Two-stage fault recovery and maintenance method for regional integrated electrical and gas energy systems

Abstract

This invention discloses a two-stage fault recovery and maintenance method for a regional integrated power-gas energy system, comprising: based on the regional integrated power-gas energy system, constructing a rapid fault recovery model for the emergency phase of the regional integrated power-gas energy system according to network operation constraints in the power distribution system, operation constraints of various distributed power sources, network reconfiguration constraints, and operation constraints in the natural gas network, and solving the model to obtain the optimal tie switch operation; based on the topology of the system after the tie switches on the distribution network lines operate in the first emergency phase, considering the relevant constraints of maintenance personnel scheduling and the relevant constraints of the system in the first phase model, establishing a second-stage regional integrated power-gas energy system network reconfiguration and maintenance scheduling optimization model; transforming the rapid fault recovery model, network reconfiguration, and maintenance scheduling optimization model into a MISOCP problem to obtain the optimal maintenance route and the tie switch operation of adjusting the optimal topology of the system as the maintenance plan progresses.

Description

Technical Field

[0001] This invention relates to the field of integrated electric and gas energy, and more particularly to a two-stage fault recovery and maintenance method for a regional integrated electric and gas energy system. Background Technology

[0002] With the increasing scarcity of fossil fuels and the growing severity of environmental pollution, the vigorous development of renewable energy and the improvement of energy efficiency have become common goals worldwide. Natural gas, due to its environmental friendliness, high efficiency, and abundant reserves, has attracted widespread attention, and the installed capacity of gas-fired power generation is continuously increasing. [1-2] As a coupling element between the power grid and the gas grid, the large-scale grid connection of gas turbines has led to increasingly close coupling between the power grid and the natural gas grid. [3] Therefore, power-gas integrated energy systems (PGIES), which primarily utilize electricity while incorporating natural gas, have experienced rapid development in recent years. [4] However, extreme disasters with low probability and high loss have occurred frequently in recent years, posing a serious threat to the safe and reliable operation of integrated electric and gas energy systems. Furthermore, the coupled nature of integrated energy systems means that any system failure or power supply blockage will affect the operating status and power supply of other systems. [5] In disaster response, fault recovery strategies can effectively reduce load loss during a disaster, while maintenance scheduling strategies can effectively restore damaged components after a disaster, enabling the system to return to normal operation. However, while current research both domestically and internationally has proposed many effective post-disaster maintenance strategies, it has not considered restoring system load in both the during-disaster and post-disaster phases.

[0003] In summary, to fully investigate the two-stage recovery strategy of PGIES during and after extreme disasters, in the first stage during the disaster, load restoration priority needs to be considered, and the system topology should be reconfigured using tie switches to achieve priority restoration of important loads in the integrated electrical-gas energy system during the first stage. In the second stage after the disaster, the optimal maintenance path for maintenance personnel in PGIES should be considered, and the system should be ensured to operate with an optimal radial topology throughout the process.

[0004] Therefore, it is of great significance to develop better strategies for disaster recovery and maintenance of PGIES under extreme disasters, thereby enhancing the overall system's resilience and ensuring its safe and stable operation. [6] . Summary of the Invention

[0005] This invention provides a two-stage fault recovery and maintenance method for a regional integrated power-gas energy system. In the first stage during a disaster, a rapid fault recovery model for the regional integrated power-gas energy system is established, considering load priority and system topology reconfiguration strategies to achieve priority and rapid recovery of critical loads during the emergency recovery phase. In the second stage after the disaster, a network reconfiguration and maintenance scheduling optimization model for the regional integrated power-gas energy system is established. Power system maintenance teams and natural gas system maintenance teams coordinate maintenance tasks, and throughout the process, a distribution network reconfiguration strategy is employed to ensure the system quickly recovers to a safe and stable operating state while operating in a radial topology. Furthermore, a bidirectional gas flow model is used in the modeling of the natural gas system, which can obtain more accurate pipeline flow results during natural gas network faults, as detailed below:

[0006] A two-stage fault recovery and maintenance method for a regional integrated electric-gas energy system, the method comprising:

[0007] Considering the synergistic effect of the power system and the natural gas system in the regional integrated electricity-gas energy system, the process from the system encountering an extreme disaster to the system returning to normal operation is divided into two stages;

[0008] Based on the regional integrated power and gas energy system, and according to the network operation constraints, various distributed power source operation constraints, network reconfiguration constraints, and natural gas network operation constraints in the power distribution system, a rapid fault recovery model for the emergency phase of the regional integrated power and gas energy system is constructed, and the optimal tie switch operation is obtained by solving the model.

[0009] Based on the topology of the distribution network after the operation of the tie switch in the first stage of emergency response, and considering the relevant constraints of maintenance personnel dispatch and the relevant constraints of the system in the first stage model, a second-stage regional electricity-gas integrated energy system network reconfiguration and maintenance dispatch optimization model is established.

[0010] The fault rapid recovery model, network reconstruction, and maintenance scheduling optimization model are transformed into the MISOCP problem to obtain the optimal maintenance route and the action of the tie switch that adjusts the optimal system topology as the maintenance plan progresses.

[0011] In the modeling of the natural gas system, a two-way gas flow model is used to obtain pipeline flow results when the natural gas network fails.

[0012] Furthermore, the bidirectional gas flow model is as follows:

[0013]

[0014]

[0015]

[0016]

[0017]

[0018]

[0019] In the formula, λ mn As a binary variable representing the direction of gas flow, and These represent the maximum gas pressures at natural gas nodes m and n, respectively. and These represent the pressures on the low-pressure and high-pressure sides of the gas in pipe mn, respectively. m and pi n These are the gas pressure values ​​at natural gas nodes m and n, respectively. Given the maximum flow rate of pipe mn, the pressure flow model is transformed from a fixed direction to bidirectional flow.

[0020]

[0021] In the natural gas pipeline model, the gas flow rate is from the high-pressure node to the low-pressure node. The gas flow direction in the pipeline is flexible and adaptable to situations where the pipeline flow direction changes under fault conditions.

[0022] The network reconstruction constraints are as follows:

[0023]

[0024]

[0025]

[0026]

[0027] Where, β ib and β bi K is a binary variable representing the order of branch ib flow. ib Let y be the state variable of branch ib. i Let β be the state variable of node i. sub,b 'sub' represents a substation node, and 'sub' represents a set of substations.

[0028] The second-stage regional integrated electricity-gas energy system network reconfiguration and maintenance scheduling optimization model includes: damaged component clustering modeling.

[0029]

[0030]

[0031] Among them, Sd,o The binary variable represents the distance between component d and warehouse o, where DN is the set of damaged components, and the constraint ensures that each component is aggregated into only one warehouse.

[0032] Furthermore, the second-stage regional integrated electricity-gas energy system network reconfiguration and maintenance scheduling optimization model also includes: eliminating the constraint of sub-loops as follows:

[0033]

[0034] in, Let be the repair sequence value for damaged component d, and n be the number of damaged components in the set of damaged components. Let c be the state variable of the repair team from the damaged component point d to the damaged component point s. It is a dummy variable.

[0035] Specifically, the transformation of the fault fast recovery model, network reconfiguration, and maintenance scheduling optimization model into the MISOCP problem to obtain the optimal maintenance route is as follows:

[0036] Solving the first-stage optimization model yields the optimal action of the tie switch and the optimal topology of the system. The solved topology is then used as the initial topology for the second-stage maintenance strategy.

[0037] The second-stage optimization model is solved using a commercial solver to obtain the optimal maintenance path, the operation status of the interconnecting switch at each time step, and the corresponding optimal topology of PGIES.

[0038] The beneficial effects of the technical solution provided by this invention are:

[0039] 1. Compared with existing methods, this invention establishes a coordinated optimization model for fault recovery and maintenance in the two stages of disaster recovery and post-disaster recovery of an integrated electric-gas energy system, based on the different characteristics of fault recovery and fault maintenance in system load loss recovery;

[0040] 2. Based on the network operation constraints and various distributed power source operation constraints in a typical regional electric-gas integrated energy system, this invention constructs a two-stage optimal model of the system. Furthermore, in the natural gas pipeline flow modeling, a bidirectional gas flow model is adopted, which can obtain more accurate load recovery results when the natural gas network fails, thereby ensuring the stability and reliability of the power distribution system during operation.

[0041] 3. This invention starts from the two stages of the system encountering extreme disasters—during and after the disaster—and provides a two-stage fault recovery and maintenance strategy model for deeply coupled regional integrated power and gas energy systems. The model is transformed into a mixed-integer second-order cone programming (MISOCP) problem for solution. The results significantly shorten the power outage time for users and improve the overall system recovery efficiency. Attached Figure Description

[0042] Figure 1 A flowchart of a two-stage fault recovery and maintenance method for a regional integrated electric-gas energy system;

[0043] Figure 2 A schematic diagram of the fault recovery and maintenance framework for a regional integrated electric-gas energy system;

[0044] Figure 3 The topology diagram of the modified 13-node distribution network and 7-node natural gas network system;

[0045] Figure 4 This is the topology diagram after the first phase of system network reconstruction;

[0046] Figure 5 Topology diagrams of the system at different times;

[0047] Figure 6 A schematic diagram of the load reduction of the regional integrated electricity-gas energy system;

[0048] Figure 7 System maintenance path diagrams for different scenarios. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below.

[0050] Example 1

[0051] A two-stage fault recovery and maintenance method for a regional integrated electric-gas energy system, comprising the following steps:

[0052] 101: Considering the synergistic effect of the power system and the natural gas system in a regional integrated electricity-gas energy system, the process from the system encountering an extreme disaster to its restoration to normal operation is divided into two stages, the framework of which is as follows: Figure 2 As shown;

[0053] 102: Based on a typical regional integrated power-gas energy system, and according to the network operation constraints, various distributed power source operation constraints, network reconfiguration constraints, and natural gas network operation constraints in the power distribution system, a rapid fault recovery model for the emergency phase of the regional integrated power-gas energy system is constructed, and the optimal tie switch operation is obtained by solving the model.

[0054] 103: Based on the topology of the system after the operation of the tie switch on the distribution network line in the first stage of emergency response, and considering the relevant constraints of maintenance personnel dispatch and the relevant constraints of the system in the first stage model, establish a second-stage regional electricity-gas integrated energy system network reconfiguration and maintenance dispatch optimization model.

[0055] 104: Transform the model proposed in steps 102 and 103 into a MISOCP problem for easy, fast and efficient solution, to obtain the optimal maintenance route and the operation of the tie switch for adjusting the optimal topology of the system as the maintenance plan progresses.

[0056] In summary, the embodiments of the present invention obtain coordinated optimization decisions for fault recovery and maintenance scheduling in the two stages of disaster recovery and post-disaster recovery of the regional integrated power-gas energy system through the above steps 101-104, which significantly shortens the power outage time for users and improves the recovery efficiency of the entire system.

[0057] Example 2

[0058] The scheme in Example 1 will be further described below with specific calculation formulas and examples:

[0059] 201: Considering the synergistic effect of the power system and the natural gas system in a regional integrated electricity-gas energy system, the process from the system encountering an extreme disaster to its restoration to normal operation is divided into two stages, the framework of which is as follows: Figure 2 As shown;

[0060] 202: Based on a typical regional integrated power-gas energy system, and according to the network operation constraints, various distributed power source operation constraints, network reconfiguration constraints, and natural gas network operation constraints in the power distribution system, a rapid fault recovery model for the emergency phase of the regional integrated power-gas energy system is constructed.

[0061] Step 202 includes:

[0062] 1) Objective function:

[0063] A fault-fast recovery optimization model for a regional integrated electricity-gas energy system is established with the objective function of minimizing load loss cost. The load loss cost coefficient is introduced into the objective function as a weight coefficient for energy load and represents the importance of different types of load. The objective function is shown in equation (1):

[0064]

[0065] In equation (1), and P represents the unit load reduction cost at each node in the power system and the natural gas system, respectively. shed,i,t and Q shed,i,t Let i represent the load reduction of the power system and the load reduction of the natural gas system, respectively. Let i be a node in the distribution network, m be a node in the natural gas network, N be the set of nodes in the distribution network, and G be the set of nodes in the natural gas network.

[0066] 2) Distribution network operation constraints:

[0067] Power balance constraints at distribution network nodes:

[0068]

[0069]

[0070] In equation (2), P DG,i,t and Q DG,i,t These represent the active and reactive power outputs of node i at time t, respectively; P ai,t and Q ai,t R represents the active power and reactive power flowing from node a to node i, respectively; ai Let be the resistance of line ai. P is the square of the current in branch ai; D,i,t and Q D,i,t These represent the active and reactive power of the load at node i, respectively; P ib,t and Q ib,t These represent the active and reactive power flowing from node i to node b in the branch, respectively, where L is the set of distribution network branches, and X... ai Let a be the reactance of branch ai.

[0071] The voltage drop equation is constrained as follows:

[0072]

[0073]

[0074] In the formula, Let be the squared value of the voltage at node i; K represents the impedance value of branch ib. ib,t A binary variable representing the branch state, where M is a very large constant and R is a variable representing the branch state. ib X is the resistance of branch ib. ib For the reactance of line ib, Let the square of the current in branch ib be . The square of the voltage at node b.

[0075] Node voltage and branch current constraints:

[0076]

[0077] y i,t ·V i min ≤V i,t ≤y i,t ·V i max (7)

[0078] In the formula, Let the square of the minimum current in branch ib be . Let the square of the current in branch ib be . K is the square of the maximum current in branch ib. ib V is the state variable of branch ib. i min V is the minimum voltage value at node i. i max V is the maximum voltage value at node i. i,t Let be the voltage value at node i.

[0079] Equation (6) represents the upper and lower limits of the current in the distribution network branch, and is affected by two variables on the line. In Equation (7), y i,t This represents a binary variable representing a node in the power grid. It's also important to note that when all adjacent connections to any node are disconnected, i.e., K... ib When y is 0, i,t It is also 0.

[0080] The load reduction amount for each node cannot exceed the node's load; therefore, the load reduction constraint is:

[0081]

[0082] DG operational constraints:

[0083]

[0084]

[0085] in, Let be the minimum active power output of the DG connected to node i. Let be the maximum active power output of the DG connected to node i. Let be the minimum reactive power output of the DG connected to node i. The maximum reactive power output of the DG connected to node i.

[0086] In equations (9) and (10), ug i,tThe binary state variable representing DG.

[0087] The second-order cone form of the branch power flow constraint is as follows:

[0088]

[0089] Among them, P ib Q is the active power flowing through branch ib. ib The reactive power flowing through branch ib, V is the square of the current in branch ib. i sqr Let be the squared value of the voltage at node i.

[0090] 3) Natural gas network operation constraints:

[0091] Natural gas system node flow balance equations:

[0092]

[0093] In equation (12), W GW,m,t For the gas supply to node m at time t; W L,m,t W represents the gas load at node m. shed,m,t Let F be the amount of reduction of node m at time t. mn,t Let B be the gas flow rate from node m to node n, and let B be the set of natural gas pipelines m and n.

[0094] Gas source output constraints:

[0095] W m,min ≤W GW,m,t ≤W m,max (13)

[0096] Among them, W m,min W represents the minimum output power of the gas source at node m. m,max This represents the maximum output power of the air source at node m.

[0097] Natural gas node pressure constraints:

[0098] pi m,min ≤pi m,t ≤pi m,max (14)

[0099] Where, pi m,t Let pi be the gas pressure value at natural gas node m at time t. m,max pi represents the maximum gas pressure at natural gas node m. m,min This represents the minimum gas pressure at natural gas node m.

[0100] Pipe flow equation:

[0101] Fmn =(C mn ·pi m ) 2 -(C mn ·pi n ) 2 (15)

[0102] Among them, F mn Let pi be the flow rate value of pipe mn. m Let pi be the air pressure value at node m. n Let C be the air pressure value at node n. mn This is the pipeline pressure-to-flow constant.

[0103] Under normal operating conditions of a natural gas system, the gas flow direction in the pipeline is fixed in the short term, i.e., it flows from node m with high pressure to node n with low pressure. However, when a natural gas system malfunctions, the gas flow direction may change. Therefore, this embodiment of the invention considers a bidirectional gas flow model:

[0104]

[0105]

[0106]

[0107]

[0108]

[0109]

[0110] In the formula, λ mn As a binary variable representing the direction of gas flow, and These represent the maximum gas pressures at natural gas nodes m and n, respectively. and These represent the pressures on the low-pressure and high-pressure sides of the gas in pipe mn, respectively. m and pi n These are the gas pressure values ​​at natural gas nodes m and n, respectively. Let mn be the maximum flow rate of the pipe. Through equations (16)-(20), the air pressure flow model in equation (21) is transformed from a fixed direction to bidirectional flow.

[0111] By performing second-order cone relaxation on equation (21), we can obtain:

[0112]

[0113] The above constraints ensure that the gas flow in the natural gas pipeline model can flow from high-pressure nodes to low-pressure nodes, making the gas flow direction in the pipeline more flexible and adapting the model to situations where the pipeline flow direction changes under fault conditions.

[0114] 4) Coupling constraints of the integrated electric-gas energy system:

[0115] In a natural gas grid, compressors consume electricity, so they can be considered as grid loads; in a distribution grid, distributed gas turbines consume natural gas, so they can be considered as natural gas loads.

[0116] The coupling elements include a distributed gas turbine and an electrically driven compressor. The energy conversion constraints of the distributed gas turbine are as follows:

[0117] W DG,m,t =B i ·P DG,i,t (twenty three)

[0118] Among them, W DG,m,t For the gas turbines supplied with gas from the nodes, B i The coefficient for converting gas into electricity.

[0119] The energy conversion of an electrically driven compressor is as follows:

[0120] P comp,i,t =C z ·F z,t (twenty four)

[0121] In the formula, B i and C z These are the conversion coefficients, P and P respectively. comp,i,t For the power consumption of the compressor, F z,t This represents the gas flow rate of the compressor branch.

[0122] 5) Network reconfiguration constraints:

[0123] During operation, the distribution network must maintain its radial structure. The reconfiguration constraints are as follows:

[0124]

[0125]

[0126]

[0127]

[0128] Where, β ib and β bi K is a binary variable representing the order of branch ib flow. ib Let y be the state variable of branch ib. iLet β be the state variable of node i. sub,b 'sub' represents a substation node, and 'sub' represents a set of substations.

[0129] 203: Based on the topology of the distribution network after the operation of the tie switch in the first stage of emergency response, and considering the relevant constraints of maintenance personnel dispatch and the relevant constraints of the system in the first stage model, establish a second-stage regional electricity-gas integrated energy system network reconfiguration and maintenance dispatch optimization model.

[0130] Step 203 includes:

[0131] 1) Clustering modeling of damaged components:

[0132]

[0133]

[0134] In equation (29), the distance is the distance between component d and warehouse o. The goal is to minimize the total distance S from the damaged component to the warehouse. d,o Let DN be a binary variable representing the distance between component d and warehouse o, and let DN be the set of damaged components. Constraint (30) ensures that each component is aggregated into only one warehouse.

[0135] 2) Objective function:

[0136]

[0137] Where T is the recovery time.

[0138] In equation (31), the first term is the cost of reducing the load on the distribution network. The second item is the cost of reducing natural gas network load. The third item represents the cost of the total repair time for all damaged components.

[0139] 3) Constraints on the dispatching of maintenance personnel:

[0140] If we group the warehouses and fault points into a single set, denoted by DN, then the maintenance personnel scheduling has the following constraints:

[0141]

[0142]

[0143]

[0144]

[0145]

[0146] In the formula, Let the state variable be the point where maintenance team c passes through the damaged component d. Let c be the state variable of the repair team from the damaged component point d to the damaged component point s. DN represents the state variables of repair team c from warehouse dp to the damaged component point d. o C is the set of damaged components o. o Assemble the maintenance team.

[0147] Equation (32) is and The correspondence; Equation (33) represents and All are binary variables; Equation (34) indicates that for each damaged component, only one repair team can repair it; Equation (35) indicates that the repair personnel should depart from the warehouse. Equation (36) indicates that after the repair team repairs the damaged component d, it should immediately proceed to the damaged component s. Assuming that the repair personnel's journey is from d to s, the relationship between their arrival time at s, repair time, and travel time is as follows:

[0148]

[0149]

[0150] In equation (37), AT d,c and AT s,c These represent the time it takes for maintenance personnel to reach the damaged components d and s, respectively; r d,c The repair time for damaged component d, tr d,s,c Let M be the time it takes for the maintenance team to travel from d to s. Equation (38) indicates that if the maintenance personnel have not passed through d, the time to reach d is 0, and M is a large constant. The maintenance state constraints for the damaged component are:

[0151]

[0152]

[0153]

[0154] In the formula, It is a binary variable representing the repair status of the damaged component, i.e. A value of 1 indicates that the damaged component was repaired at time t. A value of 0 indicates that the damaged component was not repaired at time t or that the repair was completed; t is the repair step size, t·T d,t T represents the time it takes for the damaged component to be repaired. d,t Y represents the operating state of the damaged component d at time t. d,cLet ε be a binary variable representing the damage to component d by the repair team, and let ε be a constant that is very small.

[0155] Equation (39) represents that the component must be repaired during the entire maintenance period; Equations (40) and (41) represent the repair time constraints for the damaged component, where ε is a very small number.

[0156] Eliminating Sub-Loop Constraints: Each maintenance team should find a single maintenance path, starting from the warehouse, repairing the damaged component, and then returning to the warehouse. However, due to the nature of the maintenance model, sub-loops may appear in the maintenance path, where connections between damaged components not connected to the warehouse form loops. To eliminate sub-loops in the maintenance path, this embodiment of the invention introduces a dummy variable. Its meaning is the order in which the maintenance team arrives at the damaged component d. Therefore, eliminating the constraints of the sub-loop is:

[0157]

[0158] in, Let d be the repair sequence value for the damaged component, and n be the number of damaged components in the set of damaged components.

[0159] The issue of maintenance personnel dispatching and the rapid recovery from a phase one electrical-electrical integrated energy failure are linked through the state of the damaged components, hence the following formula:

[0160]

[0161] K l,t =q d,t ,ib∈L (44)

[0162] ug i,t =q d,t ,j (45)

[0163] uz z,t =q z,t (46)

[0164] In the formula: q d,t It is a binary variable representing the state of the damaged component; ug i,t and uz z,t These represent binary variables representing the DG state and the natural gas pipeline state, respectively. Equation (43) shows the relationship between the state of the damaged component and its maintenance variable; Equation (44) shows the relationship between the state of the distribution network branch and the maintenance state of the damaged component; Equation (45) shows the relationship between the state of the distributed energy source and the maintenance state of the damaged component; Equation (46) shows the relationship between the state of the natural gas pipeline and the maintenance state of the damaged component. T d,k To determine the state of the damaged component d at time k, K l,t Let q be the state of branch l at time t.z,t This represents the operating status of the damaged natural gas pipeline at time t.

[0165] 204: Transform the model into a MISOCP problem for easy, fast and efficient solution, obtaining the optimal maintenance route and the operation of the tie switch in adjusting the optimal topology of the system as the maintenance plan progresses.

[0166] Step 204 includes:

[0167] 1) Solve the first-stage optimization model:

[0168] The optimization model for rapid recovery of the regional integrated electricity and gas energy system during the first phase of a disaster can be described as follows:

[0169] Objective function: Equation (1)

[0170] Constraints: Equations (2)-(14), (16)-(20), (22)-(28).

[0171] The optimization model contains nonlinear constraints that are difficult to solve directly. Therefore, it is linearized, transforming the optimization model into a MISOCP problem, which can be solved efficiently using a commercial solver. Solving the first-stage optimization model yields the optimal tie switch operation and the optimal system topology. The solved topology is then used as the initial topology for the second-stage maintenance strategy.

[0172] 2) Solve the second-stage optimization model:

[0173] The post-disaster second-stage regional electricity-gas integrated energy system network reconfiguration and maintenance scheduling optimization model can be described as follows:

[0174] Objective function: Equation (31)

[0175] Constraints: Equation (2)-Equation (14), Equation (16)-Equation (20), Equation (22)-Equation (28), Equation (32)-Equation (46).

[0176] The nonlinear constraints in the second-stage optimization model are linearized to transform it into a mixed-integer second-order cone programming problem. A commercial solver is then used to solve the second-stage optimization model to obtain the optimal maintenance path, the action status of the tie switch at each time step, and the corresponding optimal topology of PGIES.

[0177] In summary, this embodiment of the invention, through steps 201-204, addresses the recovery and maintenance of integrated power and gas energy systems under extreme natural disasters, and the different characteristics of fault recovery and fault repair in system load loss recovery. It establishes a two-stage coordinated optimization model for regional integrated power and gas energy system fault recovery and maintenance, dividing fault recovery and maintenance into two stages. In the first stage, the model achieves optimized power supply to the system via distributed generation (DG) by controlling the tie switches in the distribution system, and considers the recovery priority of different load levels in the system. In the second stage of maintenance and recovery, the optimal maintenance path is determined through clustering and simultaneously optimized with the network reconfiguration method, effectively shortening user power outage time and improving the system's recovery efficiency throughout the process.

[0178] Example 3

[0179] The feasibility of the solutions in Examples 1 and 2 is verified below with specific examples, as detailed in the following description:

[0180] This embodiment uses a modified IEEE-13 node distribution network and a 7-node natural gas network as examples to perform simulation analysis and verify the effectiveness of the method of the present invention. The system topology is as follows: Figure 3 As shown in the diagram. In this system, the peak electrical load is 5.22MW + 3.33MVar. The total installed capacity of DG is 4.00MW + 3.50MVar. The peak gas load is 1850Sm3 / h, and the total gas supply is 3800Sm3 / h. In the system, G1 is a photovoltaic power source; G2 and G3 are gas turbines; the compressor is an electrically driven compressor, powered by node 4 of the power system; the power system contains two tie switches T1 and T2. There are three maintenance stations in the entire system, each with one maintenance team, and power system maintenance personnel and natural gas system maintenance personnel cannot perform maintenance on each other. Assuming that a fault disconnects the distribution network from the upper-level transmission network, the maintenance time for the distribution lines and natural gas pipelines is 1 hour, and the maintenance time for the DG and compressors is 2 hours. In this example, t = 1 hour is used to represent the time step. The movement time of the maintenance team between the damaged components is proportional to their respective distances. System parameters are provided in the literature. [7] .

[0181] To verify the accuracy of this invention, the following three cases were compared:

[0182] Case 1: Analysis of the results of two-stage fault recovery and maintenance decision optimization.

[0183] To verify the effectiveness of the strategy proposed in Case 1, Scenario 1 is set up for analysis. Assume that the following faults occur in Scenario 1: In the power distribution network: branches 5-6, 8-9, 8-13, 2-7, and 7-12, and gas turbines G2 and G3 fail; In the natural gas network: pipelines 2-5, 4-7, and 5-6 fail.

[0184] Phase 1 Recovery Strategy Results: The dispatch center quickly collected fault information from both systems and then determined the optimal action for the tie switch: closing tie switch T2 while keeping tie switch T1 unchanged. This effectively and quickly restored power to the power-loss area and ensured that the system operated in a radial topology. The reconstructed system topology is shown below. Figure 4 As shown. By Figure 4 It can be seen that closing the tie switch T2 can supply power to nodes 7, 8, 10, and 11 across the broken branch 2-7. Among them, nodes 10 and 11 are important loads. It can be seen that the recovery strategy at this stage can effectively reduce the amount of system load reduction and prioritize the restoration of power supply to important loads.

[0185] The second phase of the maintenance strategy results: maintenance personnel began maintenance tasks according to the maintenance sequence determined by the dispatch center, and the dispatch center constantly adjusted the operation of the interconnection switch to optimize the topology of the entire system. The maintenance path is shown in Table 1. Figure 5 For a detailed restoration process of the system topology at different stages, the load reduction of the power system and natural gas system during maintenance is as follows: Figure 6 As shown.

[0186] Table 1 shows the repair paths for each repair team in Scenario 1.

[0187]

[0188] From hour 1 to hour 4, due to numerous damaged components, both the power and natural gas systems experienced significant load loss. At t=5h, G2 was repaired, and the load reduction in the power system began to decrease. In the natural gas system, P5 was repaired at t=4h, and could then... Figure 5 It can be seen that approximately 30% of the gas load was restored at this time. The repair time for P3 was at hour 8, by which time the natural gas load had fully returned to normal operation. At t=9h, gas turbine G3 was repaired, and most of the load in the power system had been restored. At t=12h, only branch 2-7 remained unrepaired, but the system had already returned to normal. Because the tie switch T1 was closed, even if branch 2-7 was not repaired, it did not affect the status of the loads connected to it; therefore, this branch had the lowest priority for repair during maintenance. Furthermore, the tie switch plays a crucial role in the effective restoration strategy. At hour 5, even though branch 8-9 was still in a faulty state, the system could reconnect node 9 to the power supply by reclosing the tie switch T1. As the repair work progressed, all loads in the integrated electric-gas energy system were fully restored.

[0189] In summary, when the system encounters a disaster, the use of the tie switch in the first stage can effectively prioritize the restoration of power supply to critical loads. In the second stage, the optimal maintenance route can also enable the system to return to normal status as quickly as possible. Scenario 1 demonstrates the effectiveness of the fault recovery and maintenance strategy for the integrated electric-gas energy system proposed in Case 1 in reducing load reduction costs.

[0190] Case 2: Analysis of the impact of the location of the repair station on the results of the repair strategy.

[0191] Because the time spent by the repair team traveling between damaged components affects the efficiency of the entire repair task, and consequently the recovery efficiency of the entire system, and because the location of the repair station affects the clustering of damaged components, even within the same cluster, different repair sequences can influence the entire repair process. Therefore, this case study assumes three scenarios: Scenario 2, Scenario 3, and Scenario 4, with the repair warehouse located as follows: Figure 7 As shown in Table 2, Scenario 2 and Scenario 3 have the same maintenance clustering. The load reduction costs under different scenarios are shown in Table 2. In Scenario 2, the maintenance station is closer to the damaged component, thereby reducing the time that maintenance personnel spend on the road. Therefore, it is reasonable that the load reduction cost of Scenario 2 is less than that of Scenario 3.

[0192] Table 2. Load Reduction Costs of Regional Electric-Gas Integrated Energy Systems

[0193]

[0194]

[0195] Comparing scenarios 1, 3, and 4 reveals that different warehouse locations lead to different clustering results, thus affecting overall maintenance efficiency. For example, in scenario 3, G2 and G3 are grouped into the same maintenance cluster and maintained by the same team of maintenance personnel, while in scenario 4, G2 and G3 are in different clusters. Scenario 3 prolongs the recovery time of the disaster recovery stations (DGs). Therefore, it can be demonstrated that maintenance routes are sensitive to the geographical location of maintenance stations. Planning reasonable maintenance station locations within a regional integrated power-gas energy system can effectively improve overall maintenance efficiency during disasters.

[0196] Case 3: Analysis of the impact of DG capacity on maintenance strategy results.

[0197] To investigate the impact of DG capacity on maintenance outcomes, scenarios 5 and 6 were set up in Case 3 for comparative analysis. In scenarios 5 and 6, the installed capacity of gas turbines G2 and G3 increased by 50% and decreased by 50%, respectively. Table 3 shows the optimal routes for the maintenance teams and the load reduction of the distribution network in scenarios 5 and 6. The most significant difference between scenarios 5 and 6 is that in scenario 6, the installed capacity of G1 is insufficient to meet the load of the system after repair, so the damaged DG needs to be repaired as soon as possible. Therefore, the second maintenance team prioritized the repair of the DG. In scenario 5, because the gas turbine has a larger installed capacity, more load can be restored. Therefore, after the maintenance team repaired gas turbine G2, they began to prioritize repairing the wire breakage fault. The comparison results of scenarios 5 and 6 demonstrate that the installed capacity of DG can affect the order of repairing damaged components.

[0198] Table 3 System maintenance paths and load reduction amounts for scenarios 5 and 6

[0199]

[0200] This invention proposes a coordinated optimization strategy for fault recovery and maintenance scheduling in a regional integrated power-gas energy system during and after a disaster. During the disaster phase, optimized power supply from distributed generation (DG) to the system is achieved by controlling the tie switches in the distribution system, prioritizing the restoration of critical loads. In the post-disaster maintenance scheduling phase, damaged components are clustered, an optimal maintenance plan is formulated, and a network reconfiguration method is used to simultaneously optimize the system topology during maintenance. Numerical examples verify the effectiveness of the proposed optimization model, leading to the conclusion that the proposed model can effectively shorten user power outage time and improve system recovery efficiency. Furthermore, the impact of maintenance station location and DG installed capacity on maintenance efficiency is investigated.

[0201] References

[0202] [1] Wang Weiliang, Wang Dan, Jia Hongjie, et al. A review of steady-state analysis of typical regional integrated energy systems under the background of energy internet [J]. Proceedings of the CSEE, 2016, 36(12): 3292-3305.

[0203] [2] Zhang An'an, Li Jing, Lin Dong, et al. Chain failure model of electro-gas coupled system considering the influence of the ultimate risk of natural gas pipeline network [J]. Proceedings of the CSEE, 2021, 41(21): 7275-7284.

[0204] [3] Mei Jianchun, Wei Zhinong, Zhang Yong, et al. Hybrid control method for integrated energy system with electrical-electric interconnection considering key fault screening [J]. Power System Technology, 2019, 43(1): 23-33.

[0205] [4] Wang Yingrui, Zeng Bo, Guo Jing, et al. Calculation method of multi-energy flow in integrated electric-heat-gas energy system [J]. Power System Technology, 2016, 40(10):2942-2951.

[0206] [5] Ma Rui, Wang Dashuo. Static security coupling analysis of multi-energy flow system considering natural gas N-1[J]. Proceedings of the CSEE, 2019, 39(6): 1627-1636.

[0207] [6] Bie Chaohong, Lin Chaofan, Li Gengfeng, et al. Development and prospect of resilient power systems under energy transition [J]. Proceedings of the CSEE, 2020, 40(9):2735-2745.

[0208] [7]Wang S, Sarker BR, Mann L, et al. Resource planning and a depotlocation model for electric power restoration[J]. European Journal ofOperational Research, 2004, 155(1):22-43.

[0209] Unless otherwise specified, the model numbers of the various devices in this embodiment of the invention are not limited, and any device that can perform the above functions is acceptable.

[0210] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of a preferred embodiment, and the sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0211] 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 within the protection scope of the present invention.

Claims

1. A two-stage fault restoration and repair method for regional electro-gas integrated energy systems, characterized in that, The method comprises: Considering the synergy of the power system and the natural gas system in the regional electricity-gas integrated energy system, the process from the system encountering an extreme disaster to the system returning to normal operation is divided into two stages; Based on the regional electricity-gas integrated energy system, according to the network operation constraints in the power distribution system, the operation constraints of various types of distributed power sources, the network reconfiguration constraints and the operation constraints in the natural gas network, a fault rapid recovery model of the emergency stage of the regional electricity-gas integrated energy system is constructed, and the optimal tie switch action condition is obtained by solving the model; According to the topological condition of the system after the tie switch on the line of the power distribution network in the first stage of emergency is operated, considering the related constraints of the maintenance personnel scheduling and the related constraints of the system in the first stage model, a network reconfiguration and maintenance scheduling optimization model of the second stage of the regional electricity-gas integrated energy system is established; The fault rapid recovery model, the network reconfiguration and maintenance scheduling optimization model are converted into a MISOCP problem, and the optimal maintenance route and the optimal tie switch action condition of the system are obtained with the adjustment of the maintenance plan; In the modeling of the natural gas system, a bidirectional gas flow model is adopted to obtain the pipeline flow result when the natural gas network fails; The bidirectional gas flow model is: ； ； ； ； ； ； wherein, is a binary variable representing the direction of gas flow, and are the maximum gas pressure values of natural gas nodes m and n, respectively, and are the low and high pressure values of the gas pressure in the pipeline mn, respectively, and are the gas pressure values of natural gas nodes m and n, respectively, is the maximum flow value of the pipeline mn; is the pipeline pressure to flow conversion constant; the gas pressure flow direction model is converted from a fixed direction to a bidirectional flow; ； The gas flow in the natural gas pipeline model flows from the high-pressure node to the low-pressure node, and the gas flow direction of the pipeline is flexible, which is suitable for the case that the pipeline flow direction changes under the fault condition. 2.The two-stage fault restoration and maintenance method for a regional electro-gas integrated energy system according to claim 1, characterized in that, The network reconfiguration constraint is: ； ； ； ； wherein, and denotes a binary variable for the order of branch ib flow, is a state variable for branch ib, is a state variable for node i, is a substation node, is a set of substations; N is a set of distribution network nodes; b is a node, is a set of distribution network branches. 3.The two-stage fault restoration and maintenance method for a regional electro-gas integrated energy system according to claim 1, characterized in that, The network reconfiguration and maintenance scheduling optimization model of the second stage of the regional electricity-gas integrated energy system comprises a damaged element clustering modeling: ； ； wherein, DNis a binary variable representing the distance between component d and warehouse o, DNis the set of damaged components, the constraint ensures that each component is only aggregated to one warehouse.

4. The two-stage fault restoration and maintenance method for a regional electro-gas integrated energy system according to claim 1, characterized in that, The network reconfiguration and maintenance scheduling optimization model of the second stage of the regional electricity-gas integrated energy system further comprises a constraint for eliminating sub-loops: ； wherein, is a repair sequence value for the damaged element d, is a number of damaged elements in the set of damaged elements, is a state variable for the repair team c from the damaged element point d to the damaged element point s, is a dummy variable; is a set of damaged elements o, is a set of repair teams.

5. The two-stage fault restoration and maintenance method for a regional electro-gas integrated energy system according to claim 1, characterized in that, The conversion of the fault rapid recovery model, the network reconfiguration and maintenance scheduling optimization model into a MISOCP problem to obtain the optimal maintenance route is: The optimal tie switch action condition and the optimal topological structure of the system are obtained by solving the first stage optimization model, and the solved topological structure is taken as the initial topological structure of the second stage maintenance strategy; The optimal maintenance path, the tie switch action condition at each time and the corresponding optimal topological structure of the PGIES are obtained by solving the second stage optimization model by using a commercial solver.

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