A compressed air energy storage multi-day optimal scheduling method for continuous extreme scenarios

Abstract

This invention relates to the field of power system dispatch and control technology, specifically to a multi-day optimal dispatch method for compressed air storage (CASP) energy storage systems (CASPs) oriented towards continuous extreme scenarios. This method proposes operational constraints for CASPs with unit-like combinations, characterizing practical operational constraints such as minimum continuous operating time, start-stop limits, and waiting times for charge / discharge state transitions. Furthermore, this method proposes an optimal dispatch framework for CASPs on a weekly timescale, addressing various types of extreme scenarios. In addition, the method employs a Benders decomposition-based algorithm and linearization techniques to solve the proposed large-scale mixed linear integer programming problem. This invention improves the engineering practicality and dispatch decision feasibility of CASP operation models, fully explores the long-term energy storage value of CASP in addressing energy imbalances in continuous extreme scenarios, and meets the large-scale dispatch needs of power systems.

Description

Technical Field

[0001] This invention relates to the field of power system dispatch and control technology, and more specifically, to a multi-day optimized dispatch method for compressed air energy storage for continuous extreme scenarios. Background Technology

[0002] With the acceleration of the global energy transition, the integration of a high proportion of renewable energy into the grid has become an inevitable trend in power system development. The intermittency, volatility, and uncertainty of renewable energy output such as wind and solar power pose unprecedented challenges to the real-time power balance and safe and stable operation of the power system. Especially against the backdrop of frequent extreme weather events in recent years (such as continuous windless periods and extreme cold waves), the power system may face a continuous power shortage, posing a severe challenge to the reliability of system power supply.

[0003] Against this backdrop, energy storage technology, especially compressed air energy storage (CASS), with its large-scale and long-term energy storage capabilities, is widely considered one of the key supporting technologies for building new power systems. CASS is a large-scale physical energy storage technology that uses electricity to compress air and store it in gas storage facilities (such as salt caverns, abandoned mines, and artificial chambers), releasing the high-pressure air to drive turbines for power generation when needed. Currently, my country has built several megawatt-level CASS power plants, widely used on the power supply side, grid side, and user side. CASS systems offer advantages such as long storage time (typically several hours to tens of hours), high ramp-up flexibility, low cost, long lifespan, and environmental friendliness, making them suitable for addressing energy supply and load demand mismatches that last for several days and improving the system's renewable energy absorption capacity.

[0004] In the current technological field, research on optimization and control strategies for compressed air energy storage systems (CASS) largely focuses on intraday economic dispatch under ideal conditions, aiming to leverage the long-term energy storage value of CASS to smooth out renewable energy fluctuations. However, existing technologies fail to fully consider the constraints imposed on their operational boundaries by extreme scenarios such as extreme weather and prolonged energy shortages, and also lack refined modeling of key physical and operational characteristics in practical engineering. CASS systems are characterized by large capacity, long cycles, complex equipment coordination, and diverse physical constraints. These factors are crucial for the dispatch and control of CASS systems on long-term timescales such as weeks and days. Therefore, establishing a multi-day optimized dispatch method for CASS systems oriented towards continuous extreme scenarios is urgently needed. Summary of the Invention

[0005] In view of this, in order to address the shortcomings of the prior art, the present invention proposes a multi-day optimized scheduling method for compressed air energy storage for continuous extreme scenarios, aiming to solve at least one of the problems mentioned in the background art.

[0006] This invention provides a multi-day optimized scheduling method for compressed air energy storage in continuous extreme scenarios, comprising the following steps: Step 1 is to establish a mathematical model of the compressed air energy storage system that takes into account the actual operating characteristics. The basic operating mode of the compressed air energy storage system includes three processes: compression charging, gas storage and expansion power generation. Step 2 involves establishing a mixed-integer linear programming model for day-ahead scheduling of the power system with a weekly timescale, using a 7-day scheduling cycle and an hourly time interval, taking extreme scenarios into account. Step 3 involves solving the proposed model based on the Benders decomposition algorithm framework and linearization techniques, and outputting day-ahead dispatch instructions for compressed air energy storage power stations and various generator sets.

[0007] In some embodiments, the mathematical model of the compressed air energy storage system in step 1 includes: In the formula: , These are binary variables (representing the charging and discharging conditions of the compressed air energy storage system, respectively). In the formula: express t Time of the first u The input power of the stage compressor, which is related to the air mass flow rate. and inlet temperature Proportional to the compression ratio of the compressor and efficiency Related; cp and K represent the specific heat capacity of air at constant pressure and the adiabatic index, respectively; In the formula: express t Time of the first v The output power of the stage expander is related to the air mass flow rate. Inlet temperature and the expansion ratio of the expander and efficiency related; In the formula: express t The pressure in the gas storage chamber at all times; and They are tThe air mass flow rate in the compressor and expander at all times; R g It is the gas constant; The heat transfer coefficient of the gas storage chamber; V Δ is the volume of the gas storage chamber; t It is the time step; Pr min and Pr max These represent the minimum and maximum pressures of the gas storage chamber, respectively. Furthermore, the heat transfer during the energy storage and release processes of a compressed air energy storage system can be expressed as follows: In the formula: c air The specific heat capacity of air; and They are the first u The air temperature at the outlet and inlet of the compressor; and They are the first v The air temperature at the inlet and outlet of the primary expander. and They represent t At any moment, the air passes through the first u After the first stage compressor releases heat and enters the second stage... v The power of the expander to absorb heat before the expansion stage; The change in the heat storage capacity of the thermal storage system must meet the following requirements. In the formula: express t The amount of heat stored in the thermal storage system at all times; The stored heat from the previous moment; H max This represents the thermal storage limit of the thermal storage system. In the formula: and These represent compressed air energy storage power stations in t The charging and discharging power at any given moment; and This indicates the lower and upper limits of the turbine's ramp rate; Minimum continuous charging time of compressed air energy storage system ( T The constraint (1 hour) is: Minimum duration of discharge ( T The 2-hour constraint is: Define startup flag variable and satisfy: Daily maximum number of start-stops constraint ( N max (times / day) in, It represents the set of all time periods within a day; The charging / discharging state transition waiting time constraint can be expressed as: .

[0008] In some embodiments, the week-scale day-ahead power system scheduling model considering extreme scenarios in step 2 includes: With the goal of minimizing the total operating cost of the system within the scheduling cycle, a model objective function is established that includes the power generation cost of conventional generating units, start-up and shutdown costs, operating costs of compressed air energy storage power stations, and off-load costs.

[0009] in, N g This refers to the number of conventional generating units; T This represents the total number of time periods within the scheduling cycle. For the unit i The power generation cost function; For the unit i In time t contribution; , The units i In time t Start / stop status indicator; , For the unit i Start-up and shutdown costs; , The operation and maintenance cost coefficient of a compressed air energy storage power station under charging and discharging conditions; Value of system underload; For the system in time t The amount of load shedding; The power generation cost of the unit can be expressed as a quadratic function: in, a i , bi and c i They represent the generating units. i The coefficients of the quadratic, linear, and constant terms of the power generation cost function.

[0010] The system power balance constraint is: in, For wind turbine units in time t Total output; For the photoelectric unit in time t Total output; For the system in t Load demand during different time periods; The system spin-off reserve constraint is: in, , The units i The upper and lower limits of output; For the unit i In time t The running status flag; , These represent the system at time. t The up-and-down rotation backup requirement; The operating constraints for conventional generating units are: This includes upper and lower limits of output, ramp rate constraints, minimum start and stop time constraints, and start and stop logic constraints. This is a standard unit combination model, which will not be elaborated here. The operating constraints of the compressed air energy storage power station are: As mentioned above, this includes charging and discharging power, energy constraints, and constraints on combined operation of similar units; The modeling method for renewable energy and extreme scenarios is as follows: Renewable energy output constraints can be written as: in, and They are respectively t The predicted upper limit of wind and solar power output for the specified time period; To simulate extreme conditions, this invention constructs extreme scenarios by modifying the predicted output and load; in, High load factor; This is the wind power output reduction factor; This is the photovoltaic power output reduction factor; For the duration of extreme weather events.

[0011] In some embodiments, the integrated solution strategy based on the Benders decomposition algorithm framework and linearization technique described in step 3 includes: Strategy 1 involves linearizing the objective function; This invention employs piecewise linearization technology to transform the equation Transform into linear form; The output range of unit i Divide into K line segment intervals, with the output force corresponding to the endpoints of each interval being... The cost is ; Introducing continuous auxiliary variables Let k represent the weight of the output point in segment k. Then, the output and cost of unit i in time period t can be expressed as: Auxiliary variables Must meet: Strategy 2 is a solution framework based on Benders decomposition. The Benders decomposition algorithm is used to decompose the original problem into a main problem and subproblems, and the optimal solution of the original problem is approximated by iterative solution. The main problem is responsible for solving all binary decision variables, including the operating status of conventional units. , , Operating status of compressed air energy storage power station , Its objective is to minimize the fixed cost and an auxiliary variable α representing the cost of subsequent scheduling. The subproblems are given integer solutions to the main problem. , , Under the given conditions, solve for the optimal configuration of continuous variables, including the output of conventional units. Compressed air energy storage power station charging and discharging power and load shedding The subproblem is a linear programming problem. The algorithm solution process is as follows: Step 1: Initialization, solve the relaxation master problem, and set the upper bound UB=+∞ and the lower bound LB=-∞; Step 2: Solve the main problem, obtain the integer solution and the objective value LBMP, and update the lower bound LB=LBMP; Step 3: Solve the subproblem with fixed integer variables to obtain the objective value OBJSP and the dual variable; Step 4: Convergence check, calculate the current upper bound UB=min(UB,OBJSP+fixed cost), if (UB-LB) / LB≤ε, then the algorithm terminates; Step 5: Generation and addition of cutting planes. If the subproblem is feasible, generate an optimality cut and add it to the main problem; if the subproblem is infeasible, generate a feasible cut and add it to the main problem to exclude integer solution combinations that lead to infeasible solutions. Step 6: Return to Step 2 Compared with the prior art, the beneficial effects of the present invention are as follows: (1) Operational constraints of compressed air energy storage power stations with similar unit combinations are proposed, which can characterize actual operational constraints such as minimum continuous operating time, start-stop limit, and waiting time for charging and discharging state transition, thereby improving the engineering practicality of the model and the feasibility of scheduling decisions.

[0012] (2) For various extreme scenarios, a compressed air energy storage power station optimization scheduling framework for weekly time scale is proposed, which can fully explore the long-term energy storage value of compressed air energy storage in dealing with energy imbalance in continuous extreme scenarios of the system.

[0013] (3) To address the difficulty of solving large-scale mixed linear integer programming problems, a model solving algorithm based on Benders decomposition and linearization techniques is proposed, which greatly reduces the difficulty of solving the proposed model. This method can meet the large-scale scheduling needs of power systems.

[0014] The above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this disclosure.

[0015] Other features and aspects of this disclosure will become clearer from the following detailed description of exemplary embodiments with reference to the accompanying drawings. Attached Figure Description

[0016] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific 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 from these drawings without creative effort.

[0017] Figure 1 This is a flowchart of a multi-day optimized scheduling method for compressed air energy storage in continuous extreme scenarios provided by an embodiment of the present invention; Figure 2This is a schematic diagram illustrating the changes in the operating state of a compressed air energy storage power station under different constraints in a test case of a multi-day optimized scheduling method for compressed air energy storage in continuous extreme scenarios provided in an embodiment of the present invention. Figure 3 This is a schematic diagram illustrating the changes in system power balance under different scenarios for a test example of the multi-day optimized scheduling method for compressed air energy storage in continuous extreme scenarios provided in this embodiment of the invention. Detailed Implementation

[0018] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0019] In the description of this application, it should be understood that the terms "center", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this application.

[0020] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, unless otherwise stated, "a plurality of" means two or more.

[0021] In the description of this application, it should be noted that, unless otherwise expressly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection between two components. Those skilled in the art can understand the specific meaning of the above terms in this application based on the specific circumstances.

[0022] See Figures 1-3 As shown, the embodiments of this application include the following steps: Step 1 involves establishing a mathematical model of the compressed air energy storage system that considers actual operating characteristics. The basic operating mode of a compressed air energy storage system includes three processes: compression charging, gas storage, and expansion power generation. Step 2 involves establishing a mixed-integer linear programming model for day-ahead scheduling of the power system with a weekly timescale, using a 7-day scheduling cycle and an hourly time interval, taking extreme scenarios into account. Step 3 involves solving the proposed model based on the Benders decomposition algorithm framework and linearization techniques, and outputting day-ahead dispatch instructions for compressed air energy storage power stations and various generator sets.

[0023] In some specific embodiments, the mathematical model of the compressed air energy storage system described in step 1 includes: (1) In the formula: , These are binary variables (representing the charging and discharging conditions of the compressed air energy storage system, respectively).

[0024] (2) (3) In the formula: express t Time of the first u The input power of the stage compressor, which is related to the air mass flow rate. and inlet temperature Proportional to the compression ratio of the compressor and efficiency Related; cp and K represent the specific heat capacity of air at constant pressure and the adiabatic index, respectively.

[0025] (4) (5) In the formula: express t Time of the first v The output power of the stage expander is related to the air mass flow rate. Inlet temperature and the expansion ratio of the expander and efficiency related.

[0026] (6) (7) In the formula: express t The pressure in the gas storage chamber at all times; and They are t The air mass flow rate in the compressor and expander at all times; R g It is the gas constant; The heat transfer coefficient of the gas storage chamber; V Δ is the volume of the gas storage chamber; t It is the time step; Pr min and Pr max These represent the minimum and maximum pressures of the gas storage chamber, respectively.

[0027] Furthermore, the heat transfer during the energy storage and release processes of a compressed air energy storage system can be expressed as follows: (8) In the formula: c air The specific heat capacity of air; and They are the first u The air temperature at the outlet and inlet of the compressor; and They are the first v The air temperature at the inlet and outlet of the primary expander. and They represent t At any moment, the air passes through the first u After the first stage compressor releases heat and enters the second stage... v The power of the expander to absorb heat before the expansion stage.

[0028] The change in the heat storage capacity of the thermal storage system must meet the following requirements. (9) (10) In the formula: express t The amount of heat stored in the thermal storage system at all times; The stored heat from the previous moment; H max This represents the thermal storage limit of the thermal storage system.

[0029] (11) In the formula: and These represent compressed air energy storage power stations in t The charging and discharging power at any given moment.

[0030] and This indicates the lower and upper limits of the turbine's ramp rate.

[0031] (12) Minimum continuous charging time of compressed air energy storage system ( T The constraint (1 hour) is: (13) Minimum duration of discharge ( T The 2-hour constraint is: (14) Define startup flag variable and satisfy: (15) Daily maximum number of start-stops constraint ( N max (times / day) (16) in, It represents the set of all time periods within a day.

[0032] The charging / discharging state transition waiting time constraint can be expressed as: (17).

[0033] In some specific embodiments, the week-scale day-ahead scheduling model for the power system considering extreme scenarios described in step 2 includes: With the goal of minimizing the total operating cost of the system within the scheduling cycle, a model objective function is established that includes the power generation cost of conventional generating units, start-up and shutdown costs, operating costs of compressed air energy storage power stations, and load costs.

[0034] (18) in, N g This refers to the number of conventional generating units; T This represents the total number of time periods within the scheduling cycle. For the unit i The power generation cost function; For the unit i In time t contribution; , The units i In time t Start / stop status indicator; , For the unit i Start-up and shutdown costs; , The operation and maintenance cost coefficient of a compressed air energy storage power station under charging and discharging conditions; Value of system underload; For the system in time t The shear load.

[0035] This invention expresses the unit's power generation cost as a quadratic function: (19) in, a i , b i and c i They represent the generating units. i The coefficients of the quadratic, linear, and constant terms of the power generation cost function.

[0036] The system power balance constraint is: (20) in, For wind turbine units in time t Total output; For the photoelectric unit in time t Total output; For the system in t Load demand during a given time period.

[0037] The system spin-off reserve constraint is: (twenty one) in, , The units i The upper and lower limits of output; For the unit i In time t The running status flag; , These represent the system at time. t The up-and-down rotation backup requirement.

[0038] The operating constraints for conventional generating units are: This includes upper and lower limits of output, ramp rate constraints, minimum start-stop time constraints, and start-stop logic constraints. This is a standard unit combination model, which will not be elaborated here.

[0039] The operating constraints of the compressed air energy storage power station are: As mentioned above, this includes charging and discharging power, energy constraints (1)-(12), and unit-type combined operation constraints (13)-(17).

[0040] The modeling method for renewable energy and extreme scenarios is as follows: Renewable energy output constraints can be written as: (twenty two) in, and They are respectively t The predicted upper limit of wind and solar power output for the specified time period.

[0041] To simulate extreme conditions, this invention constructs extreme scenarios by modifying the predicted output and load.

[0042] (twenty three) in, High load factor; This is the wind power output reduction factor; This is the photovoltaic power output reduction factor; For extreme weather duration windows (e.g., 72 consecutive hours).

[0043] In some specific embodiments, the integrated solution strategy based on the Benders decomposition algorithm framework and linearization technique described in step 3 includes: Strategy 1 linearizes the objective function.

[0044] This invention employs piecewise linearization technology to transform equation (19) into a linear form. The unit... i Output range Divided into K There are several line segment intervals, and the output corresponding to the endpoint of each interval is... The cost is .

[0045] Introducing continuous auxiliary variables Indicates the point of force output in the segment. k The weight, then t Time-of-use units i The output and cost can be expressed as: (twenty four) Auxiliary variables Must meet: (25) Strategy 2 is a solution framework based on Benders decomposition. This invention uses the Benders decomposition algorithm to decompose the original problem into a main problem and subproblems, and approximates the optimal solution of the original problem through iterative solution.

[0046] The Master Problem (MP) is responsible for solving all binary decision variables, including the operating status of conventional units. , , Operating status of compressed air energy storage power station , Its objective is to minimize the fixed cost and an auxiliary variable representing the cost of subsequent scheduling. α .

[0047] (26) Subproblems (SP) are problems for which integer solutions are given in the main problem. , , Under the given conditions, solve for the optimal configuration of continuous variables, including the output of conventional units. Compressed air energy storage power station charging and discharging power and load shedding The subproblem is a linear programming problem.

[0048] (27) The algorithm solution process is as follows: Step 1: Initialization. Solve the relaxation master problem and set an upper bound. UB =+∞, lower bound LB =-∞; Step 2: Solve the main problem. Obtain integer solutions and the objective value. LB MP Update the Nether LB = LB MP ; Step 3: Solve the subproblem with fixed integer variables. Obtain the target value. OBJ SP and dual variables; Step 4: Convergence check. Calculate the current upper bound. UB =min( UB , OBJ SP +fixed costs), if ( UB - LB ) / LB ≤ ε If the algorithm terminates, then the algorithm terminates. Step 5: Cut plane generation and addition. If the subproblem is feasible, generate an optimality cut and add it to the main problem; if the subproblem is infeasible, generate a feasible cut and add it to the main problem to exclude integer solution combinations that lead to infeasible solutions. Step 6: Return to Step 2.

[0049] To verify the effectiveness of the proposed model and algorithm, a simulation example based on the IEEE 30-node system was designed. The mathematical model was constructed using MATLAB 2022b software, and the optimization problem was calculated using the Gurobi 10.0 solver. The computing platform was a personal computer equipped with an Intel Core i7-12700H processor and 32GB of RAM.

[0050] (1) Test system parameters The system comprises three traditional thermal power units (specific parameters are shown in Table 1), four wind farms with an installed capacity of 500MW each, and two photovoltaic power plants with an installed capacity of 500MW each. The system peak load is approximately 2000MW, and a standard weekly load curve is used. Both positive and negative spinning reserve requirements are 5% of the total system load and the system's loss-of-load value. C voll =5000 $ / MWh. The main parameters of the compressed air energy storage system are shown in Table 2.

[0051] Table 1. Parameters of conventional units in the test system

[0052] Table 2 Parameters of the Compressed Air Energy Storage System in the Test System

[0053] (2) Scene setting Scenario 1 (Baseline Scenario): Extreme weather conditions are not considered, and there is no compressed air energy storage power station connected.

[0054] Scenario 2: Connect to a compressed air energy storage power station, but ignore all unit combination operation constraints (i.e., no minimum operating time, start-stop count, etc.). Other conditions are the same as in Scenario 1.

[0055] Scenario 3: Connect to a compressed air energy storage power station, and fully consider the operational constraints of all types of units. Other conditions are the same as in Scenario 1.

[0056] Scenario 4: Cold Wave Weather Scenario. Between hours 96 and 120 of the scheduling cycle (i.e., day 4 to day 5), the load level surged to 110% of the forecast. γ high =1.1), while photovoltaic output dropped to 80% of rated capacity due to decreased efficiency at high temperatures and possible cloudy weather. ξ cloudy =0.8). Other conditions are the same as in scenario 3.

[0057] (3) Simulation results Table 3 shows the system operating costs under four different scenarios. Comparing the system operating costs of Scenario 1 with Scenarios 2 and 3, it can be seen that integrating a compressed air energy storage system can reduce the total system operating cost, save fuel costs and start-up and shutdown costs of conventional generator units, and improve the economic efficiency of system operation. Comparing Scenario 2 with Scenario 3, it can be seen that considering the constraints of generator unit combination, the operating cost of conventional generator units will increase, while the operating cost of the compressed air energy storage system will decrease, resulting in an overall increase in the total system operating cost. Comparing the system operating costs of Scenario 1 with Scenario 4, it can be seen that the total system operating cost will increase under extreme cold wave weather scenarios.

[0058] Table 3. Cost-effectiveness of the test system operation (Unit: 10) 3 $)

[0059] Figure 2 (a)-(b) illustrate the operational differences of compressed air energy storage before and after considering unit combination constraints. The results show that the optimization model that ignores unit combination constraints leads to frequent start-ups and shutdowns and rapid high-power charging and discharging in the compressed air energy storage power station, which increases equipment wear and reduces equipment lifespan. Although the total system cost increases slightly, the system's operational reliability and equipment safety can be significantly improved.

[0060] Figure 2 (b)-(c) visualized the operating status of the compressed air energy storage power station under normal weather and extreme cold wave scenarios in the test examples. It can be observed that under extreme cold wave conditions, the operating mode of the compressed air energy storage power station underwent a significant adaptive adjustment: the power station maintained a high-power charging state from 12:00 to 14:00, with a maximum charging power reaching 244.5MW, almost simultaneously reaching full-power charging. This adjustment was to quickly pre-store sufficient energy during periods of strong system power supply to cope with the upcoming extreme system load. When entering the extreme load period, the compressed air energy storage power station demonstrated strong peak support capabilities, with a maximum discharge power reaching 88.9MW. This centralized, high-capacity, long-duration discharge mode effectively compensated for the problem of a surge in system load caused by a decrease in photovoltaic unit output due to the cold wave.

[0061] Figure 3 This study compares the power generation dispatch results of the entire system under extreme cold wave weather, demonstrating the system balancing and strengthening role of compressed air energy storage (CAES) under extreme conditions. The results show that CAES plays an irreplaceable buffering and supporting role in coping with extreme weather impacts. This system faces severe challenges under extreme weather: air conditioning load surges dramatically during midday, resulting in a steep "peak" in the system's net load curve, with the peak load reaching 1.1 times that of normal weather. To meet this extreme demand, conventional units are forced to rapidly ramp up power in a short period, with some units even operating close to their maximum technical output limit, seriously threatening equipment safety and system stability. The CAES power station continuously discharges at high power during peak load periods, reducing the system's peak load by approximately 5%, effectively "smoothing" the load peak. Units that previously required frequent start-ups and shutdowns and extreme operation can now operate within a safer and more economical output range. Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A multi-day optimized scheduling method for compressed air energy storage in continuous extreme scenarios, characterized in that, Includes the following steps: Step 1 is to establish a mathematical model of the compressed air energy storage system that takes into account the actual operating characteristics. The basic operating mode of the compressed air energy storage system includes three processes: compression charging, gas storage and expansion power generation. Step 2 involves establishing a mixed-integer linear programming model for day-ahead scheduling of the power system with a weekly timescale, using a 7-day scheduling cycle and an hourly time interval, taking extreme scenarios into account. Step 3 involves solving the proposed model based on the Benders decomposition algorithm framework and linearization techniques, and outputting day-ahead dispatch instructions for compressed air energy storage power stations and various generator sets.

2. The multi-day optimized scheduling method for compressed air energy storage in continuous extreme scenarios according to claim 1, characterized in that, The mathematical model of the compressed air energy storage system described in step 1 includes: ； In the formula: , These are binary variables (representing the charging and discharging conditions of the compressed air energy storage system, respectively). ； ； In the formula: express t Time of the first u The input power of the stage compressor, which is related to the air mass flow rate. and inlet temperature Proportional to the compression ratio of the compressor and efficiency Related; cp and K represent the specific heat capacity of air at constant pressure and the adiabatic index, respectively; ； ； In the formula: express t Time of the first v The output power of the stage expander is related to the air mass flow rate. Inlet temperature and the expansion ratio of the expander and efficiency related; ； ； In the formula: express t The pressure in the gas storage chamber at all times; and They are t The air mass flow rate in the compressor and expander at all times; R g It is the gas constant; The heat transfer coefficient of the gas storage chamber; V Δ is the volume of the gas storage chamber; t It is the time step; Pr min and Pr max These represent the minimum and maximum pressures of the gas storage chamber, respectively. Furthermore, the heat transfer during the energy storage and release processes of a compressed air energy storage system can be expressed as follows: ； In the formula: c air The specific heat capacity of air; and They are the first u The air temperature at the outlet and inlet of the compressor; and They are the first v The air temperature at the inlet and outlet of the primary expander. and They represent t At any moment, the air passes through the first u After the first stage compressor releases heat and enters the second stage... v The power of the expander to absorb heat before the expansion stage; The change in the heat storage capacity of the thermal storage system must meet the following requirements. ； ； In the formula: express t The amount of heat stored in the thermal storage system at all times; The stored heat from the previous moment; H max This represents the thermal storage limit of the thermal storage system. ； In the formula: and These represent compressed air energy storage power stations in t The charging and discharging power at any given moment; and This indicates the lower and upper limits of the turbine's ramp rate; ； Minimum continuous charging time of compressed air energy storage system ( T The constraint (1 hour) is: ； Minimum duration of discharge ( T The 2-hour constraint is: ； Define startup flag variable and satisfy: ； Daily maximum number of start-stops constraint ( N max (times / day) ； in, It represents the set of all time periods within a day; The charging / discharging state transition waiting time constraint can be expressed as: 。 3. The multi-day optimized scheduling method for compressed air energy storage in continuous extreme scenarios according to claim 2, characterized in that, Step 2 describes a week-scale day-ahead scheduling model for power systems that considers extreme scenarios, including: With the goal of minimizing the total operating cost of the system within the scheduling cycle, a model objective function is established that includes the power generation cost of conventional generating units, start-up and shutdown costs, operating costs of compressed air energy storage power stations, and their load costs. ； in, N g This refers to the number of conventional generating units; T This represents the total number of time periods within the scheduling cycle. For the unit i The power generation cost function; For the unit i In time t contribution; , The units i In time t Start / stop status indicator; , For the unit i Start-up and shutdown costs; , The operation and maintenance cost coefficient of a compressed air energy storage power station under charging and discharging conditions; Value of system underload; For the system in time t The amount of load shedding; The power generation cost of the unit can be expressed as a quadratic function: ； in, a i , b i and c i They represent the generating units. i The coefficients of the quadratic, linear, and constant terms of the power generation cost function.

4. The system power balance constraint is: ； in, For wind turbine units in time t Total output; For the photoelectric unit in time t Total output; For the system in t Load demand during different time periods; The system spin-off reserve constraint is: ； in, , The units i The upper and lower limits of output; For the unit i In time t The running status flag; , These represent the system at time. t The need for vertical rotation backup; The operating constraints for conventional generating units are: This includes upper and lower limits of output, ramp rate constraints, minimum start and stop time constraints, and start and stop logic constraints. This is a standard unit combination model, which will not be elaborated here. The operating constraints of the compressed air energy storage power station are: As mentioned above, this includes charging and discharging power, energy constraints, and constraints on combined operation of similar units; The modeling method for renewable energy and extreme scenarios is as follows: Renewable energy output constraints can be written as: ； in, and They are respectively t The predicted upper limit of wind and solar power output for the specified time period; To simulate extreme conditions, this invention constructs extreme scenarios by modifying the predicted output and load; ； in, High load factor; This is the wind power output reduction factor; This is the photovoltaic power output reduction factor; For the duration window of extreme weather.

5. The multi-day optimized scheduling method for compressed air energy storage in continuous extreme scenarios according to claim 3, characterized in that, Step 3 describes a comprehensive solution strategy based on the Benders decomposition algorithm framework and linearization techniques, which includes: Strategy 1 involves linearizing the objective function; This invention employs piecewise linearization technology to transform the equation Transform into linear form; The output range of unit i Divide into K line segment intervals, with the output force corresponding to the endpoints of each interval being... The cost is ; Introducing continuous auxiliary variables Let k represent the weight of the output point in segment k. Then, the output and cost of unit i in time period t can be expressed as: ； Auxiliary variables Must meet: ； Strategy 2 is a solution framework based on Benders decomposition. The Benders decomposition algorithm is used to decompose the original problem into a main problem and subproblems, and the optimal solution of the original problem is approximated by iterative solution. The main problem is responsible for solving all binary decision variables, including the operating status of conventional units. , , Operating status of compressed air energy storage power station , Its objective is to minimize the fixed cost and an auxiliary variable α representing the cost of subsequent scheduling. ； The subproblems are given integer solutions to the main problem. , , Under the given conditions, solve for the optimal configuration of continuous variables, including the output of conventional units. Compressed air energy storage power station charging and discharging power and load shedding The subproblem is a linear programming problem. ； The algorithm solution process is as follows: Step 1: Initialization, solve the relaxation master problem, and set the upper bound UB=+∞ and the lower bound LB=-∞; Step 2: Solve the main problem, obtain the integer solution and the objective value LBMP, and update the lower bound LB=LBMP; Step 3: Solve the subproblem with fixed integer variables to obtain the objective value OBJSP and the dual variable; Step 4: Convergence check, calculate the current upper bound UB=min(UB,OBJSP+fixed cost), if (UB-LB) / LB≤ε, then the algorithm terminates; Step 5: Generation and addition of cutting planes. If the subproblem is feasible, generate an optimality cut and add it to the main problem; if the subproblem is not feasible, generate a feasible cut and add it to the main problem to exclude integer solution combinations that lead to infeasible solutions. Step 6: Return to Step 2.

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