A multi-stage gas-electricity combined distribution network coordinated restoration method

Abstract

The present application relates to the technical field of gas-electricity combined system, and discloses a multi-stage gas-electricity combined distribution network coordinated recovery method, which first takes the minimization of the total cost of the gas-electricity combined distribution network as the target, establishes a gas-electricity combined distribution network system model considering each device and coupling relationship in the distribution / gas network and the distribution scheduling of maintenance personnel, establishes a dynamic island division model and a frequency reserve model, considers the unexpected and distributed new energy unit extreme output scene of the demand response ability and the phased development of the fault stage, forms a multi-stage gas-electricity combined distribution network coordinated recovery model, solves by using an improved step-by-step hedging algorithm, and is applied to an actual scene to form a decision tree result conforming to the unexpected condition. The present application can improve the ability of the gas-electricity combined distribution network to cope with extreme faults, reduce the influence and loss of natural disasters on the gas-electricity combined distribution network and its users, and has important research significance for formulating the gas-electricity combined distribution network coordinated recovery strategy.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of gas-electricity combined system, and particularly relates to a multi-stage gas-electricity combined distribution network coordinated recovery method considering unexpected conditions and dynamic island frequency adjustment. BACKGROUND

[0002] Natural gas, as a high-quality alternative energy source of fossil fuels, has been widely used in power generation. Through gas generator sets and power-to-gas (P2G) equipment, the mutual dependence between the gas system and the power system is increasingly strengthened. As the last mile of energy supply, the gas-electricity combined distribution network system has attracted great attention for improving the ability of the system to resist natural disasters.

[0003] The key to reducing the loss of gas-electricity combined distribution network under extreme disasters is to use multiple flexible resources for coordinated recovery, comprehensively consider the positive role of distributed generator sets, energy storage devices, network reconstruction, emergency resources, etc. of the gas-electricity combined distribution network on system recovery, and the frequency reserve recovery capability of distributed synchronous units in the gas-electricity combined island. At the same time, due to the stage-by-stage spread of disasters and the uncertainty of distributed new energy unit power generation, the multi-stage gas-electricity combined distribution network coordinated recovery method considering unexpected conditions and dynamic island frequency adjustment can ensure the effectiveness and robustness of the decision. Therefore, it is of great research significance to improve the response ability of the gas-electricity combined distribution network to extreme faults, reduce the impact and loss of extreme natural disasters on the gas-electricity combined distribution network and its users, and develop a gas-electricity combined distribution network coordinated recovery strategy.

[0004] At present, for the problem of power distribution network fault recovery, generally focuses on single-point fault recovery, such as using power distribution network reconstruction to recover the power-off load after single-point fault, which has deficiencies in the recovery of multiple-point faults formed in a short time under extreme events. And the existing research has a gap in the potential safety risks brought by the deep coupling of heterogeneous energy flow in the gas-electricity combined distribution network system, and does not consider the cascading failure problem of fault cross-system propagation. For the coordinated recovery optimization decision of the gas-electricity combined distribution network under fault, it is necessary to carry out overall modeling and unified scheduling. SUMMARY

[0005] The present application provides a multi-stage gas-electricity combined distribution network coordinated recovery method, which considers unexpected conditions and dynamic island frequency adjustment, can improve the response ability of the gas-electricity combined distribution network to extreme faults, reduce the impact and loss of extreme natural disasters on the gas-electricity combined distribution network and its users, and has important research significance for developing a gas-electricity combined distribution network coordinated recovery strategy. The technical scheme adopted by the present application is:

[0006] A multi-stage gas-electricity combined distribution network coordinated recovery method, specifically comprising the following steps:

[0007] Step 1: A model considering various devices in the power distribution network and the gas distribution network and the coupling relationship thereof is established with the minimum total cost of the combined power and gas distribution network as the target, and a combined power and gas distribution network system model is established while considering the distribution and scheduling of maintenance personnel;

[0008] Step 2: Based on the combined power and gas distribution network system model, power distribution network reconfiguration is added as an emergency resource;

[0009] Step 3: Based on step 2, a dynamic island division model and a frequency reserve model are established considering the frequency adjustment characteristics of the system;

[0010] Step 4: Based on the dynamic island division model and the frequency reserve model, the demand response capability of the combined power and gas distribution network is considered, including the demand response that can be reduced, the demand response that can be transferred and the demand response that can be replaced;

[0011] Step 5: Based on step 4, a multi-stage coordinated recovery model of the combined power and gas distribution network is formed considering the unexpectedness and extreme output scenarios of distributed new energy units in the fault stage;

[0012] Step 6: An improved step-by-step hedging algorithm is used to solve the multi-stage coordinated recovery model of the combined power and gas distribution network, and the method is applied to the actual scene of the coordinated recovery of the combined power and gas distribution network to form a decision tree result that meets the unexpected conditions.

[0013] Further, in step 1, the objective function of the combined power and gas distribution network system model is the minimization of the total cost of the combined power and gas distribution network, and the objective function is as follows:

[0014]

[0015] In the formula, t is the time index; j is the power distribution network node index; n is the gas distribution network node index; c is the distributed gas / coal-fired generator index; e is the curve segment index; C j is the unit loss load penalty cost of the power distribution network j node; n is the unit loss load penalty cost of the gas distribution network n node; is the unit cost of power purchase of the power distribution network from the upper-level power grid, is the unit cost of gas purchase of the gas distribution network from the upper-level gas grid; is the fuel cost of the distributed unit c; ce is the cost coefficient of the distributed unit c segment e; is the loss load power of the power distribution network j node at time t; is the loss load volume of the gas distribution network n node at time t; is the power purchase amount of the power distribution network from the upper-level power grid, is the gas purchase amount of the gas distribution network from the upper-level gas grid; P cetPc,e,t is the power of distributed generator c on segment e at time t; SU ct and SD ct are the start-up fuel consumption and shut-down fuel consumption of distributed generator c at time t, respectively.

[0016] Further, the constraint conditions of the gas-electricity combined distribution network system model include gas-electricity combined distribution network operation constraints, coupling constraints and gas-electricity combined distribution network fault maintenance constraints.

[0017] The gas-electricity combined distribution network operation constraints include distribution network node power balance constraints, distribution network power flow constraints, distributed generator constraints, gas network node balance constraints, gas network power flow constraints, energy storage constraints and gas-electricity combined load loss constraints; specifically as follows:

[0018] 1) Distribution network node power balance constraints:

[0019]

[0020] wherein g is the index of the electric-to-gas equipment; k is the index of the distribution network node; w is the index of the distributed wind turbine; ij and jk are the indexes of the lines, representing the distribution network line (i, j) and the distribution network line (j, k), respectively; Ω j is the set of equipment connected to the distribution network node j; is the set of child nodes of the distribution network node j; and represent the active load and the reactive load of the distribution network node j at time t, respectively; ρ jt is the active / reactive load factor of the distribution network node j at time t; is the frequency adjustment power deficiency of the distribution network node j at time t; is the demand response of the distribution network node j at time t; P gt is the power consumed by the electric-to-gas equipment g at time t; P ij,t and P jk,t are the active power transmitted by the distribution network lines (i, j) and (j, k) at time t; Q ij,t and Q jk,t are the reactive power transmitted by the distribution network lines (i, j) and (j, k) at time t; P ct and Q ct are the active power and the reactive power output by the distributed generator c at time t; P wt and Q wt are the active power and the reactive power output by the distributed wind turbine w at time t;

[0021] 2) Distribution network power flow constraints:

[0022] -M·(1-a ij,t )≤v it-v jt -(r ij ij,t +x ij ij,t )≤M·(1-a ij,t )

[0023]

[0024] where (·) min / max denotes the minimum / maximum value; M is a sufficiently large real number; a ij,t denotes the state of the distribution network line (i, j) at time t; v it and v jt are the voltage values of nodes i and j at time t, respectively; r ij and x ij are the resistance and reactance values of the distribution network line (i, j), respectively; and are the active power and reactive power maximum values of the distribution network line (i, j), respectively, is the maximum purchase of electricity by the distribution network from the upper-level power grid, is the reactive power exchange between the distribution network and the upper-level power grid, is the maximum reactive power exchange between the distribution network and the upper-level power grid; and are the minimum and maximum values of the voltage of node j, respectively;

[0025] 3) Distributed generator constraint:

[0026]

[0027] SU ct = su c ·(I ct -I c,t-1 ), SU ct ≥ 0

[0028] SD ct = sd c ·(I c,t-1 -I ct ), SD ct ≥ 0

[0029]

[0030] P ct =∑ e P cet

[0031]

[0032] where I ct ​​denotes the start-stop state of distributed generator c at time t; and denote the minimum and maximum active power output of distributed generator c, respectively; and denote the minimum and maximum reactive power output of distributed generator c, respectively; UR c and DR c denote the up and down ramp rates of distributed generator c; and denote the start-up and shut-down counting times of distributed generator c at time t; and denote the minimum start-up and shut-down times of distributed generator c at time t; su c and sd c denote the start-up and shut-down fuel consumption parameters of distributed generator c; f denotes the predicted value; denotes the maximum power of distributed generator c at time t on segment e, denotes the maximum reactive power of distributed wind generator w;

[0033] 4) Gas network node balance constraint:

[0034]

[0035] where s is the storage device index; o is the gas network node index; mn and no are the gas network pipeline indices, representing the gas network pipelines (m, n) and (n, o), respectively; Ω n denotes the set of devices connected to gas network node n; denotes the set of child nodes of gas network node n; G gt denotes the amount of natural gas produced by electric-to-gas device g at time t; and denote the outflow and inflow amounts of natural gas of storage device s at time t, respectively; denotes the demand response amount of gas network node n at time t; G mn,t and G no,t denote the transmission amounts of natural gas of gas network pipelines (m, n) and (n, o) at time t; G ct denotes the amount of natural gas consumed by distributed generator c at time t; denotes the predicted value of the natural gas load of gas network node n at time t; denotes the loss of load volume of gas network node n at time t;

[0036] 5) Gas network power flow constraint:

[0037]

[0038] wherein a mn,t denotes the state of the gas distribution network pipe (m, n); K mn is the Weymouth coefficient of the gas distribution network pipe (m, n); π mt and π nt denote the gas pressure at the nodes m and n of the gas distribution network, respectively; and denote the minimum and maximum values of the gas pressure at the node n of the gas distribution network, respectively; is the maximum value of the gas distribution network pipe (m, n) and the transmitted gas quantity;

[0039] 6) Energy storage constraint:

[0040]

[0041]

[0042] wherein E st denotes the capacity of the gas storage device s at time t; and denote the inflow and outflow natural gas efficiency of the gas storage device s, respectively; and denote the minimum and maximum values of the capacity of the gas storage device s, respectively; and are the minimum and maximum values of the outflow or inflow gas quantity of the gas storage device s, respectively;

[0043] 7) Gas-electricity combined loss-of-load constraint:

[0044]

[0045] The coupling constraints include distributed unit coupling constraints and electricity-to-gas device constraints, and are specifically as follows:

[0046] 1) Distributed unit coupling constraint:

[0047] G ct = (∑ e C ce · P cet + SU ct + SD ct ) / HHV, c e Ω GU

[0048] wherein HHV is the high calorific value coefficient of natural gas; Ω GU is the set of gas units;

[0049] 2) Electricity-to-gas device coupling constraint:

[0050] G gt = (φ · P gt·η g ) / HHV

[0051]

[0052] where φ is the energy conversion coefficient; η g is the energy conversion efficiency of the electric-to-gas equipment g; is the maximum value of the power consumed by the electric-to-gas equipment g;

[0053] The combined power and gas distribution network fault repair constraints include repair personnel constraints and repair time constraints, and are specifically as follows:

[0054] 1) Repair personnel scheduling constraints:

[0055]

[0056] where p represents the repair personnel index; μ e and μ g represent the distribution network and gas network repair station positions, respectively; Ω AN and Ω GN represent the distribution network fault set and the gas network fault set, respectively; Λ ij,jk,p represents the path of repair personnel p, and if from the distribution network line (i, j) to the distribution network line (j, k) is faulty, then Λ ij,jk,p = 1, otherwise Λ ij,jk,p = 0; N A and N G represent the number of faults in the distribution network and the gas network, respectively; and represent the node potential energy of the faulty distribution network lines (i, j) and (j, k), respectively; and represent the node potential energy of the faulty gas network lines (m, n) and (n, o), respectively; Λ mn,no,p represents the path of repair personnel p, and if from the gas network line (m, n) to the gas network line (n, o) is faulty, then Λ mn,no,p = 1, otherwise Λ mn,no,p = 0; represents that repair personnel p departs from the repair station to the distribution network line (i, j) that is faulty; represents that repair personnel p departs from the repair station to the gas network line (m, n) that is faulty;

[0057] 2) Repair time constraints:

[0058]

[0059] where d is the fault stage index; Ω AN and Ω GNrespectively represent the fault set of the power distribution network and the gas distribution network; and respectively represent the fault set of the d-stage power distribution network and the gas distribution network; and respectively represent the time for repairman p to arrive at the fault of the power distribution network line (i, j) and (j, k); and respectively represent the time for repairman p to arrive at the fault of the gas distribution network line (m, n) and (n, o); represents the repair time of repairman p for the fault of the power distribution network line (i, j), represents the repair time of repairman p for the fault of the gas distribution network line (m, n); represents the travel time of repairman p from the fault of the power distribution network line (i, j) to (j, k); represents the travel time of repairman p from the fault of the gas distribution network line (m, n) to (n, o); d represents the d-stage fault occurrence time; F ij,p and F mn,p respectively represent whether repairman p arrives at (i, j) and (m, n); and are 0-1 variables, indicating whether (i, j) and (m, n) are repaired at time t; ε is a very small real number.

[0060] Further, the mathematical model corresponding to the network reconstruction in step 2 is represented as follows:

[0061] Network reconstruction constraints:

[0062]

[0063] -M·a ij,t ≤P′ ij,t ≤M·a ij,t

[0064]

[0065] In the formula, Ω L is a set of power distribution network lines; Ω Γ is a set of reconstructed tie switches; N is the number of nodes of the power distribution network; β jt represents whether node j of the power distribution network is a root node at time t; P' ij,t and P j ' k,t respectively represent the virtual power flow of the power distribution network lines (i, j) and (j, k); represents whether the state of the tie switch on the power distribution network line (i, j) changes at time t; N total,maxReconstruct the maximum number of actions allowed in the full period.

[0066] Further, the dynamic island partition model considering the frequency adjustment characteristics in step 3 and the frequency reserve model are mathematically expressed as follows:

[0067] 1) Dynamic island partition:

[0068]

[0069] λ iht ·λ jht =a ij,t

[0070]

[0071] y ij,h,t ≤λ iht

[0072] y ij,h,t ≤λ jht

[0073] y ij,h,t ≥λ iht -λ jht +1

[0074] y ij,h,t ≥λ iht +λ jht -1

[0075] α ht ≤∑ j λ jht

[0076]

[0077] In the formula, h is the dynamic island index; Ω H is the island set; Ω DG is the distributed generator node set; λ jht and λ iht respectively represent whether the distribution network node j and i at time t belongs to the dynamic island h; y ij,h,t represents whether the distribution network line (i,j) at time t belongs to the dynamic island h; α ht represents whether the dynamic island h exists at time t; represents whether the dynamic island h contains the distributed generator at time t;

[0078] 2) Frequency reserve constraint:

[0079]

[0080]

[0081] Ω h denotes the set of devices connected to the dynamic island h; denotes the power disturbance of the distribution network node j at time t; H h is the inertia of the dynamic island h; t db and t nad are the frequency adjustment dead zone time and the frequency minimum point time; f(0) and f(t nad ) denote the initial time frequency and the frequency at t nad ; f 0 , f nad and f db denote the reference frequency, the frequency of the minimum point and the frequency at the end of the dead zone time, respectively; denotes the upper reserve of the distributed unit c at time t, denotes the maximum value of the upper reserve of the distributed unit c; J c denotes the time constant of the distributed unit c; γ denotes the frequency change rate, γ max denotes the maximum value of the frequency change rate; UR c is the upper ramp rate of the distributed unit c.

[0082] Further, the demand response constraint in step 4 is expressed as follows:

[0083]

[0084]

[0085] α rl = (α e · η e ) / (α g · η g )

[0086] Ω RL is the replaceable load node set; and denote the reducible, transferable and replaceable electric load demand response of the distribution network node j at time t, respectively; denote the reducible, transferable and replaceable gas load demand response, respectively; and denote the electric load and gas load demand response coefficients, respectively; denotes the maximum value of the reducible electric load demand response of the distribution network node j; denotes the maximum value of the reducible gas load demand response of the gas distribution network node n; and denote the electric load transfer-out and transfer-in demand response of the distribution network node j at time t, respectively; and respectively represent the gas load shedding and the load restoration demand response of the gas grid node n at time t; and respectively represent the load shedding and the load restoration state of the electric grid node j at time t; and respectively represent the gas load shedding and the load restoration state of the gas grid node n at time t; and respectively represent the minimum and maximum of the load shedding demand response of the electric grid node j; and respectively represent the minimum and maximum of the load shedding demand response of the gas grid node n; and respectively represent the minimum and maximum of the load restoration demand response of the electric grid node j; and respectively represent the minimum and maximum of the load restoration demand response of the gas grid node n; represents the maximum of the load shedding demand response of the electric grid node j; represents the maximum of the load shedding demand response of the gas grid node n; α rl is the alternative load coefficient; α e and α g are the electric and gas unit heat values; η e and η g are the electric and gas energy conversion efficiencies.

[0087] Further, the mathematical model corresponding to the multi-stage gas-electricity combined distribution network coordinated restoration model in step 5 is represented as follows:

[0088]

[0089] wherein d is the fault stage index; δ and θ are the fault scenario indexes; and σ is the wind power scenario index; S is the wind power scenario set; p dδ is the probability of the fault condition δ in the d stage; is the wind power scenario under the fault condition δ in the d stage; ξ represents the phased realization of the fault uncertainty; is the continuous variable under the wind power scenario under the fault condition δ in the d stage; is the load shedding under the wind power scenario under the fault condition δ in the d stage; a dδ , b dδ , c dδ , A, B, C, D d , E d and l dδto represent abstract matrix and vector; and respectively represent the decision under fault uncertainty ξ dδ and ξ dθ influence; z dδσ is the decision under fault scenario σ at stage d, and the decision under fault scenario σ at stage d. .

[0090] Further, in step 6, the improved step-by-step hedging algorithm is used to solve the multi-stage gas-electricity joint distribution network coordinated restoration model, which is specifically as follows:

[0091] Step 6.1: parameter initialization; let the iteration number v <- 0, and the parameter and calculate the decision under each fault scenario: wherein u d is the d-stage decision tree node; represents the iteration multiplier corresponding to u d , and is the decision of fault scenario δ at iteration number v+1;

[0092] Step 6.2: update the iteration number v <- v+1;

[0093] Step 6.3: aggregate the d-stage decision tree node u d decision to obtain the reference decision coefficient:

[0094] wherein, is the reference decision corresponding to u d , and is the decision tree node set of the d-stage uncertainty ξ, is the probability corresponding to u d , and is the solution decision corresponding to u d .

[0095] Step 6.4: for each fault scenario, update the parameter: wherein ζ is the penalty coefficient;

[0096] Step 6.5: decouple to calculate the decision of each fault scenario:

[0097]

[0098] Step 6.6: iteration exit condition: if the decision corresponding to each scenario tree node is equal, exit the iteration; otherwise, fix the decision corresponding to the equal scenario tree node as a constant, and return to step 6.2.

[0099] ​The application has the following advantages and beneficial effects:

[0100] (1) The multi-stage gas-electricity combined distribution network coordinated recovery method considering unexpected conditions and dynamic island frequency adjustment can comprehensively consider the positive effects of distributed generator units, energy storage devices, network reconstruction, emergency resources, etc. on system recovery, as well as the frequency reserve recovery capability of gas-electricity load demand response and distributed synchronous units in a gas-electricity combined island, and can more effectively recover the lost load caused by extreme faults and ensure the energy supply of the system.

[0101] (2) The multi-stage gas-electricity combined distribution network coordinated recovery method considering unexpected conditions and dynamic island frequency adjustment can consider the stage development of faults and the uncertainty of distributed new energy unit output, improve the response ability of the gas-electricity combined distribution network to actual situations, and improve the efficiency of system recovery.

[0102] (3) The improved step-by-step hedging algorithm for solving the multi-stage gas-electricity combined distribution network coordinated recovery model considering unexpected conditions and dynamic island frequency adjustment can reduce the difficulty of model solving, thereby improving the efficiency of actual decision making. BRIEF DESCRIPTION OF DRAWINGS

[0103] Figure 1 The figure is a schematic diagram of the gas-electricity combined distribution network of the application.

[0104] Figure 2 The figure is a schematic diagram of island division of the embodiment of the application.

[0105] Figure 3 The figure is a demand response analysis diagram of the embodiment of the application.

[0106] Figure 4 The figure is a fault scenario setting diagram of the embodiment of the application. DETAILED DESCRIPTION

[0107] The application will be further described below in combination with the drawings and specific embodiments.

[0108] The multi-stage gas-electricity combined distribution network coordinated recovery method considering unexpected conditions and dynamic island frequency adjustment of the application comprehensively considers the positive effects of distributed generator units, energy storage devices, network reconstruction, emergency resources, etc. on system recovery, as well as the frequency reserve recovery capability of gas-electricity load demand response and distributed synchronous units in a gas-electricity combined island, and considers the extreme situation of distributed new energy output and the randomness of stage development of gas-electricity combined distribution network faults, proposes a multi-stage gas-electricity combined distribution network coordinated recovery method considering unexpected conditions and dynamic island frequency adjustment, and solves it by using an improved step-by-step hedging algorithm. The construction method includes the following steps:

[0109] Step 1: A model considering various devices in the power distribution network and the gas distribution network and their coupling relationship is established to minimize the total cost of the combined power and gas distribution network, and a combined power and gas distribution network system model is established considering the distribution of maintenance personnel;

[0110] The objective function of the established combined power and gas distribution network system model is to minimize the total cost of the combined power and gas distribution network, under the premise of ensuring system stability:

[0111]

[0112] In the formula, t is the time index; j is the power distribution network node index; n is the gas distribution network node index; c is the index of the distributed gas / coal-fired generator; e is the curve segment index; C j is the unit loss load penalty cost of the power distribution network j node; C n is the unit loss load penalty cost of the gas distribution network n node; are respectively the unit purchase cost of electricity / gas of the power distribution network / gas distribution network to the superior power / gas network; is the fuel cost of the distributed unit c; C ce is the cost coefficient of the distributed unit c segment e; is the loss load power of the power distribution network j node at time t; is the loss load volume of the gas distribution network n node at time t; are respectively the purchase amount of electricity / gas of the power distribution network / gas distribution network to the superior power / gas network; P cet is the power of the distributed unit c on segment e at time t; SU ct , SD ct are respectively the start / stop fuel consumption of the distributed unit c at time t.

[0113] The constraint conditions of the combined power and gas distribution network system model include the combined power and gas distribution network operation constraint, coupling constraint and combined power and gas distribution network fault maintenance constraint.

[0114] Among them, the combined power and gas distribution network operation constraint includes the power distribution network node power balance constraint, power distribution network power flow constraint, distributed unit constraint, gas distribution network node balance constraint, gas distribution network power flow constraint, energy storage constraint, combined power and gas loss load constraint; the coupling constraint includes the distributed unit coupling constraint and the electric-to-gas device constraint; the combined power and gas distribution network maintenance constraint includes the maintenance personnel constraint and the maintenance time constraint.

[0115] (1) Combined power and gas distribution network operation constraint

[0116] 1) Power distribution network node power balance constraint

[0117]

[0118] where g is the index of the electric-gas conversion equipment; k is the index of the distribution network node; w is the index of the distributed wind turbine; ij, jk are the indices of the lines, representing the lines (i, j) and (j, k), respectively; Ω j is the set of equipment connected to the distribution network node j; is the set of child nodes of the distribution network node j; Pj, Qj represent the active and reactive power demand of the distribution network node j at time t, respectively; ρ jt is the active / reactive power coefficient of the distribution network node j at time t; is the frequency regulation power deficiency of the distribution network node j at time t; is the demand response of the distribution network node j at time t; P gt is the power consumed by the electric-gas conversion equipment g at time t; P ij,t , P jk,t is the active power transmitted by the distribution network lines (i, j) and (j, k) at time t; Q ij,t , Q jk,t is the reactive power transmitted by the distribution network lines (i, j) and (j, k) at time t; P ct , Q ct is the active / reactive power output by the distributed generator c at time t; P wt , Q wt is the active / reactive power output by the distributed wind turbine w at time t.

[0119] 2) Distribution network power flow constraints:

[0120] - M · (1 - a ij,t ) ≤ v it - v jt - (r ij · P ij,t + x ij · Q ij,t ) ≤ M · (1 - a ij,t )

[0121]

[0122] where (·) min / max denotes the minimum / maximum; M is a sufficiently large real number; a ij,t denotes the state of the line (i, j) at time t; v it , v jt are the voltage values of the nodes i, j at time t; r ij , x ij are the resistance and reactance values of the line (i, j), respectively. and are the active power and reactive power maximum values of the distribution network line (i, j), respectively, Pmax,up Qmax,up Qmax,up Qmax,up Vmin,j Vmax,j

[0123] 3) Distributed generator constraints:

[0124]

[0125] SU ct = su c · (I ct - I c,t-1 ), SU ct ≥ 0

[0126] SD ct = sd c · (I c,t-1 - I ct ), SD ct ≥ 0

[0127]

[0128] P ct = ∑ e P cet

[0129]

[0130] where I ct denotes the start-up / shut-down status of distributed generator c at time t; UR c , DR c are the up / down ramp rates of distributed generator c; is the on and off counting time of distributed generator c at time t; is the minimum on / off time of distributed generator c at time t; su c , sd c are the start-up / shut-down fuel consumption parameters of distributed generator c; (·) f denotes the predicted value.

[0131] 4) Gas network node balance constraints:

[0132]

[0133] where s is the gas storage device index; o is the gas network node index; mn, no are the gas network pipeline indices, denoting pipelines (m, n), (n, o); Ω n denotes the set of devices connected to gas network node n; is the set of child nodes of the gas distribution network node n; G gt is the amount of natural gas produced by the electric-to-gas device g at time t; is the amount of natural gas flowing out / in of the storage device s at time t; is the demand response amount of the gas distribution network node n at time t; G mn,t , G no,t is the amount of natural gas transmitted by the gas distribution network pipelines (m, n), (n, o) at time t; G ct is the amount of natural gas consumed by the distributed generator c at time t.

[0134] 5) Gas distribution network power flow constraints:

[0135]

[0136] wherein a mn,t represents the state of the gas distribution network pipeline (m, n); K mn is the Weymouth coefficient of the gas distribution network pipeline (m, n); π mt , π nt respectively represent the gas pressure of the gas distribution network nodes m, n.

[0137] 6) Energy storage constraints:

[0138]

[0139] wherein E st represents the capacity of the storage device s at time t; represents the inflow / outflow natural gas efficiency of the storage device s.

[0140] 7) Loss of load constraints:

[0141]

[0142] (2) Coupling constraints

[0143] 1) Distributed generator coupling constraints:

[0144] G ct = (∑ e C ce · P cet + SU ct + SD ct ) / HHV, c e Ω GU

[0145] wherein HHV is the high heating value coefficient of natural gas; Ω GU is the set of gas-fired generators.

[0146] 2) Electric-to-gas device coupling constraints:

[0147] Ggt = (φ · P gt · η g ) / HHV

[0148]

[0149] where φ is the energy conversion factor; η g is the energy conversion efficiency of the electric-gas conversion equipment g.

[0150] (3) Fault maintenance constraints of the combined electric-gas distribution network

[0151] 1) Maintenance personnel scheduling constraints:

[0152]

[0153]

[0154] where p represents the maintenance personnel index; μ e , μ g represent the distribution network / gas distribution network maintenance station positions, respectively; Ω AN , Ω GN represent the distribution network / gas distribution network fault sets, respectively; Λ ij,jk,p represents the maintenance personnel p path, and if from fault line (i, j) to fault line (j, k), then Λ ij,jk,p = 1; N A , N G represent the number of distribution network / gas distribution network faults, respectively; and represent the node potential energy of the distribution network line (i, j) and (j, k) of the fault, respectively; and represent the node potential energy of the gas distribution network line (m, n) and (n, o) of the fault, respectively.

[0155] 2) Maintenance time constraints:

[0156]

[0157] where d is the fault stage index; represent the d-stage fault sets, respectively; represent the time for maintenance personnel p to arrive at faults (i, j) and (m, n), respectively; represent the maintenance time of maintenance personnel p for faults (i, j) and (m, n), respectively; represent the travel time of maintenance personnel p from (i, j) to (j, k) and from (m, n) to (n, o), respectively; T d represents the d-stage fault occurrence time; F ij,p , F mn,prespectively represent whether the maintenance personnel p reaches (i, j) and (m, n); is a 0-1 variable, indicating whether the faults (i, j) and (m, n) are repaired at time t; ε is a very small real number.

[0158] Step 2: Based on the gas-electricity combined distribution network system model established in step 1, add distribution network reconfiguration as an emergency resource.

[0159] The mathematical model corresponding to the network reconfiguration, i.e. the network reconfiguration constraint, is as follows:

[0160]

[0161] -M·a ij,t ≤P′ ij,t ≤M·a ij,t

[0162]

[0163] In the formula, Ω L is a line set; Ω Γ is a reconfiguration tie switch set; N is the number of nodes of the distribution network; β jt represents whether node j is a root node at time t; P' ij,t is the virtual power flow of line (i, j); represents whether the state of the tie switch on line (i, j) of the distribution network changes at time t; N total,max is the maximum number of actions allowed by reconfiguration in the whole period.

[0164] Step 3: On the basis of step 2, considering the frequency adjustment characteristics of the system, a dynamic island division model and a frequency reserve model are established.

[0165] The dynamic island division model and the frequency reserve model considering the frequency adjustment characteristics are mathematically expressed as follows:

[0166] 1) Dynamic island division:

[0167]

[0168] λ iht ·λ jht =a ij,t

[0169]

[0170] y ij,h,t ≤λ iht

[0171] y ij,h,t ≤λ jht

[0172] y ij,h,t ≥λ iht -λ jht +1

[0173] y ij,h,t ≥λ iht +λ jht -1

[0174] α ht ≤∑ j λ jht

[0175]

[0176] where h is the dynamic island index; Ω H is the island set; Ω DG is the distributed generator node set; λ jht denotes whether node j belongs to dynamic island h at time t; y ij,h,t denotes whether line (i, j) belongs to dynamic island h at time t; α ht denotes whether dynamic island h exists at time t; denotes whether dynamic island h contains distributed generators at time t.

[0177] 2) Frequency reserve constraint:

[0178]

[0179] where Ω h denotes the set of devices connected to dynamic island h; denotes the power disturbance of node j at time t; H h is the inertia of dynamic island h; t db , t nad is the frequency adjustment dead zone time and the frequency minimum point time; f(0), f(t nad ) denotes the initial time and the frequency at t nad ; f 0 , f nad , f db denote the reference frequency, the frequency at the minimum point, and the frequency at the end of the dead zone time, respectively; denotes the upward reserve of distributed generator c at time t; J c denotes the time constant of distributed generator c; γ denotes the rate of change of frequency (RoCoF).

[0180] Step 4: Based on step 3, consider the demand response capability of the gas-electricity combined distribution network, including reducible, transferable, and replaceable demand response.

[0181] The demand response constraint is represented as follows:

[0182]

[0183] α rl = (α e · η e ) / (α g · η g )

[0184] In the formula, Ω RL is a replaceable load node set; and respectively represent the curable, transferable, and replaceable electrical load demand response of the distribution network node j at time t; respectively represent the curable, transferable, and replaceable gas load demand response; and respectively represent the electrical load and gas load demand response coefficients; represents the maximum value of the curable electrical load demand response of the distribution network node j; represents the maximum value of the curable gas load demand response of the gas distribution network node n; and respectively represent the electrical load export and import demand response of the distribution network node j at time t; and respectively represent the gas load export and import demand response of the gas distribution network node n at time t; and respectively represent the electrical load export state and import state of the distribution network node j at time t; and respectively represent the gas load export state and import state of the gas distribution network node n at time t; and respectively represent the minimum value and maximum value of the electrical load export demand response of the distribution network node j; and respectively represent the minimum value and maximum value of the gas load export demand response of the gas distribution network node n; and respectively represent the minimum value and maximum value of the electrical load import demand response of the distribution network node j; and respectively represent the minimum value and maximum value of the gas load import demand response of the gas distribution network node n; represents the maximum value of the transferable electrical load demand response of the distribution network node j; represents the maximum value of the transferable gas load demand response of the gas distribution network node n; α rl is a replaceable load coefficient; α e and α g are the electrical unit heat value and the gas unit heat value; η e and η gFor the electric energy conversion efficiency and the gas energy conversion efficiency.

[0185] Step 5: On the basis of step 4, considering the unexpectedness of the phased development of the fault and the extreme output scene of the distributed new energy unit, a multi-stage gas-electricity joint distribution network coordinated recovery model considering unexpected conditions and dynamic island frequency adjustment is formed.

[0186] Preferably, considering the unexpectedness of the phased development of the fault and the extreme output scene of the distributed new energy unit, a multi-stage gas-electricity joint distribution network coordinated recovery model considering unexpected conditions and dynamic island frequency adjustment is formed, which ensures the robustness of the decision to cope with the fault and the uncertainty of the basic output of new energy. The corresponding mathematical model is as follows:

[0187]

[0188] In the formula, p dδ is the probability of the d-phase fault condition δ; is the wind power scene The probability of the d-phase fault condition δ; ξ represents the phased realization of the fault uncertainty.

[0189] Step 6: The model proposed in step 5 is solved by using an improved step-by-step hedging algorithm, and the proposed method is applied to an actual scene to form a decision tree result that meets the unexpected conditions, ensuring the effectiveness and robustness of the recovery strategy.

[0190] The multi-stage gas-electricity joint distribution network coordinated recovery model proposed in step 5 is difficult to solve, in order to ensure the solving efficiency of the proposed model, an improved step-by-step hedging algorithm is proposed to solve, and the specific model is as follows:

[0191] Step 6.1: Parameter initialization. Let the iteration number v <- 0, and the parameter and calculate the decision under each fault scene:

[0192] Where, u d is the d-phase decision tree node; represents the iteration multiplier corresponding to u d , is the decision of the fault scene δ at the iteration number v+1.

[0193] Step 6.2: Update the iteration number v <- v+1.

[0194] Step 6.3: Aggregate the d-phase decision tree node u d Decision, get the reference decision coefficient:

[0195] Where, is the reference decision corresponding to u d , a set of decision tree nodes for the d-phase uncertain quantity ξ, for u d the corresponding probability, for u d the corresponding solution decision.

[0196] Step 6.4: update the parameters for each failure scenario: where ζ is a penalty coefficient.

[0197] Step 6.5: decoupling calculation of each failure scenario decision:

[0198]

[0199] Step 6.6: iteration exit condition: if the corresponding decision of each scenario tree node is equal, exit the iteration. Otherwise, fix the corresponding decision of the scenario tree node that is equal as a constant, and go back to step 6.2. Step 6.6: iteration exit condition: if the corresponding decision of each scenario tree node is equal, exit the iteration. Otherwise, fix the corresponding decision of the scenario tree node that is equal as a constant, and go back to step 6.2.

[0200] Example analysis:

[0201] The schematic diagram of the system is shown in Figure 1 The system includes 2 distributed wind turbine units, 3 distributed coal-fired units, 2 distributed gas-fired units, 5 tie switches, 1 gas storage device, and 1 electric-to-gas device. It is assumed that the system failure is divided into three stages under extreme disasters.

[0202] The present application adopts 5 scenarios to solve the deterministic gas-electricity combined distribution network collaborative recovery strategy. The elements considered in each scheme are shown in Table 1. The total cost and load loss of the above 5 schemes are shown in Table 2.

[0203] Table 1. Elements included in each scheme

[0204]

[0205]

[0206] The price parameter settings for this example are shown in Table 2.

[0207] Table 2. Comparison of total cost and load loss of each scheme

[0208]

[0209] According to step one: setting scheme 1 to solve, after the occurrence of extreme disasters, if only the gas-electricity combined distribution network failure maintenance is considered, the system will lose a total of 15.70 MWh of load, 503.27 kcf, causing an economic loss of 1922 million yuan. Based on scheme 1, considering the role of electric-to-gas devices and gas storage devices, the overall cost of the system is reduced, and the load loss is reduced.

[0210] According to step two: add network reconfiguration as an emergency resource on the basis of scheme 2. While repairing the gas-electricity combined distribution network, through network reconfiguration, the island topology of the gas-electricity combined distribution network can be adjusted to achieve partial load recovery.

[0211] According to step three: add the frequency adjustment characteristics of the gas-electricity combined distribution network system on the basis of scheme 2, so as to use the frequency reserve for partial load recovery under extreme faults. The dynamic island division result is shown in Figure 2 , and the stability of the frequency under the frequency adjustment characteristics is verified through actual simulation. Compared with scheme 3, scheme 4 can reduce 0.31 MWh of electric load loss.

[0212] According to step four: add the demand response of the gas-electricity combined distribution network load on the basis of scheme 4, including the curtailed, transferred and replaceable demand responses. The analysis, parameter setting and results of the three types of demand responses are shown in Table 3, Figure 3 .

[0213] Table 3. Setting coefficients of various types of demand responses in each scheme

[0214]

[0215] According to steps five and six: consider adding the unexpectedness of the phased development of faults and the extreme output scenarios of distributed new energy units on the basis of scheme 5, wherein the fault scenario setting is shown in Figure 4 , and an improved step-by-step hedging algorithm is used for solving. In order to more clearly illustrate the effectiveness of the method, schemes 6-7 are set on the basis of scheme 5, as shown in Table 4. The calculation results are shown in Table 5.

[0216] Table 4. Elements contained in each scheme

[0217]

[0218] Table 5. Comparison of total cost, expected load loss and worst-case scenario load loss of each scheme

[0219]

[0220] It can be seen that the total cost of scheme 8 is significantly reduced compared with scheme 6, and the result obtained by solving is a decision tree, and the ability to cope with fault scenarios is improved. Compared with scheme 7, the cost of scheme 8 is slightly higher, but it ensures smaller load loss in the worst-case scenario and has higher robustness.

Claims

1. A multi-stage gas-electric combined network coordination recovery method, characterized in that, Specifically comprising the following steps: Step 1: A model considering various devices in the power distribution network and the gas distribution network and the coupling relationship thereof is established with the minimum total cost of the combined power and gas distribution network as the target, and a combined power and gas distribution network system model is established while considering the distribution and scheduling of maintenance personnel; Step 2: Based on the combined power and gas distribution network system model, network reconfiguration of the power distribution network is added as an emergency resource; Step 3: On the basis of step 2, a dynamic island division model and a frequency reserve model are established by considering the frequency adjustment characteristics of the system; Step 4: On the basis of the dynamic island division model and the frequency reserve model, the demand response capability of the combined power and gas distribution network is considered, including the demand response that can be reduced, the demand response that can be transferred and the demand response that can be replaced; Step 5: On the basis of step 4, a multi-stage combined power and gas distribution network coordinated recovery model is formed by considering the unexpectedness and extreme output scenarios of distributed new energy units in the phased development of the fault stage; Step 6: The improved step-by-step hedging algorithm is used to solve the multi-stage combined power and gas distribution network coordinated recovery model, and the method is applied to the actual scene of the coordinated recovery of the combined power and gas distribution network to form a decision tree result that meets the unexpected condition; The mathematical model corresponding to the network reconfiguration in step 2 is as follows: Network reconfiguration constraint: ∑ ij∈ΩL a ij,t = N-∑ j β jt - M a ij,t ≤ P' ij,t ≤ M a ij,t where ΩLis the set of distribution network lines; ΩΓis the set of reconfiguration switches; N is the number of distribution network nodes; β jt denotes whether the distribution network node j is a root node at time t; P′ ij,t and P′ jk,t are the virtual power flows of distribution network lines (i, j) and (j, k), respectively; denotes whether the state of the reconfiguration switch on the distribution network line (i, j) changes at time t; Ntotal,max is the maximum number of actions allowed for the total time period of reconfiguration.

2. The multi-stage gas-electric combined network coordination restoration method according to claim 1, characterized in that, In step 1, the objective function of the combined power and gas distribution network system model is the minimization of the total cost of the combined power and gas distribution network, and the objective function is as follows: where t is the time index; j is the distribution grid node index; n is the distribution grid node index; c is the distributed gas / coal generator index; e is the curve segment index; C j is the unit penalty cost of loss of load for distribution grid j node; C n is the unit penalty cost of loss of load for distribution grid n node; is the unit cost of electricity purchase from the upper-level grid for distribution grid, is the unit cost of gas purchase from the upper-level gas grid for distribution grid; is the fuel cost of distributed generator c; C ce is the cost coefficient of distributed generator c segment e; is the loss of load power of distribution grid j node at time t; is the loss of load volume of distribution grid n node at time t; is the electricity purchase quantity from the upper-level grid for distribution grid, is the gas purchase quantity from the upper-level gas grid for distribution grid; P cet is the power of distributed generator c on segment e at time t; SU ct and SD ct are the start-up fuel consumption and shutdown fuel consumption of distributed generator c at time t, respectively.

3. The multi-stage gas-electric combined network coordination restoration method according to claim 2, characterized in that, The constraint conditions of the combined power and gas distribution network system model include combined power and gas distribution network operation constraints, coupling constraints and combined power and gas distribution network fault maintenance constraints; The combined power and gas distribution network operation constraints include power distribution network node power balance constraints, power distribution network power flow constraints, distributed unit constraints, gas distribution network node balance constraints, gas distribution network power flow constraints, energy storage constraints and combined power and gas load loss constraints; Specifically as follows: 1) Power distribution network node power balance constraint: where g is the index of the electric-gas conversion equipment; k is the index of the distribution network node; w is the index of the distributed wind turbine; ij, jk are the indices of the lines, representing the distribution network line (i, j) and the distribution network line (j, k), respectively; Ω j is the set of equipment connected to the distribution network node j; is the set of child nodes of the distribution network node j; and P represent the active and reactive load size of the distribution network node j at time t, respectively; ρ jt is the active / reactive coefficient of the distribution network node j at time t; is the frequency adjustment power deficiency of the distribution network node j at time t; is the demand response of the distribution network node j at time t; P gt is the power consumed by the electric-gas conversion equipment g at time t; P ij,t and P jk,t are the active power transmitted by the distribution network lines (i, j) and (j, k) at time t; Q ij,t and Q jk,t are the reactive power transmitted by the distribution network lines (i, j) and (j, k) at time t; P ct and Q ct are the active and reactive power output by the distributed generator c at time t; P wt and Q wt are the active and reactive power output by the distributed wind turbine w at time t; 2) Power distribution network power flow constraint: - M · (1 - a ij,t ) ≤ v it - v jt - (r ij · P ij,t + x ij · Q ij,t ) ≤ M · (1 - a ij,t ) where (·) min / max denotes minimum / maximum; M is a sufficiently large real number; a ij,t denotes the state of the distribution network line (i, j) at time t; v it and v jt are the voltage values of nodes i and j at time t, respectively; r ij and x ij are the resistance and reactance values of the distribution network line (i,j), respectively; and are the active and reactive power maximum values of the distribution network line (i,j), respectively, is the maximum value of the power purchase of the distribution network from the upper-level network, is the reactive power exchange of the distribution network with the upper-level network, is the maximum value of the reactive power exchange of the distribution network with the upper-level network; and are the minimum and maximum values of the voltage at node j, respectively; 3) Distributed unit constraint: SU ct = su c ·(I ct -I c,t-1 ), SU ct ≥ 0 SD ct = sd c · (I c,t-1 - I ct ), SD ct ≥ 0 P ct =∑ e P cet where I ct denotes the start-stop state of the distributed generator c at time t; and are the minimum and maximum values of the active power output by the distributed generator c, respectively; and are the minimum and maximum values of the reactive power output by the distributed generator c, respectively; UR c and DR c are the up and down ramp rates of the distributed generator c; and are the start-up and shut-down counting times of the distributed generator c at time t; and are the minimum start-up and shut-down times of the distributed generator c at time t; su c and sd c are the start-up and shut-down fuel consumption parameters of the distributed generator c;(·) f denotes the predicted value; is the maximum power value of the distributed generator c at time t on segment e, is the maximum reactive power value of the distributed wind generator w; 4) Gas distribution network node balance constraint: where s is the index of gas storage device; o is the index of gas distribution network node; mn and no are the indexes of gas distribution network pipeline, representing the gas distribution network pipelines (m, n) and (n, o) respectively; Ω n represents the set of devices connected to the gas distribution network node n; is the set of child nodes of the gas distribution network node n; G gt is the amount of natural gas produced by the electric-to-gas device g at time t; and are the outflow and inflow amounts of natural gas of the gas storage device s at time t, respectively; is the demand response amount of the gas distribution network node n at time t; G mn,t and G no,t are the transmission amounts of natural gas of the gas distribution network pipelines (m, n) and (n, o) at time t; G ct is the amount of natural gas consumed by the distributed generator c at time t; is the predicted value of the natural gas load of the gas distribution network node n at time t; is the loss of load volume of the gas distribution network node n at time t; 5) Gas distribution network power flow constraint: wherein a mn,t denotes the state of the gas distribution network pipe (m, n); K mn is the Weymouth coefficient of the gas distribution network pipe (m, n); π mt and π nt denote the gas pressure at the nodes m and n, respectively; and denote the minimum and maximum values of the gas pressure at the node n, respectively; is the maximum value of the gas distribution network pipe (m, n) and the transmitted amount of natural gas; 6) Energy storage constraint: wherein E st represents the capacity of the gas storage facility s at time t; and respectively represent the inflow and outflow efficiency of natural gas of the gas storage facility s; and respectively represent the minimum and maximum values of the capacity of the gas storage facility s; and respectively represent the minimum and maximum values of the amount of natural gas outflowing or inflowing from the gas storage facility s; 7) Combined power and gas load loss constraint: The coupling constraints include distributed unit coupling constraints and electric-to-gas equipment constraints, specifically as follows: 1) Distributed unit coupling constraint: G ct = (∑ e C ce · P cet + SU ct + SD ct ) / HHV, c e Ω GU In the formula, HHV is the natural gas high heat value coefficient; Ω GU is a gas unit set; 2) Electric-to-gas equipment coupling constraint: G gt = (φ · P gt · η g ) / HHV In the formula, φ is the energy conversion coefficient; η g η is the energy conversion efficiency of the electric-gas conversion device g; ηmax is the maximum value of the power consumed by the electric-gas conversion device g; The combined power and gas distribution network fault maintenance constraints include maintenance personnel scheduling constraints and maintenance time constraints, specifically as follows: 1) Maintenance personnel scheduling constraint: where p denotes the repairman index; μ e and μ g denote the electricity and gas distribution network repair station locations, respectively; Ω AN and Ω GN denote the electricity and gas distribution network fault sets, respectively; Λ ij,jk,p denotes the repairman p's path, Λ ij,jk,p = 1 if from the faulty electricity network link (i,j) to the faulty electricity network link (j,k), otherwise Λ ij,jk,p = 0; N A and N G denote the number of faults in the electricity and gas distribution networks, respectively; and denote the nodal potential energy of the faulty electricity network links (i,j) and (j,k), respectively; and denote the nodal potential energy of the faulty gas network links (m,n) and (n,o), respectively; Λ mn,no,p denotes the repairman p's path, Λ mn,no,p = 1 if from the faulty gas network link (m,n) to the faulty gas network link (n,o), otherwise Λ mn,no,p = 0; denotes the repairman p's path from the repair station to the faulty electricity network link (i,j); denotes the repairman p's path from the repair station to the faulty gas network link (m,n). 2) Maintenance time constraint: where d is the failure stage index; Ω AN and Ω GN denote the failure sets of the power and gas distribution networks, respectively; and denote the d-stage power and gas distribution network failure sets, respectively; and denote the time for repairman p to reach the failed power distribution network lines (i,j) and (j,k), respectively; and denote the time for repairman p to reach the failed gas distribution network lines (m,n) and (n,o), respectively; denotes the repair time for repairman p on the failed power distribution network line (i,j), denotes the repair time for repairman p on the failed gas distribution network line (m,n); denotes the travel time for repairman p from the failed power distribution network line (i,j) to (j,k); denotes the travel time for repairman p from the failed gas distribution network line (m,n) to (n,o); T d denotes the d-stage failure occurrence time; F ij,p and F mn,p denote whether the repairman p has reached (i,j) and (m,n), respectively; and are 0-1 variables indicating whether the repair at (i,j) and (m,n) is completed at time t; ε is a very small real number.

4. The method of claim 1, wherein, The dynamic island division model and the frequency reserve model considering the frequency adjustment characteristics in step 3 are mathematically expressed as follows: 1) Dynamic island division: λ iht • λ jht = a ij,t y ij,h,t ≤λ iht y ij,h,t ≤λ jht y ij,h,t ≥λ iht -λ jht +1 y ij,h,t ≥λ iht +λ jht -1 a ht ≤∑ j λ jht where h is the dynamic island index; Ω H is the island set; Ω DG is the distributed generator node set; λ jht and λ iht denote whether distribution network node j and i belong to dynamic island h at time t, respectively; y ij,h,t denote whether distribution network line (i, j) belongs to dynamic island h at time t; α ht denote whether dynamic island h exists at time t; denote whether dynamic island h contains distributed generators at time t; 2) Frequency reserve constraint: where Ω h represents the set of devices connected to the dynamic island h; represents the power disturbance of the distribution network node j at time t; H h is the inertia of the dynamic island h; t db and t nad are the frequency adjustment dead zone time and the frequency minimum point time; f(0) and f(t nad ) represent the initial time frequency and the frequency at t nad ; f 0 , f nad and f db represent the reference frequency, the frequency minimum point and the frequency at the end of the dead zone time, respectively; represents the upper reserve of the distributed unit c at time t, represents the maximum value of the upper reserve of the distributed unit c; J c represents the time constant of the distributed unit c; γ represents the frequency change rate, γ max represents the maximum value of the frequency change rate; UR c is the upper ramp rate of the distributed unit c.

5. The method of claim 1, wherein, The demand response constraint in step 4 is expressed as follows: a rl = (a e · η e ) / (a g · η g ) Ω RL is the set of replaceable load nodes; and denote the curtailed, shifted and replaceable electrical load demand response of distribution network node j at time t, respectively; denote the curtailed, shifted and replaceable gas load demand response, respectively; and denote the electrical and gas load demand response coefficients, respectively; denotes the maximum curtailed electrical load demand response of distribution network node j; denotes the maximum curtailed gas load demand response of distribution network node n; and denote the electrical load shifting out and in demand response of distribution network node j at time t, respectively; and denote the gas load shifting out and in demand response of distribution network node n at time t, respectively; and denote the electrical load shifting out and in state of distribution network node j at time t, respectively; and denote the gas load shifting out and in state of distribution network node n at time t, respectively; and denote the minimum and maximum electrical load shifting out demand response of distribution network node j, respectively; and denote the minimum and maximum gas load shifting out demand response of distribution network node n, respectively; and denote the minimum and maximum electrical load shifting in demand response of distribution network node j, respectively; and denote the minimum and maximum gas load shifting in demand response of distribution network node n, respectively; denotes the maximum shifted electrical load demand response of distribution network node j; denotes the maximum shifted gas load demand response of distribution network node n; a rl is the replaceable load coefficient; a e and a g are the electrical and gas unit heat values, respectively. η e and η g are the electrical and gas energy conversion efficiencies.

6. The method of claim 1, wherein, In step 5, the abstract form of the mathematical model corresponding to the multi-stage combined power and gas distribution network coordinated recovery model is as follows: where d is the fault stage index; δ and θ are the fault scenario indices; and σ is the wind power scenario index; S is the set of wind power scenarios; p dδ is the probability of the d-stage fault case δ; is the wind power scenario is the probability of the d-stage fault case δ; ξ denotes the phasic realization of fault uncertainty; is the continuous variable under the d-phase fault case δ wind scenario ; is the loss of load under the d-phase fault case δ wind scenario ζ; dδ , b dδ , c dδ , A, B, C, D d , E d , and l dδ are abstract matrices and vectors; and denote the decision under the influence of fault uncertainty ξ dδ and ξ dθ , respectively; z dδσ is the decision under the d-phase fault case δ wind scenario σ, and z dδζ is the decision under the d-phase fault case δ wind scenario ζ.

7. The method of claim 6, wherein, In step 6, the improved step-by-step hedging algorithm is used to solve the multi-stage combined power and gas distribution network coordinated recovery model, specifically as follows: Step 6.1: Parameter initialization; let iteration number v 0, parameter and calculate the decision under each failure scenario: where u d is the d-stage decision tree node; denotes the iteration multiplier corresponding to u d , is the decision of failure scenario d at iteration number v + 1; Step 6.2: Update the iteration number v <- v + 1; Step 6.3: Aggregating d-stage decision tree node u d decision, obtaining a reference decision coefficient: wherein, is u d a corresponding reference decision, is a set of decision tree nodes for the u is u d a corresponding probability, is u d a corresponding solution; Step 6.4: Update parameters for each failure scenario: where ζ is a penalty coefficient. Step 6.5: Decouple and calculate each fault scenario decision: Step 6.6: Iteration exit condition: if each scenario tree node corresponds to a decision z dδζ is equal, exit the iteration; otherwise, fix the part of the scenario tree nodes corresponding to decisions that are equal to be constant, and go back to step 6.2.

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