Urban integrated energy system toughness improving method under earthquake disasters

Abstract

The invention discloses a method for improving the toughness of an urban comprehensive energy system under earthquake disasters, and belongs to the technical field of urban comprehensive energy safety management. The method comprises the steps that a target function is established; considering a short-term load supporting effect of natural gas pipe storage, and constraining the urban comprehensive energy system model; clustering the faults of the urban integrated energy system; a first-aid repair batch and a first-aid repair sequence are assigned manually; and after the first-aid repair of each fault node is completed, the urban integrated energy system model is reconstructed again until the first-aid repair of all the fault nodes is completed. The short-term load supporting effect of the natural gas pipe storage is utilized, and energy supply of the comprehensive energy system in a short term is achieved; important load power supply is effectively recovered through the action of an interconnection switch in a power distribution network system; the load loss amount can be reduced to the maximum extent through a combined maintenance strategy among the subsystems, and meanwhile, the actions of the interconnection switches in the maintenance process can coordinate maintenance and improve the recovery efficiency of the whole system.

Description

Technical Field

[0001] The invention belongs to the field of urban integrated energy safety management technology, and in particular relates to a method for improving the resilience of urban integrated energy systems under earthquake disasters. Background Art

[0002] Earthquakes can pose a serious threat to the safe and stable operation of urban integrated energy systems. Improving the resilience of integrated energy systems is key to mitigating their impact. Improving the resilience of integrated energy systems typically involves network reconfiguration strategies. This involves rationally changing the state of interconnecting switches to reconfigure the system topology and reduce load shedding.

[0003] Research on post-disaster fault repair strategies for integrated energy systems has made significant progress. Current studies often assess the resilience of integrated energy systems using robustness metrics, identifying weak links in the system during earthquakes and optimizing system configurations accordingly. Particle swarm optimization algorithms are employed to determine optimal grid repair strategies and dispatch emergency generators during earthquakes, enabling the rapid repair and reconnection of distribution networks in key areas while ensuring continuous power supply to a wider range of loads. However, these proposed fault repair strategies fail to fully consider fault propagation between different subsystems within the integrated energy system, nor do they consider the load recovery issues associated with earthquake damage to the natural gas system.

[0004] With the increasing coupling of power systems and natural gas systems, the two are showing a trend of high interdependence. The comprehensive energy post-disaster optimization scheduling scheme that does not consider the natural gas system can no longer meet the post-disaster scheduling needs of the urban comprehensive energy system.

[0005] In existing coordinated scheduling methods for electricity and natural gas transmission that consider the energy interactions of integrated electricity and gas energy systems, natural gas pipeline storage, as a dynamic storage feature of natural gas systems, is widely used to improve system flexibility and reduce operating costs. However, these studies have not yet addressed the impact of pipeline storage on the resilience of integrated energy systems, nor have they explored how to optimize joint maintenance and scheduling of natural gas pipelines with the power system in earthquake disaster scenarios.

[0006] Therefore, a new technical solution is urgently needed in the existing technology to solve this problem. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to provide a method for improving the resilience of urban integrated energy systems under earthquake disasters to solve the technical problem that current research has not addressed the impact of pipeline storage on the resilience of integrated energy systems, nor has it addressed how to jointly optimize the maintenance and scheduling of natural gas pipelines with power systems in earthquake disaster scenarios.

[0008] A method for improving the resilience of an urban integrated energy system under earthquake disasters comprises the following steps, which are performed in sequence: Step 1: Establish the objective function; Step 2: Constrain the urban integrated energy system model; Based on the changes in the distribution network topology and the role of natural gas pipeline storage margin in supporting the natural gas load and gas turbine load of the urban integrated energy system, the urban integrated energy system model is constrained. After an earthquake disaster occurs, the urban integrated energy system model can be reconstructed based on the collected information on the location of each fault node, fault line, and maintenance team, the type of fault repair, the remaining maintenance resources of each warehouse, the working status of each maintenance team, and the restoration of power supply from distributed power generation (DG) to gas turbines through natural gas pipelines at some distribution network fault nodes. Step 3: Cluster the faults of the urban integrated energy system; Step 4: Based on the clustering results, manually formulate the repair order of the first batch of fault nodes and send it to the maintenance team for emergency repairs in sequence; Step 5: After each fault node is repaired, the city's integrated energy system model is reconstructed again, again considering the role of distribution network topology reconstruction and natural gas pipeline storage in improving system load recovery, and again manually determining the next batch of fault nodes where the fault will propagate; Step 6: Repeat step 5 to obtain more batches of fault nodes and objective function values, manually formulate the corresponding repair sequence, and send it to the maintenance team. After the emergency repair of the previous batch of faults is completed, the emergency repair of the next batch of fault nodes will be carried out in sequence until all fault nodes are repaired.

[0009] The objective function in step 1 is to minimize the sum of the load reduction of the urban integrated energy system and the fault repair time. The objective function is: (1); Where, is the set of distribution network nodes; is a collection of natural gas network nodes; Indicates a time period; is the weight coefficient of distribution network load; is the weight coefficient of natural gas load; is the load reduction amount at each node in the power system; is the load reduction at each node of the natural gas system; is the weight coefficient of the fault, is the fault type; for Emergency repair base according to the fault type; for Fault type exist t The time when the fault repair is completed.

[0010] The constraints of the urban integrated energy system model include distribution network flow constraints, node voltage and branch current constraints after distribution network reconstruction, line transmission power constraints, connectivity and radiation constraints of the distribution network after reconstruction, natural gas network model constraints, natural gas pipeline storage and use constraints, integrated energy system coupling relationship constraints, and maintenance team dispatch constraints.

[0011] The distribution network flow constraints are as follows: (2); (3); (4); (5); (6); (7); Where, 、 、 All of them are distribution network nodes; For nodes j The set of upstream nodes of the connected branches; For nodes The set of downstream nodes of the connected branches; for t Timeline Active power on for t Timeline Active power on for t Time Node Injected active power; for t Timeline Reactive power on for t Timeline Reactive power on For the line The square of the upper current; For the line The square of the upper current; For the line Previous node The square of the voltage at For the line Previous node The square of the voltage at For the line The square of the active power on the For the line The square of the reactive power; for t Time Node Injected active power; for t Time Node Injected reactive power; for t Time to node Injected reactive power; For the line resistance; For the line Active power flowing upstream; For the line reactance; For the line Reactive power flowing upstream; For the line The square of the resistance; For the line The square of the reactance; for t Time Node The active power generated by the generator; for t Time Node The reactive power generated by the generator; for t Time Node The active power of the gas turbine; for t Time Node Active load; for t Time Node Reactive load; is a collection of conducting branches; Formula (6) is a nonlinear equation. Performing second-order cone relaxation on this equation yields: (8); Where, for t Time Node The square of the voltage; for t Timeline The square of the current; Formula (7) is valid only when the line is conducting. The Big M method is used to transform Formula (7): (9); (10); Where, for t Time Node The square of the voltage; for t Timeline The open state value is a 0-1 variable, 0 means open, 1 means closed; is a set constant used to relax the constraints (9) and (10); The node voltage branch current constraints are as follows: The node voltage does not exceed the upper and lower limits, and the branch current does not exceed the upper limit. The constraints are expressed as: (11); (12); Where, for t Time Node The voltage at for t Time Node The lower voltage limit at for t Time Node The upper limit of the voltage at for t Timeline The maximum allowable current value; for t Timeline Current; The line transmission power constraints are as follows: The transmission power of each line must be within the range of the line's allowed transmission capacity. The constraint is expressed as: (13); (14); Where, for t Timeline The minimum active power; for t Timeline The maximum active power; It is a collection of distribution network lines; for t Timeline Minimum reactive power; for t Timeline Maximum reactive power; The connectivity and radiation constraints are as follows: (15); (16); (17); (18); Where, is the set of chord branches; is the number of distribution network branches; is the number of segmented regions; For nodes Parent-child matrix, node For nodes The value is 1 when it is the parent node of , otherwise it is 0; For nodes Parent-child matrix, node For nodes The value is 1 when it is the parent node of , otherwise it is 0; Indicates that node 1 is the parent node of node 2; The natural gas grid model constraints are as follows: The natural gas network model uses the Weymouth model to perform steady-state calculations on natural gas flow and node pressure, where the pipeline flow constraint is: (19); (20); Where, For gas t Time flows through the node and Pipeline flow rate; For pipeline Length-dependent constants; For nodes exist t The pressure of the moment; For nodes exist t The pressure of the moment; Indicates natural gas pipeline Traffic direction; Nodes in a natural gas network also adhere to the flow conservation principle, which states that the gas flow into a node is equal to the gas flow out of the node. The flow conservation principle is expressed as follows: (twenty one); Where, For nodes The gas source is tGas production at any time; For nodes exist t The load at the time; For natural gas generator sets t The node gas flow consumed at any moment; For nodes The connected electric compressor t Gas consumption at each moment; For nodes A collection of connected pipes; Gas source output constraints: (twenty two); Where, For nodes The gas source is t The minimum output at the moment; For nodes The gas source is t Maximum output at the moment; For nodes The gas source is t Output value at the moment; Nodal gas flow constraints consumed by gas turbines: (twenty three); Where, For gas turbines t The minimum gas consumption at the moment; For gas turbines t The maximum gas consumption at the moment; For gas turbines t Gas consumption value at the moment; Pipeline flow constraints in natural gas networks: (twenty four); Where, For pipelines exist t The minimum flow rate at any moment; For pipelines exist t Maximum flow rate at any moment; For pipelines exist t The flow value at the moment; Natural gas node pressure constraints: (25); Where: For nodes exist t Minimum pressure at the moment; For nodes exist t Maximum pressure at the moment; For nodes exist t Pressure value at the moment; The natural gas pipeline has usage constraints: After an earthquake, intact natural gas pipelines use their natural gas reserves to supply natural gas loads and gas turbines. The natural gas pipeline reserve usage constraints are expressed as follows: (26); (27); (28); Where, It is a binary variable, indicating whether the natural gas pipeline is damaged, with the value 0 for damaged and 1 for undamaged; for t Time Pipeline of custody; For pipelines Length 、 For pipelines Diameter 、 For pipelines The average pressure, Inflow pipe Natural gas flow, Outflow pipe Natural gas flow, 、 、 、 are the gas constant and temperature in the pipeline respectively 、 Compression factor 、 Gas density; Formula (26) is the pipeline exist t The expression at the pipe storage space level at all times represents the average pressure at both ends of the pipe storage and the pipeline and the relationship between pipeline parameters; Equation (27) is the expression of the average pressure in the pipeline; Equation (28) describes the pipeline exist t The temporal relationship of pipe storage at each moment reflects the dynamic changes of pipe storage between consecutive moments. The difference between the inflow and outflow of natural gas determines the charging and discharging process of pipe storage. If the inflow is greater than the outflow, the pipe storage increases, and vice versa. The coupling relationship constraints of the integrated energy system are as follows: The integrated energy system is divided into multiple subsystems according to its topological structure. In each subsystem, the distribution network and the natural gas network are coupled to achieve comprehensive resource utilization. A local fault in a subsystem may propagate to other subsystems through the coupling device, thus causing large-scale load interruption. Equations (29) to (33) express the constraints on the propagation of faults through the coupling device in the integrated energy system. A gas turbine is a power generation device that uses natural gas as fuel. In a natural gas system, it is equivalent to a load. The conversion relationship between a gas turbine's power generation and natural gas consumption is expressed as: (29); Where: express t Time Node Gas turbine power generation capacity at represents the gas turbine conversion efficiency coefficient; The natural gas pipeline uses an electric-consuming compressor, which is driven by the power distribution network and is equivalent to a load in the power system. The natural gas pipeline pressure constraint is: (30); Where: 、 Represent the nodes in the natural gas pipeline and nodes exist t The pressure value at the moment, Indicates the compression coefficient of the compressor; Energy conversion relationship of the compressor: (31); Where: express t The power consumption of the compressor at all times; Indicates the consumption coefficient of the compressor; A pipeline failure in the natural gas system may cause a gas supply interruption to the gas turbine, which in turn may cause a decrease in the power load in the urban distribution network. An earthquake disaster may cause a line interruption in the urban distribution network, which may cause a power supply interruption and cause the shutdown of power-consuming compressors, ultimately leading to a reduction in the gas load in the natural gas system. Therefore, Equation (32) indicates that when a fault occurs in the upstream node of the gas turbine, causing a gas supply interruption, the gas turbine will shut down. Equation (33) indicates that when the power supply node of the compressor is in a faulty state, the compressor will not work. The specific expression is as follows: (32); (33); Where, expresst Time Natural Gas Node Whether it is working, the value is 1 when working, and 0 when not working; Represents the distribution network node at time t Whether it is working, the value is 1 when working and 0 when not working; for t The minimum value of the compressor load at the moment; for t The maximum compressor load at that moment.

[0012] The maintenance team dispatch constraints are as follows: Because each maintenance team is responsible for a different area, before formulating a fault repair plan, it is necessary to cluster the faults. This means matching the faults with the repair team warehouses to form several small clusters. This simplifies the subsequent repair plan formulation problem into a repair path planning problem for the cluster consisting of a single repair team, thereby achieving dimensionality reduction of the fault categories. Divide the fault into The number of classes, the number of warehouses determines the number of clusters. The clustering results are indexed. σ Indicates that each warehouse corresponds to a type of failure, so the failure type Also known as warehouse ; Assume that there is a maintenance team in each warehouse, and the maintenance team uses the resources of the warehouse to perform fault repairs, where ,Through clustering, the maintenance team dispatch problem is transformed into a multiple vehicle routing problem; The input data for the clustering problem includes the travel time of the repair team to the fault location , Fault repair time , the speed of the repair team , warehouse available resources , resources required to repair the fault 、 Weighted distance of the path ,Fault For warehouses σ Total resource demand ; Using binary decision variables To determine any fault The clustering of the fault Clustering into warehouses : (34); Clustering is performed based on the shortest equivalent distance between each repair team and the fault; The equivalent distance is represented by the shortest driving time required for the repair team to reach the fault location and the sum of the repair time required for each fault type, where the shortest driving time is , where 1, 2, and 3 represent warehouse numbers; if a warehouse does not have enough resources, the fault will be clustered to the next nearest warehouse; Therefore, the fault is assigned to the warehouse with the smallest equivalent distance through formula (35), and the travel time of the repair team is solved through formula (36): (35); (36); Formula (37) ensures that the failure is assigned to a single warehouse: (37); Formula (38) ensures that the warehouse has sufficient resources to repair faults from the perspective of the total amount of warehouse resources: (38); From the perspective of failure, we can ensure that each failure is assigned to a warehouse with sufficient resources to repair it through formula (39): (39); After the fault clustering is completed, the maintenance team is dispatched to repair the fault and the clusters are grouped into the same group. Type of failure, warehouse and maintenance team as a repair base, with If , then the maintenance team scheduling formula is as follows: (40); (41); (42); (43); Where: Indicates maintenance Type of breakdown repair team; express Emergency repair base for various types of failures; Is a binary variable, indicating maintenance σ Type of breakdown repair team Whether to repair the fault ， It takes 1, not 0; Is a binary variable, indicating maintenance Type of breakdown repair team Whether the fault Geographic location to the fault The geographical location is 1, not 0; is a binary variable representing maintenance Type of breakdown repair team Whether the fault Geographic location to the fault Geographical location ， It takes 1, not 0; is a binary variable representing maintenance Type of breakdown repair team Whether from the warehouse to failure Geographical location ， It takes 1, not 0; Among them, formula (40) means that each fault can only be repaired by one maintenance team; formula (41) means that the maintenance team repairs the fault After that, go to the fault The fault point where the fault is located; Formula (42) represents 、 、 and Both are binary variables; Equation (43) indicates that the maintenance team departs from the warehouse and returns to the warehouse after completing the maintenance task; Set the repair team route from the fault Geographic location to the fault The geographical location of the The constraints on the time of day, maintenance time, and travel time of the geographical location are as follows: (44); (45); In formula (44), Representing the repair team Arrival Failure The time of day of your geographical location; Representing the repair team Arrival Failure The time of day of your geographical location; For the maintenance team Fixing a fault Time taken; For the maintenance team From the fault to failure The travel time of the geographical location, formula (45) indicates that when the maintenance team does not pass the fault Geographic location, then its arrival failure The time of the geographical location is 0; The following constraints apply to fault repairs: (46); (47); (48); (49); Where: is a binary variable of 0 or 1, representing Type of failure The required maintenance time, i.e. Equal to 1 indicates a fault At the moment t Been repaired, Equal to 0 means the fault occurs at time t Not repaired or repair has been completed; Constraints (46) to (49) express The calculation method to obtain Type of failure Required repair time ; Indicates a fault exist t The time when the fault repair is completed.

[0013] The clustering in step three is specifically as follows: after an earthquake disaster occurs, the faults of the urban integrated energy system are clustered according to the fault type and location information of the collected fault points and fault lines through the maintenance team dispatch constraints, and are dispatched to different maintenance teams according to the clustering results, thereby realizing dimensionality reduction processing of multi-type and multi-location fault maintenance.

[0014] The repair sequence of the first batch of fault nodes manually formulated in step 4 is specifically as follows: Manual analysis identifies the faulty nodes or faulty lines in the integrated energy system that cause fault propagation and marks them as the first batch of faults. At the same time, the faulty nodes or faulty lines that cause faults in the coupling device between the distribution network and the natural gas network within the urban integrated energy system are also marked as the first batch of faults. According to the objective function in step 1, the objective function value of each fault node or fault route in the first batch of faults is obtained, and step 2 is performed to achieve the first reconstruction of the urban integrated energy system model; By reconfiguring the topology of the distribution network and directly supplying power to the system load through natural gas pipelines, and combining the locations of faulty nodes with fault propagation and the corresponding objective function values, the repair sequence of the first batch of faulty nodes is manually formulated and sent to the maintenance team for emergency repairs in sequence.

[0015] The next batch of fault nodes with fault propagation are manually determined again in step five as follows: fault nodes that do not need to be prioritized by the maintenance team and the first batch of fault nodes are excluded, and the other fault nodes with fault propagation are identified as the second batch of fault nodes; the objective function value of the second batch of fault nodes is obtained through the objective function in step one, and the maintenance order of the second batch of fault nodes is manually formulated and sent to the maintenance team. After the emergency repair of the first batch of faults is completed, the emergency repair of the second batch of fault nodes is carried out in sequence.

[0016] Through the above design scheme, the present invention can bring the following beneficial effects: 1. After an earthquake disaster, the city's integrated energy system can utilize the short-term load support function of natural gas pipelines to achieve short-term integrated energy system energy supply; 2. Effectively restore power supply to important loads through the action of the tie switch in the distribution network system; 3. The joint maintenance strategy among subsystems can minimize the load loss. At the same time, the action of the interconnecting switch during the maintenance process can coordinate the maintenance and improve the recovery efficiency of the entire system. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The present invention will be further described below with reference to the accompanying drawings and specific embodiments: Figure 1 It is a disaster map of the integrated energy system in a method for improving the resilience of an urban integrated energy system under earthquake disasters according to the present invention; Figure 2 It is a fault repair and topology reconstruction diagram in a method for improving the resilience of an urban integrated energy system under earthquake disasters according to the present invention; Figure 3 It is a load recovery diagram of an urban integrated energy system in a method for improving the resilience of an urban integrated energy system under earthquake disasters according to the present invention; Figure 4 It is a flow chart of a method for improving the resilience of an urban integrated energy system under earthquake disasters in the present invention. DETAILED DESCRIPTION

[0018] In order to make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention are described in further detail below. Example

[0019] This paper develops a method for improving the resilience of urban integrated energy systems in the event of earthquakes. This method aims to minimize the load reduction and repair time of damaged components in the urban integrated energy system. This method achieves rapid load recovery in the urban integrated energy system after an earthquake, providing a solution for improving the resilience of urban integrated energy systems to earthquake disasters. The model construction includes the following steps: 101: Joint maintenance strategy for urban integrated energy system considering natural gas pipeline storage and distribution network topology reconstruction: The proposed method for improving the resilience of urban integrated energy systems aims to meet the operational constraints of both the electric and natural gas systems, taking into account the pipe-storage characteristics of the natural gas system and the role of distribution network topology reconfiguration in load recovery. Furthermore, the method considers the coupling between the electric and gas subsystems in the integrated energy system, prioritizes repairing fault nodes that cause propagation of faults in the electric-gas integrated energy system, and accounts for the time cost of fault repair, thereby achieving rapid load recovery in the urban integrated energy system after an earthquake disaster. The optimization goal is to minimize the load reduction in the urban integrated energy system and the repair time of damaged components.

[0020] The following objective function can be established: (1); Where, is the set of distribution network nodes; is a collection of natural gas network nodes; Indicates a time period; is the weight coefficient of distribution network load; is the weight coefficient of natural gas load; is the load reduction amount at each node in the power system; is the load reduction at each node of the natural gas system; is the weight coefficient of the fault, is the fault type; for Emergency repair base according to the fault type; for Fault type exist t The time when the fault repair is completed.

[0021] 201: The construction of the urban integrated energy system model includes the following steps: 1) Distribution network flow constraints: (2); (3); (4); (5); (6); (7); Where, 、 、 All of them are distribution network nodes; For nodes j The set of upstream nodes of the connected branches; For nodes The set of downstream nodes of the connected branches; for t Timeline Active power on for t Timeline Active power on for t Time Node Injected active power; for t Timeline Reactive power on for t Timeline Reactive power on For the line The square of the upper current; For the line The square of the upper current; For the line Previous node The square of the voltage at For the line Previous node The square of the voltage at For the line The square of the active power on the For the line The square of the reactive power; for t Time Node Injected active power; for t Time Node Injected reactive power; for t Time to node Injected reactive power; For the line resistance; For the line Active power flowing upstream; For the line reactance; For the line Reactive power flowing upstream; For the line The square of the resistance; For the line The square of the reactance; for tTime Node The active power generated by the generator; for t Time Node The reactive power generated by the generator; for t Time Node The active power of the gas turbine; for t Time Node Active load; for t Time Node Reactive load; is a collection of conducting branches; The power flow constraint equation (6) is a nonlinear equation. By performing a second-order cone relaxation on the equation, we can obtain: (8); Where, for t Time Node The square of the voltage; for t Timeline The square of the current; Constraint (7) is valid only when the line is conductive. The constraint can be transformed using the Big M method: (9); (10); Where, for t Time Node The square of the voltage; for t Timeline The open state value is a 0-1 variable, 0 means open, 1 means closed; is a set constant, which can be a large constant value and is used to relax the constraints (9) and (10); 2) Node voltage branch current constraints: After the distribution network is reconfigured, the node voltage and branch current must be within the allowable range. That is, the node voltage does not exceed the upper and lower limits, and the branch current does not exceed the upper limit. The constraints can be expressed as: (11); (12); Where, for t Time Node The voltage at for tTime Node The lower voltage limit at for t Time Node The upper limit of the voltage at for t Timeline The maximum allowable current value; for t Timeline of current.

[0022] 3) Line transmission power constraints: The distribution network lines need to meet certain transmission capacity constraints, that is, the transmission power of each line must be within the range of the line's allowed transmission capacity. The constraints can be expressed as: (13); (14); Where, for t Timeline The minimum active power; for t Timeline The maximum active power; It is a collection of distribution network lines; for t Timeline Minimum reactive power; for t Timeline The maximum reactive power.

[0023] 4) Connectivity and radiation constraints: The distribution network reconstruction must ensure that the distribution network after reconstruction meets the connectivity and radiation constraints. The connectivity and radiation constraints are expressed as: (15); (16); (17); (18); Where, is the set of chord branches; is the number of distribution network branches; is the number of segmented regions; For nodes Parent-child matrix, node For nodes The value is 1 when it is the parent node of , otherwise it is 0; For nodes Parent-child matrix, node For nodes The value is 1 when it is the parent node of , otherwise it is 0; Indicates that node 1 is the parent node of node 2.

[0024] 5) Natural gas grid model constraints: The natural gas network model adopts the Weymouth model to perform steady-state calculations on natural gas flow and node pressure.

[0025] The pipeline flow constraint is: (19); (20); Where, For gas t Time flows through the node and Pipeline flow rate; For pipeline Length-dependent constants; For nodes exist t The pressure of the moment; For nodes exist t The pressure of the moment; Indicates natural gas pipeline Traffic direction; Nodes in a natural gas network adhere to the flow conservation principle, which states that the gas flow into a node is equal to the gas flow out of the node. The flow conservation principle is expressed as follows: (twenty one); Where, For nodes The gas source is t Gas production at any time; For nodes exist t The load at the time; For natural gas generator sets t The node gas flow consumed at any moment; For nodes The connected electric compressor t Gas consumption at each moment; For nodes A collection of connected pipes; Gas source output constraints: (twenty two); Where, For nodes The gas source is tThe minimum output at the moment; For nodes The gas source is t Maximum output at the moment; For nodes The gas source is t Output value at the moment; Nodal gas flow constraints consumed by gas turbines: (twenty three); Where, For gas turbines t The minimum gas consumption at the moment; For gas turbines t The maximum gas consumption at the moment; For gas turbines t Gas consumption value at the moment; Pipeline flow constraints in natural gas networks: (twenty four); Where, For pipelines exist t The minimum flow rate at any moment; For pipelines exist t Maximum flow rate at any moment; For pipelines exist t The flow value at the moment; Natural gas node pressure constraints: (25); Where: For nodes exist t Minimum pressure at the moment; For nodes exist t Maximum pressure at the moment; For nodes exist t The pressure value at the moment.

[0026] 6) Natural gas pipeline storage and usage constraints: After an earthquake, only undamaged natural gas pipelines can be used to supply natural gas loads and gas turbines. The natural gas pipeline storage usage constraints are expressed as follows: (26); (27); (28); Where, It is a binary variable, indicating whether the natural gas pipeline is damaged, with the value 0 for damaged and 1 for undamaged; for t Time Pipeline of custody; For pipelines Length 、 For pipelines Diameter 、 For pipelines The average pressure, Inflow pipe Natural gas flow, Outflow pipe Natural gas flow, 、 、 、 are the gas constant and temperature in the pipeline respectively 、 Compression factor 、 Gas density.

[0027] Formula (26) is the pipeline exist t The expression at the pipe storage space level at all times represents the average pressure at both ends of the pipe storage and the pipeline and the relationship between pipeline parameters; Equation (27) is the expression of the average pressure in the pipeline; Equation (28) describes the pipeline exist t The temporal relationship of pipe storage at each moment reflects the dynamic changes of pipe storage between consecutive moments; the difference between the inlet and outlet flow rates of natural gas determines the charging and discharging process of pipe storage. If the inlet flow rate is greater than the outlet flow rate, the pipe storage increases, and vice versa, the pipe storage decreases.

[0028] 7) Constraints on coupling relationships of integrated energy systems: The subsystems of an integrated energy system achieve comprehensive resource utilization and efficient collaboration through coupling devices. While this tight coupling improves the system's energy efficiency, it also makes the system susceptible to chain reactions when faced with extreme natural disasters. A local failure in one subsystem can spread through coupling devices to other subsystems, leading to large-scale load interruptions.

[0029] A gas turbine is a type of power generation equipment that uses natural gas as fuel. It is equivalent to the load in a natural gas system. The conversion relationship between the power generation of a gas turbine and the natural gas consumption is expressed as: (29); Where: express tTime Node Gas turbine power generation capacity at Represents the gas turbine conversion efficiency coefficient.

[0030] Natural gas pipelines use power-consuming compressors, which are driven by the power distribution network and are equivalent to loads in the power system. The natural gas pipeline pressure constraints are: (30); Where: 、 Represent the nodes in the natural gas pipeline and nodes exist t The pressure value at the moment, Indicates the compression coefficient of the compressor; Energy conversion relationship of the compressor: (31); Where: express t The power consumption of the compressor at all times; Indicates the consumption coefficient of the compressor.

[0031] A pipeline failure in the natural gas system could disrupt the gas supply to the gas turbine, further causing a reduction in the power load in the city's distribution network. An earthquake could disrupt lines in the city's distribution network, causing a power outage and shutting down power-consuming compressors, ultimately leading to a reduction in the gas load in the natural gas system. The constraints are as follows: (32); (33); Where, express t Time Natural Gas Node Whether it is working, the value is 1 when working, and 0 when not working; Represents the distribution network node at time t Whether it is working, the value is 1 when working and 0 when not working; for t The minimum value of the compressor load at the moment; for t The maximum compressor load at that moment.

[0032] Equations (29) to (33) represent the constraints on the propagation of faults through coupling devices in an integrated energy system. Equation (32) indicates that when a fault occurs at the upstream node of the gas turbine, causing a gas supply interruption, the gas turbine shuts down; constraint (33) indicates that when the power supply node of the compressor is in a faulty state, the compressor does not operate.

[0033] 8) Maintenance personnel dispatch constraints: Due to the large scale and complex topological structure of the integrated energy system, each maintenance team is responsible for different areas. Therefore, before formulating a fault repair plan, it is necessary to cluster the fault points. That is, match the fault points with the repair team warehouses to form several small clusters. The subsequent repair plan formulation problem is simplified to the repair path planning problem of the cluster composed of a single repair team, thereby achieving dimensionality reduction of fault categories.

[0034] Divide the fault into The number of classes, the number of warehouses determines the number of clusters. The clustering results are indexed. σ Indicates that each warehouse corresponds to a type of failure, so the failure type Also known as warehouse ; Assume that there is a maintenance team in each warehouse, and the maintenance team uses the resources of the warehouse to perform fault repairs, where ,Through clustering, the maintenance team dispatch problem is transformed into a multiple vehicle routing problem; The input data for the clustering problem includes the travel time of the repair team to the fault location , Fault repair time , the speed of the repair team , warehouse available resources , resources required to repair the fault 、 Weighted distance of the path ,Fault For warehouses σ Total resource demand ; Using binary decision variables To determine any fault The clustering of the fault Clustering into warehouses : (34); Clustering is performed based on the shortest equivalent distance between each repair team and the fault; The equivalent distance is represented by the shortest driving time required for the repair team to reach the fault location and the sum of the repair time required for each fault type, where the shortest driving time is , where 1, 2, and 3 represent warehouse numbers; if a warehouse does not have enough resources, the fault will be clustered to the next nearest warehouse; Therefore, the fault is assigned to the warehouse with the smallest equivalent distance through formula (35), and the travel time of the repair team is solved through formula (36): (35); (36); Formula (37) ensures that damaged components are assigned to a single warehouse: (37); Formula (38) ensures that the warehouse has sufficient resources to repair faults from the perspective of the total amount of warehouse resources: (38); From the perspective of failure, we can ensure that each failure is assigned to a warehouse with sufficient resources to repair it through formula (39): (39); After the damaged components are clustered, a maintenance team needs to be dispatched to repair the damaged components. The grouped warehouses and fault points are used as the entire repair base. If , the maintenance personnel scheduling formula is as follows: (40); (41); (42); (43); Where: Indicates maintenance Type of breakdown repair team; express Emergency repair base for various types of failures; Is a binary variable, indicating maintenance Type of breakdown repair team Whether to repair the fault ， It takes 1, not 0; Is a binary variable, indicating maintenance Type of breakdown repair team Whether the fault Geographic location to the fault The geographical location is 1, not 0; is a binary variable representing maintenance Type of breakdown repair team Whether the fault Geographic location to the fault Geographical location ， It takes 1, not 0; is a binary variable representing maintenance Type of breakdown repair team Whether from the warehouse to failure Geographical location ，It takes 1, not 0; Among them, formula (40) means that each fault can only be repaired by one maintenance team; formula (41) means that the maintenance team repairs the fault After that, go to the fault The fault point where the fault is located; Formula (42) represents 、 、 and Both are binary variables; Equation (43) indicates that the maintenance team departs from the warehouse and returns to the warehouse after completing the maintenance task; Set the repair team route from the fault Geographic location to the fault The geographical location of the The constraints on the time of day, maintenance time, and travel time of the geographical location are as follows: (44); (45); In formula (44), Representing the repair team Arrival Failure The time of day of your geographical location; Representing the repair team Arrival Failure The time of day of your geographical location; For the maintenance team Fixing a fault Time taken; For the maintenance team From the fault to failure The travel time of the geographical location, formula (45) indicates that when the maintenance team does not pass the fault Geographic location, then its arrival failure The time of the geographical location is 0; The repair of damaged components is subject to the following constraints: (46); (47); (48); (49); Where: is a binary variable of 0 or 1, representing Type of failure The required maintenance time, i.e. Equal to 1 indicates a fault At the moment tBeen repaired, Equal to 0 means the fault occurs at time t Not repaired or repair has been completed; Constraints (46) to (49) express The calculation method to obtain Type of failure Required repair time ; Indicates a fault exist t The time when the fault repair is completed.

[0035] 301: Urban Integrated Energy System Data The present invention adopts the improved IEEE 33-node distribution network and 7-node natural gas network to verify the correctness and effectiveness of the proposed method. Among them, the power system includes two tie lines c1 and c2, c1 connects nodes 12 and 22, and c2 connects nodes 18 and 33; it also includes 4 distributed power sources, among which DG1, DG2, DG3 and DG4 are installed at distribution network nodes 1, 24, 33, and 22 respectively. The capacity of distributed power sources DG1 and DG2 is 1.5MW, and the capacity of DG3 and DG4 is 1MW. The total load peak of the power system is 3.53MW+2.4MVAR. The natural gas system includes two gas wells located at natural gas nodes 6 and 7 respectively, with a total gas supply peak of 1400Sm 3 / h; includes one power-consuming compressor connected to natural gas system nodes 2-4, powered by power system node 25; includes two gas turbines, GT1 and GT2, installed at natural gas network nodes 2 and 3 respectively, with a capacity of 0.6MW each, and a total natural gas system load of 850Sm 3 / h.

[0036] The model is solved in the Matlab simulation environment using the YALMIP toolbox GUROBI11.0 version solver.

[0037] After an earthquake disaster occurs, both the power system and the natural gas system will be affected to varying degrees. Figure 1 Shown is the topology and disaster situation of the 33-node distribution network and the 7-node natural gas network.

[0038] The present invention makes the following assumptions: T=1h is used in the calculation example to represent the step size of multiple time scales, and the travel time of the maintenance team between damaged components is proportional to their respective distances. The operating time of the interconnecting switch is zero. Faults F1-F6 in the distribution network are line disconnection faults, F7 is a gas turbine fault, and F8 and F9 are natural gas pipeline faults. It is assumed that all distribution network line faults occur at the midpoint of the line. There are 2 distribution network maintenance stations and 1 natural gas network maintenance station, each with a maintenance team, and the power system maintenance personnel and the natural gas system maintenance personnel can only repair components within their respective systems. It is assumed that the repair time for a distribution network line disconnection fault is 1h; the emergency repair time for a natural gas pipeline fault and the gas turbine repair time are 1h and 2h, respectively.

[0039] 302: Fault Analysis: Due to the F3 fault, the natural gas system compressor lost power and could not operate, resulting in a disruption in gas supply to its downstream natural gas nodes. Simultaneously, the F2, F4, F5, and F6 faults disrupted the load at distribution network nodes 5-17 and 26-29. The F1 fault disrupted the load at distribution network node 1. Failures at F8 and F9 resulted in a loss of natural gas supply to natural gas nodes 3 and 5. The F7 fault disabled gas turbine GT2. Following the earthquake, the distribution network load dropped to 27% of normal operating levels, and the natural gas load dropped to 38%.

[0040] The above fault scenario is used as an example to verify the accuracy of the proposed method. To illustrate the effectiveness of the present invention in improving the resilience of urban electricity-gas integrated energy systems during earthquake disasters, the following two solutions are designed and analyzed: Option 1: Rely on multi-energy coupling of urban integrated energy systems to enhance system resilience.

[0041] Solution 2: The method proposed in this invention improves system resilience.

[0042] 1) Relying on multi-energy coupling of urban integrated energy systems to enhance system resilience After an earthquake, a city's integrated electrical energy system often suffers varying degrees of loss in power load and natural gas supply, leading to energy supply interruptions or shortages, which in turn affect the city's normal operations and post-disaster recovery. In such emergency situations, gas turbines, as highly efficient energy conversion devices, can play a vital role. Gas turbines burn natural gas to produce high-temperature, high-pressure gas, which drives the turbine to rotate and drive the generator to generate electricity, thereby converting natural gas energy into electricity. This process not only achieves energy coupling between the natural gas system and the power system, but also provides rapid and flexible power replenishment when the power system is damaged or when load demand surges, alleviating power supply pressure. The results of its improved resilience are shown in Table 1: .

[0043] By using gas turbines to achieve energy coupling between the power system and the natural gas system, it is possible to use undamaged natural gas pipelines to restore the load of the urban integrated energy system, improve the disaster resilience of the urban integrated energy system, and reduce losses caused by insufficient energy supply.

[0044] By comparing the improvement of system resilience by relying on multi-energy coupling of urban integrated energy systems with the improvement of system resilience by the method proposed in the present invention, under the same fault scenario, the effectiveness of the method for improving the resilience of urban integrated energy systems under earthquake disasters proposed in the present invention in improving system resilience is demonstrated.

[0045] 2) Improving system resilience during earthquake disasters using the method proposed in this invention Based on the consideration of natural gas pipeline storage and distribution network topology reconstruction, a joint maintenance strategy for the urban electricity-gas integrated energy system was specified. The results of its resilience improvement are shown in Table 2: .

[0046] Immediately after the earthquake, natural gas pipeline reserves were utilized to power natural gas system nodes 1, 2, 3, and 5, and distribution network node 27 via gas turbines. Furthermore, considering fault propagation between subsystems of the urban integrated energy system, maintenance team 1 prioritized repairing distribution network fault F3 to ensure rapid load restoration at the compressor power supply node, thereby restoring gas supply to the downstream loads. Maintenance team 2 prioritized repairing distribution network fault F4 to ensure rapid restoration of loads downstream of DG3. Maintenance team 3 prioritized repairing natural gas fault F9 to ensure rapid energy supply from the natural gas source connected to node 6. No repair work was completed in the first two hours of the disaster, resulting in a continuous decrease in the remaining reserve on natural gas pipeline 1-2. Fault F3 was repaired at time 3, and the remaining reserve on pipeline 1-2 returned to normal at time 3. Because the reserve on pipeline 3-5 was insufficient to sustain long-term load supply, its reserve was depleted before time 2. Natural gas network fault F9 was repaired at time 3, and pipeline 3-5 returned to normal.

[0047] In the distribution network, the connectivity of the grid can be ensured by using tie switches. Since the operation time of tie switches is not taken into account in this paper, the topology of the distribution network can be adjusted immediately after an earthquake disaster occurs, thereby providing power to important loads.

[0048] like Figure 2As shown in the figure, the distribution network topology reconfiguration strategy was immediately implemented after the earthquake. Tie lines C1 and C2 were closed, providing power to some of the lost loads in the distribution network, effectively supporting the power supply near distribution network node 12 and node 18. At the same time, the gas turbine at natural gas network node 2, relying on the natural gas pipeline, continued to supply power to the distribution network, maintaining the distribution network load at 44.9% after the disaster.

[0049] At the second moment, the storage of natural gas pipelines 3-5 has been consumed, resulting in the loss of load at natural gas nodes 3 and 5; at the third moment, the distribution network fault F3 is repaired, the compressor resumes power supply, the natural gas network fault F9 is also repaired, and the natural gas system load is fully restored; at the fourth moment, the distribution network fault F4 is repaired, and part of the load downstream of DG3 is restored; at the sixth moment, the fault F8 is repaired, and the gas source connected to the natural gas system node 6 supplies gas to the load; at the seventh moment, the distribution network faults F2 and F6 are repaired; at the tenth moment, the faults F1, F5 and F7 are repaired. At this point, the fault components of the urban integrated energy system have been repaired, and the power system load is fully restored. The load recovery of the urban integrated energy system changes over time as shown below. Figure 3 shown.

[0050] 3) Comparison of load recovery efficiency of two resilience enhancement strategies under the same fault scenario In Option 1, the power system relied solely on the coupling elements of the city's integrated energy system and intact power sources to supply the load. The faulty line was not repaired, leaving downstream loads without load, resulting in a low power system load recovery percentage. Similarly, without maintenance personnel involved in post-disaster repairs, the natural gas system's lost loads could not be restored and could only be supplied through intact pipelines. Option 2 comprehensively considered the impact of natural gas pipeline storage, distribution network topology reconfiguration, and the chain reaction of failures within the city's integrated energy system on system resilience. Combined with post-disaster repairs, it achieved complete restoration of both the power and natural gas system loads.

[0051] .

[0052] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for improving the resilience of an urban integrated energy system under earthquake disasters, characterized by: The process includes the following steps, which are performed in sequence: Step 1: Establish the objective function; Step 2: Constrain the urban integrated energy system model; Based on the changes in the distribution network topology and the role of natural gas pipeline storage margin in supporting the natural gas load and gas turbine load of the urban integrated energy system, the urban integrated energy system model is constrained. After an earthquake disaster occurs, the urban integrated energy system model can be reconstructed based on the collected information on the location of each fault node, fault line, and maintenance team, the type of fault repair, the remaining maintenance resources of each warehouse, the working status of each maintenance team, and the restoration of power supply from distributed power generation (DG) to gas turbines through natural gas pipelines at some distribution network fault nodes. Step 3: Cluster the faults of the urban integrated energy system; Step 4: Based on the clustering results, manually formulate the repair order of the first batch of fault nodes and send it to the maintenance team for emergency repairs in sequence; Step 5: After each fault node is repaired, the city's integrated energy system model is reconstructed again, again considering the role of distribution network topology reconstruction and natural gas pipeline storage in improving system load recovery, and again manually determining the next batch of fault nodes where the fault will propagate; Step 6: Repeat step 5 to obtain more batches of fault nodes and objective function values, manually formulate the corresponding repair sequence, and send it to the maintenance team. After the emergency repair of the previous batch of faults is completed, the emergency repair of the next batch of fault nodes will be carried out in sequence until all fault nodes are repaired.

2. The method for improving the resilience of an urban integrated energy system under earthquake disasters according to claim 1 is characterized by: The objective function in step 1 is to minimize the sum of the load reduction of the urban integrated energy system and the fault repair time. The objective function is: (1)； Where, is the set of distribution network nodes; is a collection of natural gas network nodes; Indicates a time period; is the weight coefficient of distribution network load; is the weight coefficient of natural gas load; is the load reduction amount at each node in the power system; is the load reduction at each node of the natural gas system; is the weight coefficient of the fault, is the fault type; for Emergency repair base according to the fault type; for Fault type exist t The time when the fault repair is completed.

3. The method for improving the resilience of an urban integrated energy system under earthquake disasters according to claim 1 is characterized by: The constraints of the urban integrated energy system model include distribution network flow constraints, node voltage and branch current constraints after distribution network reconstruction, line transmission power constraints, connectivity and radiation constraints of the distribution network after reconstruction, natural gas network model constraints, natural gas pipeline storage and use constraints, integrated energy system coupling relationship constraints, and maintenance team dispatch constraints.

4. The method for improving the resilience of an urban integrated energy system under earthquake disasters according to claim 3 is characterized by: The distribution network flow constraints are as follows: (2)； (3)； (4)； (5)； (6)； (7)； Where, 、 、 All of them are distribution network nodes; For nodes j The set of upstream nodes of the connected branches; For nodes The set of downstream nodes of the connected branches; for t Timeline Active power on for t Timeline Active power on for t Time Node Injected active power; for t Timeline Reactive power on for t Timeline Reactive power on For the line The square of the upper current; For the line The square of the upper current; For the line Previous node The square of the voltage at For the line Previous node The square of the voltage at For the line The square of the active power on the For the line The square of the reactive power; for t Time Node Injected active power; for t Time Node Injected reactive power; for t Time to node Injected reactive power; For the line resistance; For the line Active power flowing upstream; For the line reactance; For the line Reactive power flowing upstream; For the line The square of the resistance; For the line The square of the reactance; for t Time Node The active power generated by the generator; for t Time Node The reactive power generated by the generator; for t Time Node The active power of the gas turbine; for t Time Node Active load; for t Time Node Reactive load; is a collection of conducting branches; Formula (6) is a nonlinear equation. Performing second-order cone relaxation on this equation yields: (8)； Where, for t Time Node The square of the voltage; for t Timeline The square of the current; Formula (7) is valid only when the line is conducting. The Big M method is used to transform Formula (7): (9)； (10)； Where, for t Time Node The square of the voltage; for t Timeline The open state value is a 0-1 variable, 0 means open, 1 means closed; is a set constant used to relax the constraints (9) and (10); The node voltage branch current constraints are as follows: The node voltage does not exceed the upper and lower limits, and the branch current does not exceed the upper limit. The constraints are expressed as: (11)； (12)； Where, for t Time Node The voltage at for t Time Node The lower voltage limit at for t Time Node The upper limit of the voltage at for t Timeline The maximum allowable current value; for t Timeline Current; The line transmission power constraints are as follows: The transmission power of each line must be within the range of the line's allowed transmission capacity. The constraint is expressed as: (13)； (14)； Where, for t Timeline The minimum active power; for t Timeline The maximum active power; It is a collection of distribution network lines; for t Timeline Minimum reactive power; for t Timeline Maximum reactive power; The connectivity and radiation constraints are as follows: (15)； (16)； (17)； (18)； Where, is the set of chord branches; is the number of distribution network branches; is the number of segmented regions; For nodes Parent-child matrix, node For nodes The value is 1 when it is the parent node of , otherwise it is 0; For nodes Parent-child matrix, node For nodes The value is 1 when it is the parent node of , otherwise it is 0; Indicates that node 1 is the parent node of node 2; The natural gas grid model constraints are as follows: The natural gas network model uses the Weymouth model to perform steady-state calculations on natural gas flow and node pressure, where the pipeline flow constraint is: (19)； (20)； Where, For gas t Time flows through the node and Pipeline flow rate; For pipeline Length-dependent constants; For nodes exist t The pressure of the moment; For nodes exist t The pressure of the moment; Indicates natural gas pipeline Traffic direction; Nodes in a natural gas network also adhere to the flow conservation principle, which states that the gas flow into a node is equal to the gas flow out of the node. The flow conservation principle is expressed as follows: (21)； Where, For nodes The gas source is t Gas production at any time; For nodes exist t The load at the moment; For natural gas generator sets t The node gas flow consumed at any moment; For nodes The connected electric compressor t Gas consumption at each moment; For nodes A collection of connected pipes; Gas source output constraints: (22)； Where, For nodes The gas source is t The minimum output at the moment; For nodes The gas source is t Maximum output at the moment; For nodes The gas source is t Output value at the moment; Nodal gas flow constraints consumed by gas turbines: (23)； Where, For gas turbines t The minimum gas consumption at the moment; For gas turbines t The maximum gas consumption at the moment; For gas turbines t Gas consumption value at the moment; Pipeline flow constraints in natural gas networks: (24)； Where, For pipelines exist t The minimum flow rate at any moment; For pipelines exist t Maximum flow rate at any moment; For pipelines exist t The flow value at the moment; Natural gas node pressure constraints: (25)； Where: For nodes exist t Minimum pressure at the moment; For nodes exist t Maximum pressure at the moment; For nodes exist t Pressure value at the moment; The natural gas pipeline has usage constraints: After an earthquake, intact natural gas pipelines use their natural gas reserves to supply natural gas loads and gas turbines. The natural gas pipeline reserve usage constraints are expressed as follows: (26)； (27)； (28)； Where, It is a binary variable, indicating whether the natural gas pipeline is damaged, with the value 0 for damaged and 1 for undamaged; for t Time Pipeline of custody; For pipelines Length 、 For pipelines Diameter 、 For pipelines The average pressure, Inflow pipe Natural gas flow, Outflow pipe Natural gas flow, 、 、 、 are the gas constant and temperature in the pipeline respectively 、 Compression factor 、 Gas density; Formula (26) is the pipeline exist t The expression at the pipe storage space level at all times represents the average pressure at both ends of the pipe storage and the pipeline and the relationship between pipeline parameters; Equation (27) is the expression of the average pressure in the pipeline; Equation (28) describes the pipeline exist t The temporal relationship of pipe storage at each moment reflects the dynamic changes of pipe storage between consecutive moments. The difference between the inflow and outflow of natural gas determines the charging and discharging process of pipe storage. If the inflow is greater than the outflow, the pipe storage increases, and vice versa. The coupling relationship constraints of the integrated energy system are as follows: The integrated energy system is divided into multiple subsystems according to its topological structure. In each subsystem, the distribution network and the natural gas network are coupled to achieve comprehensive resource utilization. A local fault in a subsystem may propagate to other subsystems through the coupling device, thus causing large-scale load interruption. Equations (29) to (33) express the constraints on the propagation of faults through the coupling device in the integrated energy system. A gas turbine is a power generation device that uses natural gas as fuel. In a natural gas system, it is equivalent to a load. The conversion relationship between a gas turbine's power generation and natural gas consumption is expressed as: (29)； Where: express t Time Node Gas turbine power generation capacity at represents the gas turbine conversion efficiency coefficient; The natural gas pipeline uses an electric-consuming compressor, which is driven by the power distribution network and is equivalent to a load in the power system. The natural gas pipeline pressure constraint is: (30)； Where: 、 Represent the nodes in the natural gas pipeline and nodes exist t The pressure value at the moment, Indicates the compression coefficient of the compressor; Energy conversion relationship of the compressor: (31)； Where: express t The power consumption of the compressor at all times; Indicates the consumption coefficient of the compressor; A pipeline failure in the natural gas system may cause a gas supply interruption to the gas turbine, which in turn may cause a decrease in the power load in the urban distribution network. An earthquake disaster may cause a line interruption in the urban distribution network, which may cause a power supply interruption and cause the shutdown of power-consuming compressors, ultimately leading to a reduction in the gas load in the natural gas system. Therefore, Equation (32) indicates that when a fault occurs in the upstream node of the gas turbine, causing a gas supply interruption, the gas turbine will shut down. Equation (33) indicates that when the power supply node of the compressor is in a faulty state, the compressor will not work. The specific expression is as follows: (32)； (33)； Where, express t Time Natural Gas Node Whether it is working, the value is 1 when working, and 0 when not working; Represents the distribution network node at time t Whether it is working, the value is 1 when working and 0 when not working; for t The minimum value of the compressor load at the moment; for t The maximum compressor load at that moment.

5. The method for improving the resilience of an urban integrated energy system under earthquake disasters according to claim 3 is characterized by: The maintenance team dispatch constraints are as follows: Because each maintenance team is responsible for a different area, before formulating a fault repair plan, it is necessary to cluster the faults. This means matching the faults with the repair team warehouses to form several small clusters. This simplifies the subsequent repair plan formulation problem into a repair path planning problem for the cluster consisting of a single repair team, thereby achieving dimensionality reduction of the fault categories. Divide the fault into The number of classes, the number of warehouses determines the number of clusters. The clustering results are indexed. σ Indicates that each warehouse corresponds to a type of failure, so the failure type Also known as warehouse ; Assume that there is a maintenance team in each warehouse, and the maintenance team uses the resources of the warehouse to perform fault repairs, where ,Through clustering, the maintenance team dispatch problem is transformed into a multiple vehicle routing problem; The input data for the clustering problem includes the travel time of the repair team to the fault location , Fault repair time , the speed of the repair team , warehouse available resources , resources required to repair the fault 、 Weighted distance of the path ,Fault For warehouses σ Total resource demand ; Using binary decision variables To determine any fault The clustering of the fault Clustering into warehouses : (34)； Clustering is performed based on the shortest equivalent distance between each repair team and the fault; The equivalent distance is represented by the shortest driving time required for the repair team to reach the fault location and the sum of the repair time required for each fault type, where the shortest driving time is , where 1, 2, and 3 represent warehouse numbers; if a warehouse does not have enough resources, the fault will be clustered to the next nearest warehouse; Therefore, the fault is assigned to the warehouse with the smallest equivalent distance through formula (35), and the travel time of the repair team is solved through formula (36): (35)； (36)； Formula (37) ensures that the failure is assigned to a single warehouse: (37)； Formula (38) ensures that the warehouse has sufficient resources to repair faults from the perspective of the total amount of warehouse resources: (38)； From the perspective of failure, we can ensure that each failure is assigned to a warehouse with sufficient resources to repair it through formula (39): (39)； After the fault clustering is completed, the maintenance team is dispatched to repair the fault and the clusters are grouped into the same group. Type of failure, warehouse and maintenance team as a repair base, with If , then the maintenance team scheduling formula is as follows: (40)； (41)； (42)； (43)； Where: Indicates maintenance Type of breakdown repair team; express Emergency repair base for various types of failures; Is a binary variable, indicating maintenance σ Type of breakdown repair team Whether to repair the fault ， It takes 1, not 0; Is a binary variable, indicating maintenance Type of breakdown repair team Whether the fault Geographic location to the fault The geographical location is 1, not 0; is a binary variable representing maintenance Type of breakdown repair team Whether the fault Geographic location to the fault Geographical location ， It takes 1, not 0; is a binary variable representing maintenance Type of breakdown repair team Whether from the warehouse to failure Geographical location ， It takes 1, not 0; Among them, formula (40) means that each fault can only be repaired by one maintenance team; formula (41) means that the maintenance team repairs the fault After that, go to the fault The fault point where the fault is located; Formula (42) represents 、 、 and Both are binary variables; Equation (43) indicates that the maintenance team departs from the warehouse and returns to the warehouse after completing the maintenance task; Set the repair team route from the fault Geographic location to the fault The geographical location of the The constraints on the time of day, maintenance time, and travel time of the geographical location are as follows: (44)； (45)； In formula (44), Representing the repair team Arrival Failure The time of day of your geographical location; Representing the repair team Arrival Failure The time of day of your geographical location; For the maintenance team Fixing a fault Time taken; For the maintenance team From the fault to failure The travel time of the geographical location, formula (45) indicates that when the maintenance team does not pass the fault Geographic location, then its arrival failure The time of the geographical location is 0; The following constraints apply to fault repairs: (46)； (47)； (48)； (49)； Where: is a binary variable of 0 or 1, representing Type of failure The required maintenance time, i.e. Equal to 1 indicates a fault At the moment t Been repaired, Equal to 0 means the fault occurs at time t It has not been repaired or the repair has been completed; Constraints (46) to (49) express The calculation method to obtain Type of failure Required repair time ; Indicates a fault exist t The time when the fault repair is completed.

6. The method for improving the resilience of an urban integrated energy system under earthquake disasters according to claim 1 is characterized by: The clustering in step three is specifically as follows: after an earthquake disaster occurs, the faults of the urban integrated energy system are clustered according to the fault type and location information of the collected fault points and fault lines through the maintenance team dispatch constraints, and are dispatched to different maintenance teams according to the clustering results, thereby realizing dimensionality reduction processing of multi-type and multi-location fault maintenance.

7. The method for improving the resilience of an urban integrated energy system under earthquake disasters according to claim 1 is characterized by: The repair sequence of the first batch of fault nodes manually formulated in step 4 is specifically as follows: Manual analysis identifies the faulty nodes or faulty lines in the integrated energy system that cause fault propagation and marks them as the first batch of faults. At the same time, the faulty nodes or faulty lines that cause faults in the coupling device between the distribution network and the natural gas network within the urban integrated energy system are also marked as the first batch of faults. According to the objective function in step 1, the objective function value of each fault node or fault route in the first batch of faults is obtained, and step 2 is performed to achieve the first reconstruction of the urban integrated energy system model; By reconfiguring the topology of the distribution network and directly supplying power to the system load through natural gas pipelines, and combining the locations of faulty nodes with fault propagation and the corresponding objective function values, the repair sequence of the first batch of faulty nodes is manually formulated and sent to the maintenance team for emergency repairs in sequence.

8. The method for improving the resilience of an urban integrated energy system under earthquake disasters according to claim 7 is characterized by: The next batch of fault nodes with fault propagation are manually determined again in step five as follows: fault nodes that do not need to be prioritized by the maintenance team and the first batch of fault nodes are excluded, and the other fault nodes with fault propagation are identified as the second batch of fault nodes; the objective function value of the second batch of fault nodes is obtained through the objective function in step one, and the maintenance order of the second batch of fault nodes is manually formulated and sent to the maintenance team. After the emergency repair of the first batch of faults is completed, the emergency repair of the second batch of fault nodes is carried out in sequence.

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