negative reserves (GPD, G2S, G2C) during power generation.

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[0115]

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[0119] In the formula, The state that provides negative backup for A-CAES through operating condition transition, X can be G2S, G2C, or S2C. When negative backup is provided through mode X, this variable is 1; otherwise, it is 0.

[0120] ⑤ Provides positive backup (S2G) during standby operation.

[0121]

[0122]

[0123]

[0124]

[0125] ⑥ Provides negative backup (S2C) during standby operation.

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[0128]

[0129] (4) Other constraints In addition to A-CAES constraints, the energy-reserve joint dispatch model also includes constraints on thermal power units (power constraints, ramp rate constraints, start-up and shutdown time constraints), wind power constraints, and system constraints (power flow constraints, line power constraints, node voltage constraints, power balance constraints, reserve response constraints, and reserve continuity constraints). This section focuses on reserve response and continuity constraints; other constraints are well-established and fundamental, and can be found in relevant materials, so they will not be elaborated upon further.

[0130] ①Alternate response constraints The positive and negative reserves provided by thermal power units and A-CAES should be sufficient to compensate for power prediction errors in the power system and achieve full response within 15 minutes.

[0131]

[0132]

[0133] In the formula, , These are the prediction errors for wind power and load, respectively.

[0134] ② Backup continuity constraints The continuous adjustable reserve provided by thermal power units should be sufficient to compensate for the reserve dead zone of A-CAES.

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[0141] In step C, the iterative solution method for solving the nonlinear scheduling model described in step B is as follows: The scheduling model contains energy and reserve safety constraints of A-CAES, namely boundary constraints for gas storage chamber pressure, hot water tank mass, and air flow rate of expansion subsystem. These constraints need to be solved using the thermodynamic model in step A. However, the model contains a large number of nonlinear functions and continuous variable product terms, and there is also a strong coupling relationship between binary variables and nonlinear terms, making traditional methods such as sequential linear programming, sequential quadratic programming, and Benders decomposition difficult to apply. A common compromise is the parameter-fixed linearization method, but this method leads to optimistic decisions, posing safety risks to actual operation. Therefore, as a further preferred solution of this invention, an iterative solution method based on the principal-subproblem framework is proposed. Since this method can classify and handle the nonlinear energy and reserve safety constraints of A-CAES according to temporal characteristics, it is called the multi-temporal-feature iterative method (MTFIM).

[0142] MTFIM breaks down the original scheduling problem in step B into a main problem and subproblems. The main problem is a linear scheduling problem, inheriting the objective function and most constraints of the original scheduling problem. The core difference lies in that the main problem replaces the nonlinear thermodynamic model of A-CAES with an idealized linear model, which may overestimate the performance of A-CAES during decision-making. To address this, the subproblems serve as a subsequent verification step. They substitute the solution results of the main problem into the original thermodynamic model and calculate the gas storage chamber pressure, hot water tank mass, and expansion subsystem airflow to determine if they exceed limits. If constraints are exceeded, the main problem tightens the boundaries of the corresponding indices and reschedules. Through iterative interaction, the main problem and subproblems complete the solution to the energy-reserve joint scheduling problem.

[0143] (1) Main problem The idealized linear model of A-CAES in the main problem needs to meet two requirements. First, its performance must be superior to the thermodynamic model in step A, thus allowing for a margin of convergence in the iterations. If the model is too conservative, the result of the main problem, although it may pass the subproblem verification in the first iteration, will only be a local optimum. Second, its performance must be sufficiently close to the thermodynamic model in step A. If the two models deviate too much, the number of iterations required for convergence will increase significantly.

[0144] Among the many state variables in A-CAES, power, gas storage chamber pressure, hot water tank mass, and expansion subsystem airflow are the core concerns of the scheduling problem. Power is the decision variable, gas storage chamber pressure and hot water tank mass characterize the available capacity of the A-CAES, and expansion subsystem airflow serves as a safety indicator for the A-CAES. The main problem requires constructing idealized linear expressions for the latter three.

[0145] The rate of change of pressure in the gas storage chamber and the airflow rate are both closely related to power and gas storage chamber pressure. Simulations based on the original thermodynamic model of A-CAES can obtain operating data as samples, thus fitting the former two to linear functions of the latter two. That is, the rate of change of pressure in the gas storage chamber is fitted to a linear function of power and gas storage chamber pressure, and the airflow rate is fitted to a linear function of power and gas storage chamber pressure.

[0146] Based on the fitting function, the gas storage chamber pressure, hot water tank mass, and expansion subsystem airflow rate in the A-CAES energy security constraints of the main problem can be calculated as follows:

[0147]

[0148]

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[0152]

[0153] in, , , X is the fitting coefficient for the rate of change of gas storage chamber pressure under compression or power generation conditions (X is either C or G). , , X is the fitting coefficient for the airflow of the compression or expansion subsystem (X is either C or G).

[0154] Based on the fitting function, the gas storage chamber pressure, hot water tank mass, and expansion subsystem air flow rate in the A-CAES backup safety constraints of the main problem can be calculated as follows:

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[0169] To ensure smooth interaction between the main problem and subproblems during the iteration process and to fully leverage the guiding role of subproblems on the main problem, the safety boundaries of the gas storage chamber pressure, hot water tank mass, and expansion subsystem air flow rate need to be dynamically updated based on the verification results of the subproblems. To achieve this function, the following connection constraints can be used to replace the safety constraints of the above three variables in the main problem, namely the energy safety constraints and backup safety constraints of the above three variables. The prototypes to be replaced are detailed in step B (the energy safety constraints of the gas storage chamber pressure, hot water tank mass, and expansion subsystem air flow rate are the gas storage chamber pressure and hot water tank mass constraints and expansion subsystem air flow rate constraints of the A-CAES energy constraints in step B. The backup safety constraints of the gas storage chamber pressure, hot water tank mass, and expansion subsystem air flow rate are the constraints related to the gas storage chamber pressure, hot water tank mass, and expansion subsystem air flow rate in backup constraints ① to ⑥ of A-CAES, such as the last three constraints in backup constraint ①).

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[0186]

[0187]

[0188] in, , These represent the upper and lower limits, respectively, imposed by the subproblem on the pressure of the gas storage chamber in the main problem; , These represent the upper and lower limits imposed by the subproblems on the mass of the hot water tank in the main problem; The upper limit imposed by the subproblem on the airflow rate of the expansion subsystem of the main problem; The subproblem provides the boundary for the applied gas storage chamber pressure after the backup through method X (which can be CPI, C2G, GPI, G2C, S2C, S2G); The subproblems provide the boundary conditions for the mass of the hot water tank after standby by means of method X (which can be CPI, C2G, GPI, G2C, S2C, S2G); The subproblem provides the boundary for the airflow applied to the expansion subsystem after the backup by means of mode X (which can be C2G, GPI, S2G).

[0189] (2) Subproblems A-CAES energy security constraints and backup security constraints have different temporal characteristics: the former are dynamic and time-coupled constraints, while the latter are static and time-independent constraints. Tightening the boundary of a backup security constraint at a certain point in time only affects the backup plan at that point in time; however, tightening the boundary of an energy security constraint at a certain point in time will have an impact on all subsequent charging and discharging plans. Therefore, subproblems should be checked in chronological order, and limit exceedance issues should be handled according to the temporal characteristics of the constraints. Specifically, if an energy security constraint exceedance is detected at a certain point in time, the boundary of that constraint should be tightened, and the boundary of the backup security constraint at that point in time should be initialized. Then, the current check should be terminated, subsequent constraints should not be checked, and the process should return directly to the main problem to start the next iteration.

[0190] The operation process of the subproblem is as follows, such as Figure 5 As shown: ① Set the initial boundary of the connection constraints, as shown in Table 3.

[0191] Table 3

[0192] ② Solve the main problem and pass some key results to the subproblems. These results are shown in Table 4.

[0193] Table 4

[0194] In Table 4, the superscript " "" indicates that the variable to which it belongs is the result of solving the main problem.

[0195] ③ Substitute the power and backup results obtained from the main problem (i.e., the results in the first and second rows of Table 4) into the original thermodynamic model of A-CAES to calculate the pressure of the gas storage chamber, the mass of the hot water tank, the air flow rate of the expansion subsystem, and the changes in the pressure of the gas storage chamber, the mass change of the hot water tank, and the air flow rate of the expansion subsystem after A-CAES provides backup, as shown in Table 5.

[0196] Table 5

[0197] In Table 5, the superscript " "" indicates that the variable to which it belongs is the result of solving the subproblem.

[0198] Understandably, in the alternative calculation results in Table 5, the following is used: For example, the calculation process is as follows: Given the compression power to be solved in the main problem... And the negative backup provided under compression conditions Then, the compression power of A-CAES after providing backup is Substituting the power into the thermodynamic model, we can obtain the pressure of the storage chamber after providing backup power. This pressure is related to the pressure calculated by the subproblem. By taking the difference, we can obtain .

[0199] ④ Settings .

[0200] ⑤ Based on the backup scheduling result, update the boundary of the time-independent connection constraint.

[0201] If the subproblem verification shows that the pressure of the backup gas storage chamber, the mass of the hot water tank, and the air flow of the expansion subsystem provided by A-CAES exceed the limit, then the boundaries of the corresponding connection constraints are tightened, as shown in Table 6.

[0202] Table 6

[0203] ⑥ Update the boundaries of time-coupled connection constraints based on the energy scheduling results.

[0204] If the subproblem verification shows that the pressure of the gas storage chamber, the mass of the hot water tank, and the air flow of the expansion subsystem of A-CAES exceed the limits when operating according to the output plan, then the boundaries of the corresponding connection constraints are tightened, as shown in Table 7.

[0205] Table 7

[0206] ⑦ Control the iteration process based on the over-limit situation of the two types of constraints.

[0207] If an arbitrary boundary update occurs in step ⑥, then initialize the corresponding time point. t Determine the boundaries of all spare connection constraints and return to step ② to start the next iteration.

[0208] like And if no boundary update occurs in step ⑥, then let Then return to step ⑤ to continue this round of iteration.

[0209] like If no boundary update occurs in steps ⑤ and ⑥, it indicates that the energy-reserve joint scheduling model has been solved. Otherwise, return to step ② and start the next iteration.

[0210] In step C, the solution results of the scheduling model are as follows: 1) Thermal power units: Start-up / shutdown status, power, and standby status. 2) Wind farm: power 3) A-CAES: Compression status, power generation status, compression power, power generation power, standby, gas storage chamber pressure, hot water tank mass, expansion subsystem air flow rate 4) Optimization objective: Total system cost Example 1 This embodiment focuses on the energy-reserve joint dispatch method for power systems containing A-CAES as described in this invention, and the specific steps are as follows: Step A: The model in this embodiment is constructed as follows.

[0211] (1) Taking into account the operating constraints of thermal power units, A-CAES operating constraints, wind farm operating constraints, and system operating constraints, the scheduling model is constructed with the goal of minimizing the sum of thermal power unit operating costs, thermal power unit standby costs, thermal power unit start-up and shutdown costs, and wind curtailment penalty costs.

[0212] (2) For the specific mathematical expressions in the above model, please refer to the A-CAES thermodynamic model and the power system energy-reserve joint dispatch model containing A-CAES described in steps A and B of the invention content.

[0213] Step B: The parameter settings for this embodiment are as follows.

[0214] (1) Implementation environment: The implementation was tested on a computer with an Intel Xeon Gold 2.70GHz CPU and 256GB of memory. The scheduling model was solved by calling Yalmip through MATLAB R2022a, and the solver was Gurobi 9.1.

[0215] (2) Optimized time scale of the example: The total scheduling time is 1 day, and the unit scheduling time is 15 minutes.

[0216] (3) Implementation example topology diagram: The topology diagram is as follows Figure 6 As shown in the figure. TPU represents thermal power units, and WF represents wind farms.

[0217] (4) CAES parameters of Example A: as shown in Table 8.

[0218] Table 8

[0219] (5) Parameters of thermal power units in the embodiment: as shown in Table 9.

[0220] Table 9

[0221] (6) Wind power, load power, and ambient temperature prediction curves of the embodiment: as shown Figure 7 As shown.

[0222] Step C: Optimize the solution for this embodiment and analyze the results.

[0223] To verify the effectiveness of the energy-reserve joint scheduling method proposed in this invention, two cases were set up: Case 1 and Case 2 employed MTFIM and the traditional constant-parameter linearization method, respectively. The A-CAES power for both is as follows: Figure 7 As shown, the pressure in the gas storage chamber, the mass of the hot water tank, and the air flow rate of the expansion subsystem are as follows: Figure 9 As shown (MP and SP represent the main problem and subproblem, respectively), the positive and negative spares are respectively as follows: Figure 10 , Figure 11 As shown (TPU represents thermal power unit), the standby gas storage chamber pressure, hot water tank mass, and expansion subsystem air flow are provided as follows: Figure 12 As shown in Table 10, the cost and wind power utilization rate are as follows.

[0224] Table 10

[0225] Table 10 shows that Case 2's cost is 0.71% lower than Case 1, seemingly giving Case 2 a slight economic advantage. Combined with... Figure 9 (a~b) and Figure 12As shown in (a), although the scheduling process in Case 2 assumes that both energy and reserve security constraints are fully met, its actual implementation will lead to a series of problems. Specifically, the gas storage chamber pressure and hot water tank mass cannot be restored to their initial values ​​by the end of the day, and after the full use of the positive reserve provided by A-CAES through GPI at time point 87, the gas storage chamber pressure will fall below the lower limit. These phenomena indicate that Case 2 achieves only a slight economic optimization by overestimating the operating performance of A-CAES. In contrast, Case 1, while ensuring reasonable scheduling of A-CAES, has a total cost that is basically the same as Case 2. This proves that MTFIM can effectively solve the energy-reserve joint scheduling problem.

[0226] Depend on Figure 8 It is known that at the end of the day, A-CAES needs to be compressed to restore the pressure in the gas storage chamber and the mass of the hot water tank to their initial levels. However, Case 2 overestimated the operational performance of A-CAES, assuming that a short compression process would be sufficient to restore the equipment to its original state. This unrealistic assessment will reduce the availability of A-CAES the following day, and long-term operation will inevitably lead to high-risk operational problems for A-CAES.

[0227] Depend on Figure 9 It can be seen that the calculation results of the main problem and subproblems in Case 1 are very similar. This indicates that the idealized A-CAES linear model is highly consistent with the original model and meets the modeling requirements of the main problem. Furthermore, a comparison of the scheduling results and simulation results for Case 2 shows that Case 2 overestimates the pressure increase in the gas storage chamber under the same compression power, while underestimating the compressed air consumption under the same expansion power, ultimately causing the gas storage chamber pressure and hot water tank mass to exceed limits. This phenomenon fully demonstrates that MTFIM can more comprehensively consider the operational safety constraints of A-CAES.

[0228] Depend on Figure 10 , Figure 11 It can be seen that under the standby coordination mode with A-CAES as the primary mechanism and thermal power units as the secondary mechanism, the system's standby requirements can be fully met. Due to the characteristics of the standby dead zone, the system will generate a small amount of standby redundancy, which will lead to additional costs. Since the expansion-side dead zone (120MW) is larger than the compression-side dead zone (50MW), the scale of standby redundancy provided by S2G and G2S is relatively larger. At the same time, the overall standby redundancy rate of Case 2 is higher than that of Case 1, and its corresponding standby cost is also slightly higher.

[0229] Summary of Example 1 Based on the steps outlined in Example 1, the energy-reserve joint dispatch method for power systems with large-scale A-CAES described in this invention can fully leverage the reserve supply advantages of A-CAES and significantly alleviate the regulation pressure on thermal power units. Because it comprehensively considers the variable-parameter thermodynamic characteristics of A-CAES and addresses both time-coupled energy security constraints and time-independent reserve security constraints in a categorized manner, rather than simplifying or ignoring them, the dispatching problem can be solved using MTFIM, enabling the formulation of dispatching plans that better meet the operational safety requirements of A-CAES without sacrificing economic efficiency.

[0230] This invention provides an electronic device, including: a computer-readable storage medium and a processor; The computer-readable storage medium is used to store executable instructions; The processor is configured to read executable instructions stored in the computer-readable storage medium and execute the method as described in any of the above embodiments.

[0231] This invention provides a computer-readable storage medium storing computer instructions that cause a processor to perform the method described in any of the above embodiments.

[0232] This invention provides a computer program product, including a computer program or instructions, which, when executed by a processor, implement the method described in any of the above embodiments.

[0233] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for joint energy-reserve scheduling of adiabatic compressed air energy storage, characterized in that, include: With the goal of minimizing the total operating cost of the power system, a day-ahead energy-reserve joint dispatch model of the power system containing A-CAES is established, and the model is solved under preset constraints to obtain the optimal dispatch scheme of the generating units and the A-CAES in the power system. The power system also includes thermal power units and wind farms; the preset constraints include A-CAES energy constraints, A-CAES reserve constraints, reserve response constraints, reserve continuity constraints, thermal power unit constraints, wind power constraints, and power system constraints.

2. The method as described in claim 1, characterized in that, The energy constraints of A-CAES include the state variable operational boundary constraints of A-CAES and the state variable analytical expressions of A-CAES. The state variable operating boundary constraints of the A-CAES include operating state constraints, power constraints, gas storage chamber pressure and hot water tank mass constraints, and expansion subsystem air flow constraints. The alternative constraints of A-CAES include: ① Provides positive standby constraints under compression conditions: in, , They are used for characterization t The state variable indicating whether the A-CAES provides positive reserve through C2S or C2G methods during the time period. C2S indicates that the A-CAES provides positive reserve by switching from compression mode to shutdown mode, while C2G indicates that the A-CAES provides positive reserve by switching from compression mode to generation mode. For characterization t Is the A-CAES time period a compressed state variable? This is the positive backup provided by A-CAES under compression conditions. The total compression power of A-CAES This represents the minimum compression power per line. = 10 10 , , Let be the maximum and minimum power generation values ​​of the power station, respectively. for t Gas storage chamber pressure during the period To provide backup for A-CAES in C2G mode, resulting in pressure changes in the gas storage chamber. The change in hot water tank mass caused by providing backup for A-CAES in C2G mode; , , All are backup safety constraints; ② Provide negative reserve constraints under compression conditions: in, This serves as a negative backup for A-CAES under compression conditions. To compress the number of lines, This represents the maximum compression power of a single line. The pressure change in the gas storage chamber caused by A-CAES providing a reserve in CPI mode. CPI refers to the negative reserve provided by A-CAES by increasing compression power. This represents the maximum pressure in the gas storage chamber. for t The quality of the hot water tank during the period Provides the amount of change in hot water tank mass due to standby in the CPI method for A-CAES. This represents the maximum mass of the hot water tank. , All are backup safety constraints; ③ Provide positive reserve constraints under power generation conditions: in, For characterization t The state variable indicating whether time period A-CAES is in a generating state. This serves as the positive backup for A-CAES during power generation. This refers to the pressure change in the gas storage chamber caused by A-CAES providing backup in GPI mode. GPI refers to A-CAES providing negative backup by increasing power generation. This represents the minimum pressure in the gas storage chamber. Provides the amount of hot water tank mass change caused by backup in A-CAES under GPI mode. This represents the minimum mass of the hot water tank. , , All are backup safety constraints; ④ Provide negative reserve constraints under power generation conditions: in, , They are used for characterization t The state variable indicating whether the A-CAES provides positive reserve through G2S or G2C methods during the time period. G2S refers to the A-CAES providing negative reserve by switching from generation mode to shutdown mode, and G2C refers to the A-CAES providing negative reserve by switching from generation mode to compressor mode. The negative reserve provided by A-CAES during power generation operation. Let t be the power generation of A-CAES. This represents the minimum power generation capacity of the power plant. This represents the maximum compression power of a single line. To provide backup for A-CAES in G2C mode, resulting in pressure changes in the gas storage chamber. The change in hot water tank mass caused by providing backup for A-CAES in G2C mode; , All are backup safety constraints; ⑤ Provide positive standby constraints during standby operation: in, For characterization t Whether the A-CAES provides positive reserve status variables during the time period via S2G means that the A-CAES provides positive reserve by switching from shutdown condition to generation condition. This is the positive backup provided by A-CAES in standby mode. To provide backup for A-CAES in S2G ​​mode, resulting in pressure changes in the gas storage chamber. Provides the amount of hot water tank mass change caused by backup in the S2G mode for A-CAES. To provide the backup airflow for the expansion subsystem of A-CAES in S2G ​​mode. This is the upper limit of the airflow rate for the expansion subsystem. , , All are backup safety constraints; ⑥ Provide negative standby constraints under standby conditions: in, For characterization t The state variable indicating whether A-CAES provides negative backup via S2C during the time period. S2C refers to A-CAES providing negative backup by switching from shutdown mode to compression mode. To provide the gas storage chamber pressure change caused by backup in S2C mode for A-CAES. The change in hot water tank mass caused by providing backup for A-CAES in S2C mode; , All are backup safety constraints; The backup response constraints include: The backup continuity constraints include: in, for t Periodic thermal power units g It is ready for use. for t Periodic thermal power units g Negative backup, for t Periodic wind farm h The prediction error for t Time-period load forecasting error.

3. The method as described in claim 2, characterized in that, The total operating cost of the power system is: in, , , These are the operating, standby, and start-up / shutdown costs of thermal power units. The cost of curtailing wind power; , , , , , thermal power units g The operating cost is a constant coefficient; , thermal power units g Positive and negative reserve cost coefficients; The cost of a single start-up and shutdown of a thermal power unit; This represents the cost coefficient for wind curtailment penalties. , These are used to characterize thermal power units g exist t Time period t +1 time period running status variables; For thermal power units g exist t Power during a given time period; , thermal power units g exist t Positive and negative backup time slots; , Wind farm h exist t Predicted output and scheduled output for different time periods.

4. The method as described in claim 3, characterized in that, Solving the day-ahead energy-reserve joint dispatch model of the power system containing A-CAES under preset constraints includes: S1, replace the gas storage chamber pressure and hot water tank mass constraints, and the expansion subsystem air flow constraints in the preset constraints with the corresponding energy connection constraints; replace the backup safety constraints ① to ⑥ of the A-CAES in the preset constraints with the corresponding backup connection constraints; replace the analytical expressions of the gas storage chamber pressure, hot water tank mass, and expansion subsystem air flow in the preset constraints with the corresponding linear analytical expressions to obtain the target constraints; initialize the boundaries of each energy connection constraint and each backup connection constraint in the target constraints; S2 will be obtained by solving the day-ahead energy-reserve joint dispatch model of the power system containing A-CAES under the objective constraints. t The first period Compression power of compressed lines Power generation of the expansion subsystem A-CAES provides positive and backup power during compression, power generation, and standby operation. , , A-CAES provides negative backup power during compression, power generation, and standby operation. , , Substitute the state variable analytical expression of A-CAES into the preset constraints to obtain the expression that satisfies the analytical expression. t +1 period gas storage chamber pressure Hot water tank quality and t Airflow of the expansion subsystem during the time period A-CAES provides the storage chamber pressure change caused by standby under CPI, GPI, S2G, C2G, G2C, and S2C modes, respectively. , , , , , A-CAES provides the change in hot water tank mass due to standby under CPI, GPI, S2G, C2G, G2C, and S2C modes, respectively. , , , , , A-CAES provides the working fluid flow rate of the backup expansion subsystem under GPI, C2G, and S2G operating conditions, respectively. , , ; t =1,2,…, T , T Total scheduling duration; S3, let t=1; S4, determine if it occurs , , , , , , , , , , , , , , If any of the following out-of-bounds conditions occurs, then the boundary of the state variable where the out-of-bounds condition occurred will be updated accordingly. , , , , , , , , , , , , , , ; in, , They are respectively satisfying the analytical expression t The pressure in the gas storage chamber and the quality of the hot water tank during different time periods. , , Each satisfies the analytical expression t The A-CAES during the time period provides the working fluid flow rate of the backup expansion subsystem in C2G, GPI, and S2G modes, respectively; , , , , , The backup gas storage chamber pressure is provided for A-CAES in CPI, C2G, GPI, G2C, S2C, and S2G modes, respectively. t Time period boundaries, , , , , , The backup hot water tank mass is provided for A-CAES under CPI, C2G, GPI, G2C, S2C, and S2G modes respectively. t Time period boundaries, , , Provide backup airflow to the expansion subsystem of A-CAES in C2G, GPI, and S2G modes respectively. t Time period boundaries; , The results are obtained by solving the day-ahead energy-reserve joint dispatch model of the power system containing A-CAES under objective constraints. t The pressure in the gas storage chamber and the quality of the hot water tank during different time periods. , , The above describes the solution of the day-ahead energy-reserve joint dispatch model of the power system containing A-CAES under objective constraints, where A-CAES provides the working fluid flow of the post-reserve expansion subsystem in C2G, GPI, and S2G modes. S5, determine if it occurs , , , , If any of the following out-of-bounds conditions occurs, then the boundary of the state variable where the out-of-bounds condition occurred will be updated to... , , , , ; in, , They are respectively t The upper and lower limits of the gas storage chamber pressure during the +1 period. , They are respectively t +1. Upper and lower limits of the hot water tank's mass during the time period; S6, if an arbitrary boundary update occurs in S5, then initialize the corresponding time point. t The boundaries of all spare connection constraints are checked, and S2 is returned to start the next iteration. And if no boundary update occurs in S5, then let And return to S4 to continue this iteration; if If no boundary update occurs in S4 and S5, the iteration ends; otherwise, it returns to S2 to start the next iteration.

5. The method as described in claim 4, characterized in that, The linear analytical expressions for the gas storage chamber pressure, hot water tank mass, and expansion subsystem air flow rate are as follows: in, , , These are the fitting coefficients for the rate of change of gas chamber pressure under compression conditions. , , These are the fitting coefficients for the rate of change of gas storage chamber pressure under power generation conditions. , , These are the fitting coefficients for the airflow of the compression subsystem, respectively. , , These are the fitting coefficients for the airflow of the expansion subsystem, respectively. The specific heat capacity of air at constant pressure. The specific heat capacity of water, , These are the compression stage and the expansion stage, respectively. , They are respectively t +1 period: gas storage chamber pressure and hot water tank quality.

6. The method as described in claim 4, characterized in that, The energy connectivity constraints corresponding to the preset constraints of gas storage chamber pressure, hot water tank mass, and expansion subsystem air flow are as follows: in, , They are respectively t The target upper and lower limits of the gas storage chamber pressure during a given period. for t The quality of the hot water tank during the period , They are respectively t The upper and lower limits of the target quality for hot water tanks during specific time periods. The airflow rate of the expansion subsystem. for t The target upper limit for airflow in the time-segmented expansion subsystem; The alternative connection constraints corresponding to the alternative safety constraints in the A-CAES alternative constraints ① to ⑥ of the preset constraints are as follows: in, , , , , , , , , , , , , , , ; The initialization of the boundaries of each energy connection constraint and each spare connection constraint in the target constraint includes: Will , , , , , , The initial values ​​are set to respectively , , , , , , ;Will , , The initial values ​​are all set to ;Will , , The initial values ​​are all set to ;Will , , The initial values ​​are all set to ;Will , , The initial values ​​are all set to ;Will , , The initial values ​​are all set to .

7. The method as described in claim 4, characterized in that, In step S5, if t= T Then determine whether it occurs. , , , , If any of the following out-of-bounds conditions occurs, then the boundary of the state variable where the out-of-bounds condition occurred will be updated to... , , , , ; in, , They are respectively satisfying the analytical expression t +1 period: gas storage chamber pressure and hot water tank quality.

8. An electronic device, characterized in that, include: Computer-readable storage media and processors; The computer-readable storage medium is used to store executable instructions; The processor is configured to read executable instructions stored in the computer-readable storage medium and execute the method as described in any one of claims 1-7.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions for causing a processor to perform the method as described in any one of claims 1-7.

10. A computer program product, comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by a processor, they implement the method as described in any one of claims 1-7.

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