A unit commitment recovery decision method considering coupling characteristics of power grid and natural gas grid

Abstract

The application provides a unit recovery decision-making method considering the coupling characteristics of power grids and natural gas networks. The method comprises the following steps: establishing an integer linear programming model of power grid unit recovery and load recovery, applying a solver to solve the integer linear programming model, and obtaining the key load recovery time of the power grid unit; using a natural gas pipeline network simulation software to establish a simulation model of the natural gas network, running the pipeline network dynamic simulation using the simulation model, and obtaining the gas supply recovery time of the gas unit; comprehensively optimizing the key load recovery time of the power grid unit and the gas supply recovery time of the gas unit, and formulating a power grid and natural gas network unit recovery strategy. The method can effectively consider the bidirectional coupling influence of the power grid and the natural gas network, quickly recover the unit, and support the rapid recovery of the power system. The method can obtain the optimal decision-making unit recovery time, power transmission path recovery time and gas pipeline network electrically-driven facility recovery time.

Description

Technical Field

[0001] This invention relates to the field of unit restoration technology for power grids and natural gas networks, and in particular to a unit restoration decision-making method that takes into account the coupling characteristics of power grids and natural gas networks. Background Technology

[0002] Currently, the coupling between the power grid and the natural gas grid is becoming increasingly close. On the one hand, against the backdrop of my country's new power system construction and the "3060 dual-carbon" target, the proportion of gas turbine units, as a regulating power source with high power generation efficiency, high flexibility, and low CO2 emission intensity, continues to increase. On the other hand, for environmental and economic considerations, electrically driven compressors and electrically driven gas sources are widely used in natural gas systems. This close connection between the two grids may trigger cascading failures and pose challenges to system recovery. After a major power outage, if the interdependence between the power grid and the natural gas grid is fully considered and a correct and effective system unit recovery strategy is formulated, the outage time can be effectively shortened and economic losses minimized.

[0003] The system recovery process can be divided into three stages based on the different optimization objectives at different recovery stages: unit black start, grid reconfiguration, and load restoration. Unit restoration is one of the core tasks of the grid reconfiguration stage, forming the foundation of the entire system recovery control and ensuring accelerated network reconfiguration and full load restoration. The task of unit restoration is to start up non-black start units in the system, quickly restoring the system's power generation capacity. Research on grid unit restoration is extensive and relatively mature. Because the power grid and natural gas grid are closely interconnected, the restoration of gas turbine units in the power grid is affected by the natural gas grid, and the operation of the natural gas grid is also affected by the power grid restoration.

[0004] In the field of coordinated recovery of power grids and natural gas networks, existing technologies have studied the resilience of integrated power-gas systems under extreme events. Results show that coupled operation of the power grid and gas network exhibits stronger recovery capabilities, but specific recovery steps are not addressed. Other existing technologies propose a joint scheduling method for maintenance personnel in coupled power-gas systems from the perspective of post-disaster maintenance personnel dispatch, achieving coordinated optimization of the equipment repair order in both systems. For load recovery of energy distribution networks, existing technologies consider the independence of distribution network and natural gas network operations, proposing a distributed load recovery method for integrated power-gas energy systems. For the load recovery problem of three-phase unbalanced distribution networks and gas distribution networks, existing technologies model this problem as a mixed-integer linear programming model and employ a rolling optimization algorithm based on a two-stage method for efficient solution.

[0005] Currently, there is no existing technology that considers the coupling effects of the power grid and the natural gas grid in terms of unit recovery scheme. Summary of the Invention

[0006] The embodiments of the present invention provide a unit recovery decision-making method that considers the coupling characteristics of the power grid and the natural gas grid, so as to effectively consider the bidirectional coupling effect of the power grid and the natural gas grid and quickly restore all units.

[0007] To achieve the above objectives, the present invention adopts the following technical solution.

[0008] A unit recovery decision-making method considering the coupling characteristics of the power grid and the natural gas grid includes:

[0009] An integer linear programming model for power grid unit restoration and load restoration is established, and a solver is applied to solve the integer linear programming model to obtain the critical load restoration time of the power grid units.

[0010] A simulation model of the natural gas network is established using simulation tools, and the simulation model is used to run a dynamic simulation of the pipeline network to obtain the gas supply recovery time of the gas turbine unit.

[0011] Based on the critical load recovery time of grid units and the gas supply recovery time of gas turbine units, a unit recovery optimization model considering all units is established. The solver is then used to solve the unit recovery optimization model to obtain the unit recovery strategies for grid and natural gas grid units.

[0012] Preferably, the step of establishing an integer linear programming model for power grid unit restoration and load restoration, and applying a solver to solve the integer linear programming model to obtain the critical load restoration time of the power grid units includes:

[0013] In the unit recovery sequence model that considers critical load recovery:

[0014] Let S NBS For non-black starter units, S BS For black starter units, S F For a collection of gas turbine units, S T For the set of time periods to be restored, S t S is the set of recovery periods up to time t. G For all units, S B Let S be the set of busbars. L For a collection of transmission lines, S B-BS S is the busbar set connecting the black starter unit. B / S B-Bs S represents the set of all buses except the bus connecting the black starter unit. l-b,i S represents the set of lines connecting bus i. LD Represents the set of critical loads;

[0015] Let C i K represents the capacity of the generator unit. i Indicates the unit's climb rate. This indicates the maximum output power of the generator set. Indicates the starting power of the generator unit. Indicates the start-up time of the unit. This indicates the maximum start-up time of the generator unit. Indicates the minimum start-up time of the unit;

[0016] set up Indicates the unit's recovery status. This indicates the gas supply status of the gas turbine unit. Indicates the recovery status of the busbar. This indicates the recovery status of the busbar connected to the generator unit. This indicates the recovery status of the transmission line. Indicates the recovery status of critical loads. Indicates the recovery status of the busbar connected to the critical load;

[0017] Substations powered by electrically driven compressors are the critical loads;

[0018] 3) Objective function

[0019] The objective function for fault recovery is set to maximize the system's power generation capacity and restore critical loads as quickly as possible. Its expression is:

[0020]

[0021] 4) The constraints for fault recovery include:

[0022] (5) Linearization of unit output function

[0023]

[0024] In the formula, the ceil and res functions are defined as follows:

[0025]

[0026] res(x)=ceil(x)-x (4)

[0027] (6) Unit start-up constraints

[0028]

[0029]

[0030]

[0031]

[0032]

[0033] Constraint (5) is the unit start-up time constraint, that is, for all units, the start-up time should be within the range of the earliest start-up time and the latest start-up time; constraint (6) is the system power constraint, that is, the system should have sufficient power generation to meet the start-up power requirements of non-black start units during each recovery period; constraint (7) indicates that non-black start units can only be started after the bus connected to the unit is restored; constraint (8) indicates that the unit will not be shut down after recovery; constraint (9) indicates that the gas turbine unit cannot be restored due to lack of gas supply.

[0034] (7) Transmission path constraints

[0035] By searching the recovery status of the busbars and lines, the optimal start-up path for non-black start units and the critical load recovery path are determined.

[0036]

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043] Constraint (10) indicates that if a line is energized at time t+1, then at least one of the busbars connected to it will be energized at time t; Constraint (11) indicates that if a busbar is energized at time t, then at least one of the busbars connected to it will be energized at time t; Constraints (12) and (13) indicate that the transmission line and busbar will not be de-energized again after restoration; Constraints (14)-(16) indicate the initial state of the line and busbar.

[0044] (8) Critical load recovery constraints

[0045] By determining the recovery status of critical loads, the recovery of critical loads can be coordinated with the recovery of non-black start units.

[0046]

[0047]

[0048]

[0049] Constraint (17) is a system power constraint, which means that there is sufficient power generation capacity to carry the critical load; constraint (18) means that the bus connected to the critical load should be energized before the load is restored; constraint (19) means that once the load is restored, it will not be de-energized.

[0050] The unit recovery sequence model considering critical load recovery is an integer linear programming problem. The critical load recovery time of the power grid units is obtained by solving the unit recovery sequence model considering critical load recovery using a commercial optimizer.

[0051] Preferably, the step of establishing a simulation model of the natural gas network using simulation tools, and using the simulation model to run a dynamic simulation of the pipeline network to obtain the gas supply recovery time of the gas turbine unit includes:

[0052] A simulation model of the natural gas network is established using natural gas pipeline network simulation software. The critical load recovery time of the power grid units is used as the input data of the simulation model. The simulation model is solved using a solver. The gas supply recovery time of the gas turbine units is obtained by running a dynamic simulation of the pipeline network using the simulation model.

[0053] Preferably, the comprehensive optimization of the critical load restoration time of the power grid units and the gas supply restoration time of the gas turbine units, and the formulation of restoration strategies for the power grid and natural gas grid units, includes:

[0054] Establish a unit recovery optimization model that considers all grid units and natural gas grid units. This unit recovery optimization model is an integer linear programming problem, expressed as:

[0055]

[0056] Constraints: (2)-(8), (10)-(16)

[0057] The unit recovery optimization model is solved using a solver to obtain the recovery strategies for all units. These strategies include the recovery times of all grid units and natural gas grid units, the recovery times of power transmission paths, the recovery times of gas transmission network electric drive facilities, and the start-up power time of gas turbine units. The gas supply recovery time of gas turbine units is determined through simulation calculations based on their start-up power time. The recovery time of gas turbine units is based on the latest time between the start-up power time and the gas supply recovery time. The recovery strategies for all units are then updated based on the gas pressure recovery time of the gas turbine units.

[0058] As can be seen from the technical solutions provided by the embodiments of the present invention above, the unit recovery decision-making method based on optimization modeling and simulation updates of the present invention can effectively consider the bidirectional coupling effect of the power grid and the natural gas grid, enabling rapid unit recovery and supporting the rapid recovery of the power system. The method of the present invention can obtain the optimal recovery time for the decision-making unit, the recovery time for the transmission path, and the recovery time for the gas transmission network's electrically driven facilities.

[0059] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and will become apparent from the description or may be learned by practice of the invention. Attached Figure Description

[0060] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0061] Figure 1 A flowchart illustrating a unit recovery decision-making method considering the coupling characteristics of the power grid and natural gas grid, provided in an embodiment of the present invention;

[0062] Figure 2 A topology diagram of a testing system provided in an embodiment of the present invention;

[0063] Figure 3 This is a recovery strategy diagram provided in an embodiment of the present invention. Detailed Implementation

[0064] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0065] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. It should be understood that when we say an element is “connected” or “coupled” to another element, it can be directly connected or coupled to the other element, or there may be intermediate elements. Furthermore, “connected” or “coupled” as used herein can include wireless connections or couplings. The term “and / or” as used herein includes any and all combinations of one or more of the associated listed items.

[0066] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0067] To facilitate understanding of the embodiments of the present invention, the following will provide further explanation and description with reference to the accompanying drawings and several specific embodiments. These embodiments do not constitute a limitation on the embodiments of the present invention.

[0068] This invention aims to address the problem that existing methods cannot accurately formulate unit recovery strategies in power grid systems closely linked to natural gas grids. It proposes a unit recovery decision-making method that considers the coupling characteristics of the power grid and natural gas grid. The processing flow of this method is as follows: Figure 1 As shown, the processing steps include the following:

[0069] Step S10: For the problems of power grid unit restoration and critical load restoration, establish an integer linear programming model (GSU-CLR), apply a mature optimization solver to solve the integer linear programming model, and determine the critical load restoration time;

[0070] Step S20: Use natural gas pipeline network simulation software to establish a simulation model of the natural gas network, take the critical load recovery time as the simulation input, simulate the pipeline network dynamics after the electric drive facilities are restored, and obtain the gas supply recovery time of the gas turbine unit.

[0071] Step S30: Comprehensively optimize the above-mentioned critical load recovery time and gas turbine gas supply recovery time, and formulate a unit recovery strategy. Establish a unit recovery (GSUS-ALL) model that considers all units, obtain the recovery sequence of all units, and update the unit recovery strategy based on the gas turbine gas pressure recovery time (simulation results).

[0072] Specifically, step S10 above includes: establishing an integer linear programming model for the power grid unit restoration and critical load restoration problems.

[0073] 5) Symbol Definition

[0074] Set: Let S NBs For non-black starter units, S Bs For black starter units, S F For a collection of gas turbine units, S T For the set of time periods to be restored, S t S is the set of recovery periods up to time t. G For all units, S B Let S be the set of busbars. L For a collection of transmission lines, S B-BS S is the busbar set connecting the black starter unit. B / S B-BS S represents the set of all buses except the bus connecting the black starter unit. l-b,i S represents the set of lines connecting bus i. LD This represents the set of critical loads.

[0075] Parameter: C i K represents the capacity of the generator unit. i Indicates the unit's climb rate. This indicates the maximum output power of the generator set. Indicates the starting power of the generator unit. Indicates the start-up time of the unit. This indicates the maximum start-up time of the generator unit. This indicates the minimum startup time of the generator unit.

[0076] Decision variables: Indicates the unit's recovery status. This indicates the gas supply status of the gas turbine unit. Indicates the recovery status of the busbar. This indicates the recovery status of the busbar connected to the generator unit. This indicates the recovery status of the transmission line. Indicates the recovery status of critical loads. This indicates the recovery status of the busbar connected to the critical load.

[0077] 6) Objective function

[0078] The objective function for fault recovery is to maximize the system's power generation capacity and quickly restore critical loads, and its expression is:

[0079]

[0080] 7) Constraints

[0081] (9) Linearization of unit output function

[0082]

[0083] In the formula, the ceil and res functions are defined as follows:

[0084]

[0085] res(x)=ceil(x)-x (4)

[0086] (10) Unit start-up constraints

[0087]

[0088]

[0089]

[0090]

[0091]

[0092] Constraint (5) is the unit start-up time constraint, meaning that for all units, the start-up time should be within the range of the earliest start-up time and the latest start-up time; constraint (6) is the system power constraint, meaning that the system should have sufficient power generation to meet the start-up power requirements of non-black start units during each recovery period; constraint (7) indicates that non-black start units can only start after the bus connected to the unit is restored; constraint (8) indicates that the unit will not be shut down again after recovery. Constraint (9) indicates that the gas turbine unit cannot be restored due to lack of gas supply.

[0093] (11) Transmission path constraints

[0094] By searching the recovery status of the busbars and lines, the optimal start-up path for non-black start units and the critical load recovery path are determined.

[0095]

[0096]

[0097]

[0098]

[0099]

[0100]

[0101]

[0102] Constraint (10) indicates that if a line is energized at time t+1, then at least one of the buses connected to it will be energized at time t. Constraint (11) indicates that if a bus is energized at time t, then at least one of the buses connected to it will be energized at time t. Constraints (12) and (13) indicate that the transmission line and bus will not be de-energized again after restoration. Constraints (14)-(16) indicate the initial state of the line and bus.

[0103] (12) Critical load recovery constraints

[0104] During power system restoration, it is necessary to simultaneously activate non-black start units to restore the system's power generation capacity and restore power to the electrically driven compressors as quickly as possible to ensure the smooth restoration of gas turbine units. Therefore, the restoration of critical loads is considered within the power constraints of unit restoration. By determining the restoration status of critical loads, coordination between the restoration of critical loads and the restoration of non-black start units can be achieved.

[0105]

[0106]

[0107]

[0108] Constraint (17) is a system power constraint, meaning there is sufficient generating capacity to support the critical load. Constraint (18) states that the bus connected to the critical load should be energized before the load is restored. Constraint (19) states that once the load is restored, it will not be de-energized. This invention uses a substation powered by an electrically driven compressor as the critical load.

[0109] The Server Recovery Sequence Considering Critical Load Recovery (GSUS-CLR) model is as described above. GSUS-CLR is an integer linear programming problem that can be solved using a commercial optimizer.

[0110] Specifically, step S20 includes: using simulation tools (such as PipelineStudio pipeline network simulation software) to establish a simulation model of the natural gas network, taking the critical load recovery time as the simulation input, and running the pipeline network dynamic simulation to obtain the gas supply recovery time, that is, simulating and calculating the gas pressure recovery time of the gas turbine unit based on the determination of critical load recovery and line recovery.

[0111] Specifically, step S30 includes: establishing a unit recovery (GSUS-ALL) model that considers all units, obtaining the recovery sequence of all units, and updating the unit recovery strategy based on the gas pressure recovery time of the gas turbine units (simulation results).

[0112] (1) GSUS-ALL optimization model

[0113] Compared to the GSU-CLR model, the GSU-ALL optimization model considers all units in the system but does not account for the recovery of critical loads. Therefore, the GSU-ALL optimization model can be expressed as:

[0114]

[0115] Constraints: (2)-(8), (10)-(16)

[0116] GSUS-ALL is also an integer linear programming problem that can be easily solved using commercial solvers such as Mosek.

[0117] (2) Determine the recovery time of the gas turbine unit

[0118] The recovery of gas turbine units is affected by both the starting power supplied by the external power grid and the gas supply from the natural gas grid. Recovery requires simultaneously meeting both starting power and gas supply requirements. The starting power time of the gas turbine unit is obtained by running GSUS-ALL, and the gas supply recovery time is determined by PipelineStudio simulation. The recovery time of the gas turbine unit is based on the latest of the starting power time and the gas supply recovery time.

[0119] exist Figure 2 In the test system shown, the left side represents the power grid, with 39 bus nodes, 34 lines, and 10 generating units (G10 is a black-start unit, and G1, G3, and G4 are gas turbine units). The right side represents the natural gas network, including 20 nodes, 19 gas pipelines, 2 compression stations, and 6 gas sources. Both compression stations are electrically driven. The interconnection between the power grid and natural gas network systems is shown by the dotted lines in the diagram. In the test scenario, after a major power outage, the power grid needs to perform a black start. Due to the loss of power to the electrically driven facilities, the gas pressure in the natural gas pipeline network drops, affecting the natural gas supply to the gas turbine units.

[0120] The implementation steps are as follows:

[0121] Step 1: According to Figure 1 Based on the information and scenario information of the test system shown, establish and solve an integer linear programming model for the power grid unit recovery and critical load recovery problems, and determine the critical load recovery time.

[0122] Step 2: Using the PipelineStudio simulation model of the natural gas network, input the recovery time of the electrically driven facilities (i.e., the recovery time of the critical load), run the dynamic simulation of the pipeline network, and obtain the gas pressure recovery (i.e., gas supply recovery) time.

[0123] Step 3: Establish a unit recovery model that considers all units, obtain the recovery sequence of all units, and update the unit recovery strategy based on the gas pressure recovery time of the gas turbine units.

[0124] See system recovery results Figure 3 The unit recovery times are shown in Table 1, and the recovery times of the electrically driven compressors are shown in Table 2. It can be seen that this invention can consider the bidirectional coupling effects of the power grid and the natural gas grid, as well as the dynamic processes of the natural gas grid, and effectively determine the unit recovery strategy, including the recovery times of the units, the power transmission paths, and the electrically driven facilities of the gas transmission network, to support the rapid recovery of the power system.

[0125] Table 1 Unit Resumption Schedule

[0126]

[0127] Table 2 Resumption Schedule of Electric Drive Compressor

[0128]

[0129] In summary, this invention addresses the problem of mutual influence and interdependence between the power grid and the natural gas network during the unit restoration process after a major power outage. It proposes a unit restoration decision-making method that considers the bidirectional coupling effect of the power grid and the natural gas network, and formulates unit restoration strategies.

[0130] The unit recovery decision-making method based on optimization modeling and simulation updates of this invention can effectively consider the bidirectional coupling effect of the power grid and the natural gas grid, enabling rapid unit recovery and supporting the rapid recovery of the power system. This invention's method can obtain the optimal recovery time for the decision-making unit, the transmission path, and the gas transmission network's electrically driven facilities.

[0131] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of one embodiment, and the modules or processes shown in the drawings are not necessarily essential for implementing the present invention.

[0132] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that the present invention can be implemented by means of software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in various embodiments or some parts of the embodiments of the present invention.

[0133] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, for apparatus or system embodiments, since they are basically similar to method embodiments, the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments. The apparatus and system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0134] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A unit recovery decision-making method considering the coupling characteristics of the power grid and the natural gas grid, characterized in that, include: An integer linear programming model for power grid unit restoration and load restoration is established, and a solver is applied to solve the integer linear programming model to obtain the critical load restoration time of the power grid units. A simulation model of a natural gas network is established using natural gas pipeline network simulation software. The critical load recovery time of the power grid units is used as the input data of the simulation model. The simulation model is solved using a solver. The gas supply recovery time of the gas turbine units is obtained by running a dynamic simulation of the pipeline network using the simulation model. Based on the critical load restoration time of grid units and the gas supply restoration time of gas turbine units, a unit restoration optimization model considering all units is established. A solver is applied to solve the unit restoration optimization model to obtain the unit restoration strategies for both the grid and natural gas grids; including: Establish a unit recovery optimization model that considers all grid units and natural gas grid units. This unit recovery optimization model is an integer linear programming problem, expressed as: （20） Constraints: (2)-(8), (10)-(16) The unit recovery optimization model is solved using a solver to obtain the recovery strategies for all units. These recovery strategies include the recovery times of all grid units and natural gas grid units, the recovery times of power transmission paths, the recovery times of gas transmission network electric drive facilities, and the start-up power time of gas turbine units. The gas supply recovery time of gas turbine units is determined by simulation calculation based on the start-up power time. The recovery time of gas turbine units is based on the latest time between the start-up power time and the gas supply recovery time. The recovery strategies for all units are updated based on the gas pressure recovery time of the gas turbine units. The aforementioned process involves establishing an integer linear programming model for power grid unit restoration and load restoration, and applying a solver to solve the integer linear programming model to obtain the critical load restoration time of the power grid units, including: In the unit recovery sequence model that considers critical load recovery: set up This is a collection of non-black start units. For black starter units For the collection of gas turbine units, To restore the set of time periods, The set of recovery periods up to time t. For all units, For the set of busbars, For the collection of transmission lines, For the busbar set connecting the black starter unit, This represents the collection of all busbars except those connected to the black starter unit. This represents the set of lines connecting bus i. Represents the set of critical loads; Let C i K represents the capacity of the generator unit. i Indicates the unit's climb rate. This indicates the maximum output power of the generator set. Indicates the starting power of the generator unit. Indicates the start-up time of the unit. This indicates the maximum start-up time of the generator unit. Indicates the minimum start-up time of the unit; set up Indicates the unit's recovery status. This indicates the gas supply status of the gas turbine unit. Indicates the recovery status of the busbar. This indicates the recovery status of the busbar connected to the generator unit. This indicates the recovery status of the transmission line. Indicates the recovery status of critical loads. Indicates the recovery status of the busbar connected to the critical load; Substations powered by electrically driven compressors are the critical loads; 1) Objective function The objective function for fault recovery is set to maximize the system's power generation capacity and restore critical loads as quickly as possible. Its expression is: （1） 2) The constraints for fault recovery include: (1) Linearized unit output function （2） In the formula, the ceil and res functions are defined as follows: （3） （4） (2) Unit start-up constraints （5） （6） （7） （8） （9） Constraint (5) is the unit start-up time constraint, that is, for all units, the start-up time should be within the range of the earliest start-up time and the latest start-up time; Constraint (6) is the system power constraint, that is, the system should have sufficient power generation to meet the start-up power requirements of non-black start units during each recovery period; Constraint (7) indicates that non-black start units can only be started after the bus connected to the unit is restored; Constraint (8) indicates that the unit will not be shut down again after recovery; Constraint (9) indicates that the gas turbine unit cannot be restored due to lack of gas supply; (3) Transmission path constraints By searching the recovery status of the bus and lines, the optimal start-up path for non-black start units and the critical load recovery path are determined. （10） （11） （12） （13） （14） （15） （16） Constraint (10) indicates that if a line is energized at time t+1, then at least one of the busbars connected to it will be energized at time t; Constraint (11) indicates that if a busbar is energized at time t, then at least one of the busbars connected to it will be energized at time t; Constraints (12) and (13) indicate that the transmission line and busbar will not be de-energized again after restoration; Constraints (14)-(16) indicate the initial state of the line and busbar. (4) Critical load recovery constraints By determining the recovery status of critical loads, the recovery of critical loads can be coordinated with the recovery of non-black start units. （17） （18） （19） Constraint (17) is a system power constraint, which means that there is sufficient power generation capacity to carry the critical load; constraint (18) means that the bus connected to the critical load should be energized before the load is restored; constraint (19) means that once the load is restored, it will not be de-energized. The unit recovery sequence model considering critical load recovery is an integer linear programming problem. The critical load recovery time of the power grid units is obtained by solving the unit recovery sequence model considering critical load recovery using a commercial optimizer.

Images