A power system restoration method containing large-scale adiabatic compressed air energy storage

Abstract

This invention discloses a power system restoration method incorporating large-scale adiabatic compressed air energy storage, belonging to the field of power system dispatching. This method uses A-CAES as a black-start power source, establishes a variable-parameter thermodynamic model allowing simultaneous operation of the compression and expansion subsystems, constructs a frequency response model with SSPR as the disturbance, and embeds maximum frequency deviation and maximum rate of change constraints into the system restoration optimization model. A safe and executable restoration plan is obtained through solving these constraints. This method enables A-CAES to simultaneously undertake grid construction, power supply, and frequency support functions in the early stages of restoration, improving the applicability of A-CAES in system restoration. Furthermore, this method models the power disturbance in system restoration as SSPR, consistent with the actual restoration process, and can avoid the risks of conservative decision-making or frequency exceeding limits due to unreasonable disturbance modeling.

Description

Technical Field

[0001] This invention belongs to the field of power system dispatching, and more specifically, relates to a power system restoration method with large-scale adiabatic compressed air energy storage. Background Technology

[0002] Following a major power outage, the power system needs to be restored to normal operation as quickly as possible from a complete or partial power failure. A complete restoration process typically includes system partitioning, pre-restoration preparation, subsystem restoration, subsystem synchronization and paralleling, and restoration of remaining components. Among these, subsystem restoration, which handles the startup of black-start power supplies and subsequent system reconfiguration, is a crucial step determining the success of system restoration. In the early stages after a power outage, the number of online power sources is small, system inertia is low, and primary frequency regulation capability is weak. If the restoration plan does not adequately constrain frequency changes, the maximum frequency deviation or frequency change rate may exceed limits during actual execution, potentially triggering the operation of generating units, loads, or protection devices. Summary of the Invention

[0003] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a power system restoration method incorporating large-scale adiabatic compressed air energy storage. This method uses A-CAES as the black-start power source, establishes a variable-parameter thermodynamic model that allows the compression subsystem and expansion subsystem to operate simultaneously, constructs a frequency response model with SSPR as the perturbation, and embeds maximum frequency deviation (MFD) and rate of change of frequency (RoCoF) constraints into the system restoration optimization model. By solving these constraints, a safe and executable restoration plan is obtained.

[0004] To achieve the above objectives, according to a first aspect of the present invention, a method for restoring a power system containing large-scale adiabatic compressed air energy storage is provided, comprising: With the goal of restoring the thermal power unit TPU, wind farm WF, load, line, and node in the power system as soon as possible, a power system frequency security constraint restoration model containing A-CAES is established and solved under preset constraints to obtain the optimal restoration strategy for TPU and WF and the optimal scheduling scheme for A-CAES. The preset constraints include A-CAES operation constraints, frequency constraints, system recovery 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 by this invention, targeting power systems with large-scale A-CAES, proposes an optimized strategy for system outage recovery that takes into account frequency security constraints. This strategy can be applied to the recovery of subsystems after partitioning, as well as to the recovery of small power systems without partitioning. Compared with existing technologies, the main advantages of this invention are as follows: (1) This invention uses a large-scale A-CAES as a black start power source and allows the compression subsystem and expansion subsystem to operate simultaneously, enabling the A-CAES to simultaneously undertake the functions of network construction, power supply and frequency support in the early stage of recovery, thereby improving the applicability of A-CAES in system recovery.

[0009] (2) The present invention models the power disturbance in system recovery as SSPR, which is consistent with the actual recovery process and can avoid the risk of conservative decision-making or frequency over-limit due to unreasonable disturbance modeling. Attached Figure Description

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

[0011] Figure 2 The isentropic compression and expansion efficiency curves provided for embodiments of the present invention.

[0012] Figure 3 (a) and (b) in the figure are schematic diagrams of the frequency response model of the power system and the frequency response model of the SSPR frequency response model recovery process provided in the embodiments of the present invention.

[0013] Figure 4 In the examples (a) to (c), the first, second, and third parts of the present invention are respectively provided in the embodiments of the present invention. g The first TPU, A-CAES expansion subsystem, and A-CAES compression subsystem. k A schematic diagram of the frequency response model recovery process.

[0014] Figure 5 This is a schematic diagram of the equivalent frequency response model for the power system recovery process provided in an embodiment of the present invention.

[0015] Figure 6 In the examples (a) to (c), the simplified first step for MFD provided in the embodiments of the present invention is respectively... g The first TPU, A-CAES expansion subsystem, and A-CAES compression subsystem. k A schematic diagram of the frequency response model of the line.

[0016] Figure 7 This is a topology diagram of Embodiment 1 of the present invention.

[0017] Figure 8 In the figures (a) to (c), the wind power and ambient temperature prediction curves of wind farm 1 and wind farm 2 in Embodiment 1 of the present invention are respectively.

[0018] Figure 9 This is a schematic diagram of the topology recovery results for Cases 1-3 of Embodiment 1 of the present invention.

[0019] Figure 10 In the diagrams (a) to (c), the TPU recovery results of Cases 1 to 3 of Embodiment 1 of the present invention are shown respectively.

[0020] Figure 11 This is a schematic diagram of the wind power recovery results for Cases 1-3 of Embodiment 1 of the present invention.

[0021] Figure 12 In the diagrams (a) to (c), A-CAES power diagrams for Cases 1 to 3 of Embodiment 1 of the present invention are shown respectively.

[0022] Figure 13 In the diagrams (a) to (b), the pressure of the A-CAES gas storage chamber and the mass of the hot water tank are respectively the schematic diagrams of Case 1 to 3 of Embodiment 1 of the present invention.

[0023] Figure 14 In the diagrams (a) to (c), the load recovery results of each node in Cases 1 to 3 of Embodiment 1 of the present invention are shown respectively.

[0024] Figure 15 This is a schematic diagram of the total load recovery results for Cases 1-3 of Embodiment 1 of the present invention.

[0025] Figure 16 In the diagrams (a) to (c), the maximum RoCoF values ​​for Cases 1 to 3 of Embodiment 1 of the present invention are shown respectively. Figure 16 In the diagrams (d) to (f), MFD diagrams for Cases 1 to 3 of Embodiment 1 of the present invention are shown respectively. Detailed Implementation

[0026] 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.

[0027] During power system restoration, large-scale A-CAES (Automatic Power Supply-Driven Systems) possesses advantages such as fast start-up speed, strong ramp-up capability, good islanded operation capability, and the ability to provide mechanical inertia and primary frequency regulation services, making it a potential candidate for black-start power sources in power system restoration. On the other hand, actual restoration operations typically follow a "power source first, load second" sequence, meaning that the source-side power linearly ramps up from the current moment to the next moment before connecting the corresponding load. Therefore, the actual disturbance manifests as SSPR (Short-Side Power Regulator).

[0028] Based on this, this invention proposes a frequency security constraint recovery method applicable to power systems with large-scale A-CAES (Automatic Space Array) energy storage, to accurately constrain frequency deviations and frequency change rates caused by SSPR (Speed ​​Spectrum Reduction) while satisfying component recovery logic, power balance, and A-CAES operational safety, thereby improving the executability and safety of the recovery plan. Specifically, this invention provides a power system recovery method with large-scale adiabatic compressed air energy storage, comprising: With the goal of restoring the thermal power unit TPU, wind farm WF, load, line, and node in the power system as soon as possible, a power system frequency security constraint restoration model containing A-CAES is established and solved under preset constraints to obtain the optimal restoration strategy for TPU and WF and the optimal scheduling scheme for A-CAES. The preset constraints include A-CAES operation constraints, frequency constraints, system recovery constraints, and power system constraints.

[0029] Specifically, the method provided by this invention includes the following steps: Step A: Construct an A-CAES variable parameter thermodynamic model. This model integrates parallel compression and constant sliding pressure expansion design, allowing the compression and expansion sides to operate simultaneously, and taking into account the variation characteristics of key parameters such as temperature, pressure, and efficiency.

[0030] In step A, the structure and operating mechanism of A-CAES are described as follows: A-CAES structure as follows Figure 1 As shown. Figure 1 In the text, variables are indicated in red; italic subscripts are used. 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 air flow rates of the compression subsystem and the expansion subsystem, 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.

[0031] During system recovery, the compression and expansion subsystems are allowed to operate simultaneously and independently. When the compression subsystem is running, the multi-stage compressor consumes electrical energy to compress ambient air stage by stage. Simultaneously, circulating water flows from the cold water tank and convects with the air in the interstage heat exchanger to absorb the heat of compression. Finally, the compressed air enters the storage chamber, and the heated circulating water enters the hot water tank. When the expansion subsystem is running, the storage chamber releases high-pressure air to drive the multi-stage expander and generator, while high-temperature circulating water flows from the hot water tank and reheats the air in the interstage heat exchanger to enhance its work capacity.

[0032] In step A, the thermodynamic model of the A-CAES compression subsystem is as follows: (1) Compression power

[0033] In the formula, The specific heat capacity of air at constant pressure; This is the specific heat ratio of air.

[0034] (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.

[0035]

[0036] (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.

[0037] (4) Inlet working fluid temperature of the compressor

[0038] (5) Inlet working fluid temperature of the gas storage chamber

[0039] (6) Temperature of the heat transfer medium at the outlet of the heat exchanger

[0040] In step A, the thermodynamic model of the A-CAES expansion subsystem is as follows: (1) Power generation

[0041] (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.

[0042]

[0043] (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 red line.

[0044] (4) Inlet working fluid temperature of the expander

[0045] In step A, the thermodynamic model of the A-CAES gas storage chamber is as follows: (1) Gas storage chamber pressure

[0046] In the formula, italic subscripts t Number the time; The duration between adjacent moments;R is the gas constant of air; 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.

[0047] (2) Gas storage chamber quality

[0048] (3) Temperature of the gas storage chamber

[0049] In step A, the thermodynamic model of the A-CAES hot water tank is as follows: (1) Quality of hot water tank

[0050] (2) Temperature of hot water tank

[0051] In the formula, This is the specific heat capacity of water.

[0052] Step B involves constructing a system frequency response model with SSPR as the disturbance and proposing an equivalent calculation method for frequency security indicators, including MFD and maximum RoCoF.

[0053] In step B, the frequency response model with SSPR as the perturbation is as follows: During system recovery, adjacent recovery times t and t The SSPR between +1 and +1 is the primary cause of frequency shift. Source-side power includes thermal power unit (TPU) power, wind farm (WF) power, and A-CAES compression / expansion power. t Before time +1, the load corresponding to the power increment on the source side has not yet been connected, resulting in a positive power imbalance in the system and a gradual increase in frequency; t When the load is connected at +1, the power imbalance is canceled out, and the frequency returns to the rated value after attenuation oscillation.

[0054] In the above process, the grid-connected TPUs can provide inertia support, and the TPUs that have been restored to normal operation can further participate in primary frequency regulation; the operating A-CAES expansion and compression subsystems can both participate in primary frequency regulation and provide mechanical inertia to the system. The frequency response model with SSPR as the disturbance is as follows: Figures 3-4 As shown.

[0055] Figures 3-4In Chinese, variable coefficients are indicated in red; superscripts "~" indicate per-unit values; italic subscripts... g Number the TPU; This is the inertial response function; s For the Laplace operator; This is for frequency deviation; The frequency response coefficient of the load; The total system load that has been restored (including node load and TPU startup power); , , These are the valve time constants for the TPU, the A-CAES expansion subsystem, and the A-CAES compression subsystem, respectively. The time constant of the high-pressure cylinder front steam chamber of TPU; The reheater volume time constant of the TPU; , These are the volumetric time constants of the A-CAES compressor and expander, respectively. The percentage of high-pressure cylinder output power for TPU; , These are the power output per unit flow of air consumed by a single expander and expansion subsystem of A-CAES, respectively. , These are the power consumed by a single compressor and a single line of air production per unit flow rate in the A-CAES compression subsystem, respectively. This represents the maximum power of the TPU; , , These are the droop coefficients for the TPU, A-CAES expansion subsystem, and A-CAES compression subsystem, respectively. , , These represent the operating status of the TPU, A-CAES expansion subsystem, and A-CAES compression subsystem, respectively. The value is 1 when the system is running and 0 otherwise. , These are the maximum airflow rates for a single row of the A-CAES expansion subsystem and the A-CAES compression subsystem, respectively. , , These represent the primary frequency modulation power variation for a single line of the TPU, A-CAES expansion subsystem, and A-CAES compression subsystem, respectively.

[0056] , , , , , It can be calculated using the following formula:

[0057]

[0058]

[0059]

[0060]

[0061]

[0062]

[0063] In the formula, This refers to the system's operating inertia. This indicates the grid connection status of the TPU; 1 indicates it is connected to the grid, and 0 indicates it is not. , , These are the inertial time constants of the TPU, the A-CAES expansion subsystem, and the A-CAES compression subsystem, respectively. , These represent the maximum power of a single row in the A-CAES expansion subsystem and the A-CAES compression subsystem, respectively; italic subscripts n Number the nodes; For the node load that has been restored; This refers to the startup power of the TPU; This indicates the TPU's startup status; it is set to 1 if the TPU is started, and 0 otherwise. It should be noted that, as the unit being started, the TPU should first draw power from the grid to begin startup during the recovery process. Only after sufficient preparation can it be connected to the grid, and then gradually increase its power output to enter the normal power operating range.

[0064] In step B, the equivalent frequency response model used to calculate the frequency security index is as follows: Since SSPR is a continuous ramping disturbance, and the system state changes continuously during the ramping process, it is difficult to give a concise closed-form expression for frequency security indicators. Considering that the time scale of primary frequency modulation is usually on the order of seconds, while the time scale of SSPR during system recovery is usually on the order of tens of minutes, primary frequency modulation can be regarded as a fast process relative to SSPR. Therefore, at any point during SSPR, it can be assumed that primary frequency modulation has reached a quasi-steady state.

[0065] Based on the above assumptions, the original SSPR frequency response problem can be equivalent to a step perturbation frequency response problem. MFD can be equivalent to the steady-state frequency deviation under a negative step power perturbation; the maximum RoCoF can be equivalent to the initial frequency change rate under a positive step power perturbation. The amplitudes of both equivalent perturbations are taken as the final values ​​of the SSPR between adjacent recovery times. The equivalent frequency response model is as follows: Figure 5 As shown.

[0066] Calculating MFD and maximum RoCoF based on the equivalent model can significantly reduce computational complexity while maintaining computational accuracy, allowing frequency safety constraints to be embedded into the recovery optimization model.

[0067] Step C: Construct a power system frequency security constraint recovery model containing A-CAES.

[0068] In step C, the power system frequency security constraint recovery model containing A-CAES is as follows: The model aims to restore TPU, WF, load, lines, and nodes as quickly as possible, and on this basis, to maximize the available energy of A-CAES for unforeseen circumstances.

[0069] (1) Objective function

[0070] In the formula, , , , , The weights of each objective are assigned in descending order; italic subscripts. l , h These are the line and WF numbers, respectively; This indicates the recovery status of the line; 1 indicates recovery, and 0 indicates otherwise. This refers to the output power of WF.

[0071] (2) A-CAES operational constraints ① Power Constraint

[0072]

[0073]

[0074]

[0075] In the formula, This represents the operating status of the A-CAES compression subsystem; it is set to 1 when the system is running and 0 otherwise. This represents the total compression power of A-CAES. , These are the minimum power generation capacity and minimum single-row compression capacity of A-CAES, respectively. The principle of row-by-row allocation of compression power for A-CAES is based on the fact that isentropic compression efficiency is usually a convex monotonically increasing function with respect to compression power. Therefore, given a fixed total compression power, the fewest compression rows should be put into operation, and the power should be evenly distributed among the rows in operation.

[0076] ② Pressure constraints in the gas storage chamber and mass constraints of the hot water tank

[0077]

[0078] In the formula, , 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. T This represents the total number of time points in the recovery process.

[0079] ③ Airflow constraints of the expansion subsystem

[0080] In the formula, M It is a sufficiently large positive number.

[0081] (3) Frequency constraints Frequency constraints include the equivalent frequency response model described in step B for calculating the frequency security indices MFD and maximum RoCoF, as well as the boundary constraints for both indices. It should be noted that at the first recovery time point, only the node containing A-CAES has recovered; there is no load recovery or SSPR, therefore, frequency indices do not need to be constrained. The MFD and maximum RoCoF constraints are as follows:

[0082]

[0083] In the formula, and These are the maximum RoCoF and its upper limit, respectively. and These represent the maximum RoCoF and its upper limit, respectively.

[0084] exist Figure 5 At the instant the equivalent step disturbance occurs, due to the frequency dead zone, the primary frequency modulation of the TPU and A-CAES has not yet responded. Therefore, when calculating the maximum RoCoF based on the equivalent frequency response model, the negative feedback loops of the TPU and A-CAES in the model can be removed. Accordingly, the above maximum RoCoF constraint can be strictly linearized into the following equation:

[0085] In the formula, This is the system's rated frequency.

[0086] When MFD occurs, the primary frequency modulation of TPU and A-CAES has already responded. Therefore, the calculation of MFD involves a complex nonlinear process, and the above-mentioned MFD constraint is also a nonlinear constraint, which can be handled by the iterative solution method in step D.

[0087] (4) System recovery constraints System recovery constraints are used to describe the recovery logic of TPU, WF, load, node, and line.

[0088] ①TPU recovery constraint Once its node recovers, the TPU is ready to recover. During the recovery process, it should first absorb power to start the necessary plant power equipment. After preparation, it should be connected to the grid. Then, it should continuously increase the power until the power enters the normal operating range and operates stably within this range.

[0089]

[0090]

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

[0097] In the formula, To indicate the node's recovery status, set 1 if the node has recovered, and 0 otherwise. A set of TPU IDs connected to a single node; Preparation time for the TPU startup phase; m It is a sufficiently small positive number; This represents the minimum power of the TPU; r This represents the maximum gradeability of the TPU. This refers to the output power of the TPU.

[0098] ②WF Restoration Constraints WF has the conditions to recover after its own node recovers, and can be adjusted within the predicted power range after recovery.

[0099]

[0100] In the formula, The predicted power of WF; This is the set of WF numbers connected to a single node.

[0101] ③ Load recovery constraints The load can only be restored after its node has recovered, and the power that has been restored will not be cut off again.

[0102]

[0103]

[0104] In the formula, This represents the total power that the node needs to restore.

[0105] ④ Node recovery constraints At the start of system recovery, all nodes except the one connected to the A-CAES power supply for black boot are not yet restored. Any node can only be restored after any line connected to it has been restored, and it will not be disconnected after restoration.

[0106]

[0107]

[0108]

[0109] In the formula, A set of numbers for the lines connected to a single node.

[0110] ⑤ Line restoration constraints Any line can only be restored after either of its two ends has been restored, and it will not be disconnected again after restoration. A line can only be restored after it has been fully charged. Once a line is restored, both of its two ends are restored.

[0111]

[0112]

[0113]

[0114] In the formula, Charging time for the line; n' Indicates different n The node number.

[0115] (5) Other constraints In addition to A-CAES constraints, the recovery model also includes grid construction constraints, power flow constraints, line power constraints, node voltage constraints, power balance constraints, and reserve constraints. Grid construction constraints require that at any given time, at least one synchronous generator (TPU or A-CAES expansion subsystem) must be connected to the grid to establish grid voltage. Other constraints are well-established and fundamental; please refer to relevant materials for details, and will not be elaborated further.

[0116]

[0117] Step D proposes a solution method for the nonlinear recovery model described in step C.

[0118] In step D, the iterative solution method for solving the nonlinear recovery model described in step C is as follows: The system recovery model contains boundary constraints for A-CAES safety indices (gas storage chamber pressure, hot water tank mass, and expansion subsystem airflow). These variables all need to be calculated using the nonlinear thermodynamic model in step A; therefore, the aforementioned boundary constraints are all nonlinear inequality constraints. Furthermore, in the frequency constraints, MFD needs to be calculated using the nonlinear equivalent frequency response model in step B; therefore, its boundary constraints are also nonlinear inequality constraints. These constraints make traditional methods such as sequential linear programming, sequential quadratic programming, and Benders decomposition difficult to apply. A common compromise to address this problem is the parameter-fixed linearization method, but this method leads to optimistic decision-making, posing safety risks to actual operation. Therefore, as a further preferred solution of this invention, an iterative solution method is adopted.

[0119] The iterative solution method splits the original recovery problem into a main problem and subproblems. The main problem is a linear recovery problem, inheriting the objective function and linear constraints of the original recovery problem. The nonlinear thermodynamic model and equivalent frequency response model are replaced with their respective idealized linear models, used to calculate the A-CAES safety index and MFD within the main problem. To avoid the main problem overestimating A-CAES performance and system frequency behavior, leading to an overly aggressive system recovery plan, the subproblems verify the solution results of the main problem, substituting these results into the original nonlinear thermodynamic model and equivalent frequency response model to calculate the true A-CAES safety index and MFD. If any limits are exceeded, the main problem is required to tighten the boundaries of the corresponding indexes and re-optimize. The main problem and subproblems interact iteratively to complete the solution of the system recovery problem.

[0120] (1) Main problem ① Linear calculation of A-CAES gas storage chamber pressure, hot water tank mass, and air flow rate of expansion and compression subsystems For A-CAES, the rate of change of pressure in the gas storage chamber and the air flow rate can both be fitted as linear functions of power and gas storage chamber pressure. Based on the fitted function, the air flow rate of the expansion and compression subsystems can be calculated by the following formula:

[0121]

[0122]

[0123]

[0124] The rate of change of pressure in the gas storage chamber can be calculated using the following formula:

[0125]

[0126]

[0127]

[0128] The mass of the hot water tank can be calculated using the following formula:

[0129] The pressure in the gas storage chamber can be calculated using the following formula:

[0130] In the formula, , , X is the fitting coefficient for the rate of change of gas chamber pressure caused by the compression or expansion process (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). For the air flow rate of the compression subsystem; , These represent the rate of change of gas storage chamber pressure caused by the compression and expansion processes, respectively.

[0131] ②Linear calculation of MFD As shown in step B, the MFD can be replaced by the steady-state frequency difference of the equivalent frequency response model. After a sufficiently long time following the disturbance, the first-order frequency modulation process of the equivalent model tends to stabilize, at which point the first-order inertial element can be considered as a straight-through path. Therefore, the TPU and A-CAES frequency response models in the equivalent model, that is... Figure 4 In the equations (a) to (c), we can simplify them as follows: Figure 6 .

[0132] Based on the simplified equivalent model, the primary frequency modulation power provided by the TPU can be calculated using the following formula:

[0133]

[0134]

[0135] The primary frequency modulation power provided by the A-CAES expansion subsystem can be calculated using the following formula:

[0136]

[0137]

[0138] The primary frequency modulation power provided by the A-CAES compression subsystem can be calculated using the following formula:

[0139]

[0140]

[0141] Based on the above primary frequency modulation power, MFD can be calculated using the following formula:

[0142] In the formula, , , The power consumed by the compression subsystem to produce a unit flow rate of air per line. ), or the power output per unit flow of air consumed by the expansion subsystem ( The fitting coefficients of the two (X takes C or G); , , These are the frequency modulation dead zone widths of the TPU, A-CAES expansion subsystem, and A-CAES compression subsystem, respectively. , , These are the power limiting functions for the TPU, the A-CAES expansion subsystem, and the A-CAES compression subsystem, respectively. The reference value is usually set to 50Hz.

[0143] After calculating the MFD using the above formula, the penalty term for the MFD needs to be taken into account in the objective of the main problem, as shown in the following formula:

[0144] ③Connection constraints 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 gas storage chamber pressure, hot water tank mass, expansion subsystem air flow rate, and MFD safety boundaries 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 boundary constraints of these variables in the main problem; the prototypes to be replaced are detailed in step C.

[0145]

[0146]

[0147]

[0148]

[0149] In the formula, , 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 upper bound imposed by the subproblem on the main problem MFD.

[0150] (2) Subproblems The operation process for the subproblems is as follows: ① Set the initial boundary of the connection constraints. , , , , , The initial values ​​are respectively set to , , , , , For the first four dynamic boundaries, For the latter two dynamic boundaries, .

[0151] ② Solve the main problem and pass some key results to subproblems, including TPU results ( , , , A-CAES results ( , , , , , , ) and system results ( , (The superscript ") "" indicates that the variable to which it belongs is the result of solving the main problem. For , , The results of the remaining main questions, .

[0152] ③ The solution to the main problem , The thermodynamic model is transferred to step A for calculation. , , , , The solution to the main problem is... , , , , , , , , and the computation of subproblems , The equivalent frequency response model is passed to step B for calculation. Superscript " "" indicates that the variable it belongs to is the result of solving a subproblem. For , , The results of the remaining main problems or subproblems, .

[0153] ④ Settings .

[0154] ⑤ Update the boundaries of the connection constraints based on the exceedance conditions, as shown in Table 1: Table 1

[0155] ⑥ Control the iteration process based on the exceedance of the two types of constraints: If an arbitrary boundary update occurs in step ⑤, return to step ② to begin the next iteration.

[0156] like And if no boundary update occurs in step ⑤, then let Then return to step ⑤ to continue this round of iteration.

[0157] like If no boundary update occurs in step ⑤, it means that the system recovery model has been solved.

[0158] In step D, the key solution results of the system recovery model are as follows: 1) Thermal power units: Start-up status, grid connection status, operating status, power; 2) Wind farm: power; 3) A-CAES: Compression status, power generation status, compression power, power generation power, gas storage chamber pressure, hot water tank mass, expansion subsystem air flow; 4) System: Maximum RoCoF, MFD, node recovery status, line recovery status, load recovery amount; 5) Optimization goals: Recovery of nodes, lines, loads, TPUs, and WFs throughout the day.

[0159] The method provided by the present invention will be further illustrated below with a specific example.

[0160] Example 1 This embodiment focuses on the power system restoration method 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.

[0161] (1) Taking into account A-CAES operation constraints, frequency constraints, system recovery constraints, etc., the recovery optimization model is constructed with the goal of maximizing the sum of the recovery amounts of nodes, lines, loads, TPUs, and WFs throughout the time period.

[0162] (2) For the specific mathematical expressions in the above model, please refer to the A-CAES thermodynamic model, system frequency response model, and power system frequency security constraint recovery model containing A-CAES described in steps A, B, and C of the invention content.

[0163] Step B: The parameter settings for this embodiment are as follows.

[0164] (1) Implementation environment: The implementation was tested on a computer with an Intel Xeon Gold 2.70GHz CPU and 256GB of memory. The recovery optimization model was solved by calling Yalmip through MATLAB R2022a. The solver used was Gurobi 9.1.

[0165] (2) Optimization time scale of the example: The total recovery time is 6 hours and the unit optimization time is 15 minutes.

[0166] (3) Implementation example topology diagram: The topology diagram is as follows Figure 7 As shown.

[0167] (4) CAES parameters of Example A: as shown in Table 2.

[0168] Table 2

[0169] (5) TPU parameters of the example: as shown in Table 3.

[0170] Table 3

[0171] (6) Load ratio of each node in the embodiment: as shown in Table 4.

[0172] Table 4

[0173] (7) Wind power and ambient temperature prediction curves of the embodiment: as shown Figure 8 As shown.

[0174] (8) Other parameters of the embodiment: The total load of the system to be restored is 1200 MW, the rated frequency is 50 Hz, the frequency response coefficient of the load is 1, the maximum RoCoF and MFD limits are 0.3 Hz / s and 0.2 Hz, respectively, and the objective function weights are... , , , , The values ​​are 10000, 1000, 100, 1, and 0.1 respectively, and the charging time is 30 minutes.

[0175] Step C: Optimize the solution for this embodiment and analyze the results.

[0176] To verify the effectiveness of the system recovery method proposed in this invention, three cases were set up: Cases 1 and 2 respectively considered frequency security constraints with SSPR and load step increase (a commonly used simplified form) as power disturbances, while Case 3 did not consider frequency security constraints. The topology recovery results for the three cases are as follows: Figure 9 As shown, the TPU recovery results are as follows: Figure 10 As shown, the wind power recovery results are as follows: Figure 11 As shown, the A-CAES power is as follows Figure 12 As shown, the pressure in the A-CAES gas storage chamber and the mass of the hot water tank are as follows: Figure 13 As shown, the load recovery results for each node are as follows: Figure 14 As shown, the total load recovery result is as follows: Figure 15 As shown, the maximum RoCoF and MFD are as follows Figure 16 As shown in Table 5, the cumulative recovery of TPU, WF, lines, load, and A-CAES cumulative energy are as follows.

[0177] Table 5

[0178] As shown in Table 5 and Figure 9 , Figure 10 , Figure 11 As shown, the recovery sequence of the nodes, lines, TPU, and WF in the three cases is completely consistent, all following the principle of minimizing recovery time. Specifically, after a node completes recovery, the connected lines can be restored by charging; after a line is restored, both nodes at both ends of the line are restored; the TPU and WF can only be connected to the grid after their connected buses are restored and preparatory work is completed. These results demonstrate that the proposed recovery method is logically sound and can meet the need for rapid restoration of power supply capacity after a major power outage.

[0179] Furthermore, the output of the TPU and WF in Case 3 is significantly higher than in Cases 1 and 2. Case 3 does not impose frequency safety constraints; load recovery is limited only by the system's generating capacity and ramp rate, and these constraints are less stringent than the frequency specifications. Therefore, if... Figure 14 As shown in (c), most loads can be fully reenergized immediately after their respective busbars are restored. Meanwhile, by Figure 15 It is evident that, compared to Cases 1 and 2, Case 3 achieved full recovery of overall workload three time periods earlier.

[0180] The need for rapid load restoration and power balancing increases the power supply output in Case 3, but this comes at the cost of frequency safety. Combined with... Figure 16 As shown in (c) and (f), the maximum RoCoF and MFD exceed the limits in almost all load recovery periods. This demonstrates that frequency safety constraints are an indispensable constraint for system recovery optimization.

[0181] like Figure 12 , Figure 13 As shown, the operation of A-CAES in Cases 1 and 2 can be clearly divided into three stages: emergency power supply, frequency support, and energy replenishment. 1. First Phase (Segments 1-11) A-CAES performs compression and expansion simultaneously, with a non-negative net output power. It is used to rebuild voltage, start the TPU unit, restore load, and ensure frequency safety until the gas storage chamber pressure drops to the lower limit.

[0182] 2. Second Phase (Periods 12-16) To maintain frequency stability, the A-CAES continuously performs synchronous compression and expansion until all loads are restored. During this time, the unit's net output power is negative to offset cycle losses and prevent pressure exceedances in the gas storage chamber. Although the A-CAES absorbs scarce active power from the grid during the recovery phase, it can mitigate frequency rises caused by SSPR (Self-Suppressed Circulation Ratio) and increase the single-period load recovery capacity. Considering its overall benefits, this energy absorption has practical value.

[0183] 3. The third phase (period 17-24) The load, generating units, and grid topology have all been fully restored, and A-CAES has been compressed to full power to store energy in preparation for any subsequent failures.

[0184] For Case 3, since no frequency safety constraints were set, the optimization objective was to maximize the accumulated energy of A-CAES, and the unit almost never used the compression-expansion synchronous operation mode. Although the final gas storage chamber pressure increased by 3 bar in this scenario, the system frequency safety was sacrificed, and the overall solution was not feasible.

[0185] As shown in Table 5 and Figure 15 As shown, the load recovery rate of Case 1 was slightly faster than that of Case 2, and this difference was particularly pronounced after time period 6. Combined with... Figure 12 As shown in (a) and (b), during the period from 5 to 11, the compression power of Case 1 and Case 2 remained at similar low levels. For Case 1, the decision model incorporates frequency security constraints based on SSPR, requiring the compression subsystem to have positive primary frequency regulation capability, which can be met under low-power operation. For Case 2, the decision model incorporates frequency security constraints based on a sudden increase in load. This disturbance is a positive power disturbance, requiring the compression subsystem to provide power for the next primary frequency regulation; however, the adjustment margin is insufficient under low-power operation. Due to the limitation of the overall primary frequency regulation capability of the system, Case 2 can only slow down the load recovery rate. In summary, an inappropriate disturbance modeling scheme can lead to a conservative recovery decision.

[0186] like Figure 16 As shown, in Case 3, where no frequency safety constraints were set, various frequency indicators significantly exceeded the safety thresholds, posing a risk of unit disconnection during load restoration operations. Although Case 2 incorporated frequency safety constraints, the minimum dynamic frequency (MFD) still exceeded the limit due to discrepancies between the disturbance modeling and actual operating conditions. Therefore, frequency safety constraints based on SSPR are an indispensable condition for optimizing decision-making during large-scale power outage recovery.

[0187] Summary of Example 1 Based on the steps described in Embodiment 1, the power outage recovery method for power systems with large-scale A-CAES described in this invention can accurately characterize the actual SSPR disturbance during the system recovery process and avoid frequency security risks in the execution of recovery commands through maximum RoCoF and MFD constraints. Simultaneously, this invention utilizes the simultaneous compression and expansion capabilities of A-CAES to provide support for grid construction, power supply, inertia, and primary frequency regulation in the early stages of recovery, which helps improve the system recovery speed and the feasibility of the recovery plan.

[0188] 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.

[0189] 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.

[0190] 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.

[0191] 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 restoring a power system containing large-scale adiabatic compressed air energy storage, characterized in that, include: With the goal of restoring the thermal power unit TPU, wind farm WF, load, line, and node in the power system as soon as possible, a power system frequency security constraint restoration model containing A-CAES is established and solved under preset constraints to obtain the optimal restoration strategy for TPU and WF and the optimal scheduling scheme for A-CAES. The preset constraints include A-CAES operation constraints, frequency constraints, system recovery constraints, and power system constraints.

2. The method as described in claim 1, characterized in that, The objective function of the power system frequency security constraint recovery model is: in, , , , , All are weighting coefficients. for t Time period nodes g The running status variables of the connected TPU, For nodes g The maximum power of the connected TPU. for t Time period nodes n The maximum power of the connected TPU. for t Time-of-day routes l The recovery state variables, for t Periodic wind farm h 'output power' for t Pressure in the gas storage chamber during a given time period.

3. The method as described in claim 2, characterized in that, The operational constraints of the A-CAES include the analytical expression of the state variables of the A-CAES, power constraints, pressure of the gas storage chamber and mass of the hot water tank, air flow constraints of the expansion subsystem and frequency constraints. The frequency constraint includes Operational boundary constraints and analytical expression Operational boundary constraints ; in, for t Maximum MFD over a period of time This is the upper limit of the maximum MFD; The system's rated frequency, for t System inertia during time period , They are respectively t Time period t The total system load that has been restored during the -1 period is now complete. This is the upper limit of the maximum RoCoF; The system recovery constraints include: ①TPU recovery constraint: in, , They are respectively t Time period t -1 time period node g The startup status variables of the connected TPU. for t Time period nodes n The restored state variables; For nodes n The set of serial numbers of the connected TPUs; , , They are respectively Time period t +1 time period t Time period nodes g The grid-connected state variables of the connected TPU Preparation time for the TPU startup phase. The time interval between adjacent time points; , They are respectively t Time period t +1 time period node g The output power of the connected TPU, , They are nodes g The minimum and maximum power of the connected TPU; m =10 -10 , M =10 10 ; , For respectively t Time period t +1 time period node g The running status variables of the connected TPU, For nodes g The maximum ramp rate of the connected TPU; ②WF Restoration Constraints: in, for t +1 time period wind farm h The predicted power; For nodes n The set of WF numbers received. for t +1 time period wind farm h ; output power; ③ Load recovery constraints: in, For nodes n Total power required to be restored , They are respectively t Time period t -1 time period node n The recovered node load; ④ Node recovery constraints: in, For nodes n The set of numbers of the connected lines, For nodes n The recovery state variable at time point 1, for t Time-of-day routes a The restored state variables; ⑤ Line restoration constraints: in, For the line b Charging time, n' Indicates different n The node number, For nodes n' The set of numbers of the connected lines, , , They are respectively Time period t Time period t +1 time slot route b The recovery state variables, for t Time period nodes n' The restored state variables.

4. The method as described in claim 3, characterized in that, Solving the power system frequency security constraint recovery model under preset constraints includes: S1, replace the objective function of the power system frequency security constraint recovery model with... Once the target model is obtained, the frequency constraint in the preset constraints is applied. The constraints on the gas storage chamber pressure and hot water tank mass, and the air flow rate of the expansion subsystem, are replaced with the corresponding connection constraints. This includes replacing the preset constraints on the gas storage chamber pressure, hot water tank mass, and air flow rate of the expansion and compression subsystems. The analytical expressions are replaced with the corresponding linear analytical expressions to obtain the target constraints; the boundaries of the connection constraints are initialized. for The per-unit value; S2, obtained by solving the target model under the target constraints. t Power generation of the expansion subsystem during the time period , No. k Compression power of compressed lines Substitute the state variable analytical expression of A-CAES in the preset constraints to obtain the expression that satisfies the analytical expression. t +1 period gas storage chamber pressure , and t Airflow of the expansion subsystem during the time period , No. j The power output per unit flow of air consumed by an expander , No. i The power consumed by a single compressor to produce a unit flow rate of air. ;Will , and the result obtained by solving the target model under the target constraints t Time period nodes g The startup status variables of the connected TPU Grid connection state variables Running state variables Output power Operating state variables of the expansion subsystem , No. k State variables of compressed lines , t Power generation of the time-expansion subsystem , No. k Compression power of compressed lines Node load that has been restored Substitute into the preset constraints The analytical expression is obtained t Estimated maximum MFD for the time period ; t=1,2,…,T, where T is the total scheduling duration; S3, let t=1; S4, Determine , , If an out-of-bounds situation occurs, the boundary of the state variable where the out-of-bounds situation occurred will be updated. S5, if an arbitrary boundary update occurs in S4, then return to S2 to begin the next iteration; if And since no boundary update occurred in S4, let And return to S4 to continue this iteration; if If no boundary update occurs in S4, then the process ends.

5. The method as described in claim 4, characterized in that, In step S1, the frequency constraint in the preset constraints The connection constraints corresponding to the pressure in the gas storage chamber, the mass of the hot water tank, and the air flow constraints in the expansion subsystem are as follows: in, for The target upper limit, The pressure in the gas storage chamber during time period t. , These represent the target upper and lower limits of the gas storage chamber pressure during time period t. For the mass of the hot water tank during time period t, , These represent the upper and lower limits of the target quality of the hot water tank during time period t. Let t be the airflow rate of the expansion subsystem during time period t. The target upper limit for the airflow of the expansion subsystem during time period t; The preset constraints include the gas storage chamber pressure, the hot water tank mass, and the air flow rate of the expansion and compression subsystem. The linear analytical expression corresponding to the analytical expression is: 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, hot water tank mass; This represents the total compression power of A-CAES; for t Airflow rate of the time-limited compression subsystem; , These represent the rate of change of gas storage chamber pressure caused by the compression and expansion processes during time period t. for t Time period nodes g The change in primary frequency modulation power of the connected TPU, for t The change in primary frequency modulation power of the time-dilation subsystem for t Time period k The change in primary frequency modulation power of the compressed line; for t The operating state variables of the time-compression subsystem for t Operating state variables of the time-segmented expansion subsystem; The boundary of the connection constraint , , , , , The initial values ​​are respectively , , , , , ; In step S4, if the following occurs , , , , , If any of the following conditions are exceeded, the boundary of the state variable where the exceedance occurred will be updated to... , , , , , .

6. 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 1-5.

7. 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 1-5.

8. 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 1-5.

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