Multi-stage gas-electricity combined distribution network coordination recovery method

Abstract

The invention relates to the technical field of gas-electricity combined systems, and discloses a multi-stage gas-electricity combined distribution network coordinated recovery method, which comprises the following steps of: firstly, establishing a gas-electricity combined distribution network system model considering each device and coupling relationship in a power distribution / gas network and distribution scheduling of maintenance personnel by taking the minimization of the total cost of the gas-electricity combined distribution network as a target; establishing a dynamic island division model and a frequency reserve model; a multi-stage gas-electricity combined distribution network coordination recovery model is formed by considering demand response capability, unpredictability of fault stage development and an extreme output scene of a distributed new energy unit; an improved step-by-step hedging algorithm is adopted for solving and is applied to an actual scene, and a decision tree result meeting unexpected conditions is formed. According to the method, the extreme fault handling capacity of the gas-electricity combined distribution network can be improved, the influence and loss of natural disasters on the gas-electricity combined distribution network and users of the gas-electricity combined distribution network are reduced, and the method has important research significance in formulating the collaborative recovery strategy of the gas-electricity combined distribution network.

Description

Technical Field

[0001] The present invention relates to the technical field of gas-electricity combined systems, and in particular to a multi-stage gas-electricity combined distribution network coordination recovery method that takes into account unexpected conditions and dynamic island frequency adjustment. Background Art

[0002] As a high-quality alternative to fossil fuels, natural gas has been widely used in power generation. Through gas-fired generator sets and power-to-gas (P2G) equipment, the interdependence between gas and power systems is increasing. As the last mile of energy supply, the gas-electricity combined distribution system has attracted great attention for improving the system's ability to resist natural disasters.

[0003] The key to reducing the loss of load in the gas-electricity combined distribution network under extreme disasters is to use a variety of flexible resources for coordinated recovery, comprehensively consider the positive role of distributed generators, energy storage equipment, network reconstruction, emergency resources, etc. in the gas-electricity combined distribution network on system recovery, as well as the gas-electricity load demand response and the frequency backup recovery capability of distributed synchronous units in the gas-electricity combined island. At the same time, due to the uncertainty of the staged propagation of disasters and the power generation of distributed new energy units, 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 gas-electricity combined distribution network's ability to respond to extreme faults, reduce the impact and losses of extreme natural disasters on the gas-electricity combined distribution network and its users, and formulate a coordinated recovery strategy for the gas-electricity combined distribution network.

[0004] At present, the problem of distribution network fault recovery generally focuses on single-point fault recovery, such as using distribution network reconstruction to restore the load that is powered off after a single-point fault. However, it is insufficient to recover from multiple-point faults in a short period of time under extreme events. In addition, there is a lack of research on the potential safety risks brought about by the deep coupling of heterogeneous energy flows in the gas-electricity combined distribution network, and the problem of cascading faults caused by the cross-system propagation of faults has not been considered. It is necessary to conduct overall modeling and unified scheduling for the coordinated recovery optimization decision of the gas-electricity combined distribution network under faults. Summary of the invention

[0005] The present invention provides a multi-stage gas-electricity joint distribution network coordinated recovery method for the prior art, taking into account unexpected conditions and dynamic island frequency adjustment, which can improve the gas-electricity joint distribution network's ability to respond to extreme faults, reduce the impact and losses of extreme natural disasters on the gas-electricity joint distribution network and its users, and formulate a gas-electricity joint distribution network coordinated recovery strategy, which has important research significance. The technical solution adopted by the present invention is:

[0006] A multi-stage gas-electricity combined distribution network coordinated restoration method specifically comprises the following steps:

[0007] Step 1: With the goal of minimizing the total cost of the gas-electricity combined distribution network, a model is established that takes into account the various equipment in the distribution network and the gas distribution network and their coupling relationships. At the same time, a gas-electricity combined distribution network system model is established by considering the distribution and scheduling of maintenance personnel;

[0008] Step 2: Based on the gas-electricity combined distribution network system model, adding distribution network reconstruction as an emergency resource;

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

[0010] Step 4: Based on the dynamic island division model and the frequency reserve model, the demand response capability of the gas-electricity combined distribution network is considered, including curtailable demand response, transferable demand response and replaceable demand response;

[0011] Step 5: Based on step 4, the unexpected nature of the staged development of faults and the extreme output scenarios of distributed renewable energy units are considered to form a multi-stage gas-electricity joint distribution network coordinated recovery model;

[0012] Step 6: Use the improved step-by-step hedging algorithm to solve the multi-stage gas-electricity distribution network coordinated restoration model, apply the proposed method to the actual scenario of gas-electricity distribution network coordinated restoration, and form a decision tree result that meets unexpected conditions.

[0013] Furthermore, in step 1, the objective function of the gas-electricity combined distribution network system model established is to minimize the total cost of the gas-electricity combined distribution network, and the objective function is as follows:

[0014]

[0015] Where t is the time index; j is the distribution network node index; n is the gas distribution network node index; c is the distributed gas / coal-fired generator group index; e is the curve segment index; C j is the penalty cost of unit load loss at node j in the distribution network; C n is the penalty cost of unit load loss of n nodes in the gas distribution network; The unit cost of the distribution network purchasing electricity from the upper grid, The unit cost of purchasing gas from the upper gas grid for the gas distribution network; is the fuel cost of distributed unit c; C ce is the cost coefficient of distributed unit c segment e; is the load loss power at node j of the distribution network at time t; is the load loss volume of node n of the gas distribution network at time t; Purchase electricity from the upper power grid for the distribution network. The gas volume purchased by the gas distribution network from the upper gas network; P cetis the power of distributed unit c on segment e at time t; SU ct and SD ct are the startup fuel consumption and shutdown fuel consumption of distributed unit c at time t respectively.

[0016] Furthermore, the constraints 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 flow constraints, distributed unit constraints, gas distribution network node balance constraints, gas distribution network flow constraints, energy storage constraints and gas-electricity combined load loss constraints; the details are as follows:

[0018] 1) Power balance constraints of distribution network nodes:

[0019]

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

[0021] 2) Distribution network flow constraints:

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

[0023]

[0024] In the formula, (·) min / max Indicates the minimum / maximum value; M is a sufficiently large real number; a ij,t represents 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 maximum active power and reactive power of the distribution network line (i, j), is the maximum amount of electricity that the distribution network can purchase from the upper grid. For reactive power exchange between distribution network and upper grid, It is the maximum value of reactive power exchange between the distribution network and the upper grid; and are the minimum and maximum voltages at node j respectively;

[0025] 3) Distributed unit constraints:

[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] In the formula, I ctIndicates the start and stop status of distributed unit c at time t; and are the minimum and maximum values ​​of the active power output by the distributed generator set c respectively; and are the minimum and maximum values ​​of reactive power output by distributed generator set c; UR c and DR c is the ramp-up rate and ramp-down rate of distributed unit c; and is the startup count time and shutdown count time of distributed unit c at time t; and is the minimum startup time and minimum shutdown time of distributed unit c at time t; su c and sd c are the startup fuel consumption parameters and shutdown fuel consumption parameters of distributed unit c; (·) f represents the predicted value; is the maximum power of distributed unit c in segment e at time t, is the maximum reactive power of the distributed wind turbine w;

[0033] 4) Gas distribution network node balance constraints:

[0034]

[0035] Where s is the gas storage equipment index; o is the gas distribution network node index; mn and no are the gas distribution network pipeline indexes, 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 sub-node set of gas distribution network node n; G gt is the amount of natural gas produced by the power-to-gas equipment g at time t; and are the outflow and inflow of natural gas from gas storage equipment s at time t, respectively; is the demand response of gas distribution network node n at time t; G mn,t and G no,t is the amount of natural gas transmitted by gas distribution network pipelines (m,n) and (n,o) at time t; G ct is the amount of natural gas consumed by distributed unit c at time t; is the predicted value of natural gas load at gas distribution network node n at time t; is the load loss volume of gas distribution network node n at time t;

[0036] 5) Gas distribution network flow constraints:

[0037]

[0038] In the formula, a mn,t Indicates the status of the gas distribution network pipeline (m,n); K mn is the Weymouth coefficient of the gas distribution network pipeline (m,n); π mt and π nt They represent the gas pressures at nodes m and n of the gas distribution network respectively; and They represent the minimum and maximum values ​​of the gas pressure at node n of the gas distribution network respectively; is the maximum value of gas distribution network pipelines (m, n) and the amount of natural gas transmitted;

[0039] 6) Energy storage constraints:

[0040]

[0041]

[0042] In the formula, E st represents the capacity of gas storage equipment s at time t; and They represent the efficiency of natural gas flowing into and out of the gas storage equipment s respectively; and They represent the minimum and maximum values ​​of the capacity of the gas storage device s respectively; and are the minimum and maximum values ​​of the natural gas outflow or inflow of gas storage equipment s, respectively;

[0043] 7) Gas-electricity joint load loss constraints:

[0044]

[0045] The coupling constraints include the coupling constraints of distributed units and the power-to-gas equipment constraints, which are as follows:

[0046] 1) Distributed unit coupling constraints:

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

[0048] Where HHV is the high heating value coefficient of natural gas; Ω GU Assemble for gas units;

[0049] 2) Coupling constraints of power-to-gas equipment:

[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 power-to-gas device g; is the maximum value of power consumption of the power-to-gas device g;

[0053] The gas-electricity combined distribution network fault maintenance constraints include maintenance personnel constraints and maintenance time constraints, which are as follows:

[0054] 1) Maintenance personnel scheduling constraints:

[0055]

[0056] Where p represents the maintenance personnel index; μ e and μ g Respectively represent the locations of the maintenance stations for the distribution network and gas distribution network; Ω AN and Ω GN They represent the distribution network fault set and the gas distribution network fault set respectively; Λ ij,jk,p represents the path of maintenance personnel p. If it is from the faulty distribution network line (i, j) to the faulty distribution network line (j, k), then Λ ij,jk,p =1, otherwise Λ ij,jk,p =0; N A and N G represent the number of faults in the power distribution network and the gas distribution network respectively; and They represent the node potential of the faulty distribution network lines (i, j) and (j, k), respectively; and Respectively represent the node potential energy of the faulty gas distribution network lines (m,n) and (n,o); Λ mn,no,p represents the path of maintenance personnel p. If it is from the faulty gas distribution network line (m,n) to the faulty gas distribution network line (n,o), then Λ mn,no,p =1, otherwise Λ mn,no,p =0; It indicates that maintenance personnel p departs from the maintenance station to the faulty distribution network line (i, j); It represents the route (m,n) from the maintenance station to the faulty gas distribution network where maintenance personnel p departs;

[0057] 2) Maintenance time constraints:

[0058]

[0059] Where d is the fault stage index; Ω AN and Ω GNrepresent the fault sets of the power distribution network and the gas distribution network respectively; and They represent the fault sets of the distribution network and gas distribution network in stage d respectively; and They represent the time when maintenance personnel p arrives at the faulty distribution network lines (i, j) and (j, k), respectively; and They represent the time when maintenance personnel p arrives at the faulty gas distribution network lines (m,n) and (n,o), respectively; represents the maintenance time of maintenance personnel p for the faulty distribution network line (i, j), It represents the maintenance time of maintenance personnel p on the faulty gas distribution network line (m,n); represents the travel time of maintenance personnel p from the faulty distribution network line (i, j) to (j, k); T represents the travel time of maintenance personnel p from the faulty gas distribution network line (m,n) to (n,o); d Indicates the time when the fault occurs in stage d; F ij,p and F mn,p Respectively indicate whether maintenance personnel p has arrived at (i, j) and (m, n); and It is a 0-1 variable, indicating whether the maintenance of (i, j) and (m, n) is completed at time t; ε is a very small real number.

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

[0061] Network Reconfiguration Constraints:

[0062]

[0063] -M·a ij,t ≤P′ ij,t ≤M·a ij,t

[0064]

[0065] In the formula, Ω L is the distribution network line set; Ω Γ is the set of reconstructed tie switches; N is the number of distribution network nodes; β jt Indicates whether the distribution network node j is the root node at time t; P' ij,t and P j ' k,t They are the virtual power flows of distribution network lines (i, j) and (j, k) respectively; Indicates whether the state of the tie switch on the distribution network line (i, j) changes at time t; N total,maxThe maximum number of actions allowed for the reconstruction in the entire period.

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

[0067] 1) Dynamic island division:

[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] Where h is the dynamic island index; Ω H is an island set; Ω DG is the set of distributed unit nodes; jht and λ iht They respectively indicate whether the distribution network nodes j and i belong to the dynamic island h at time t; y ij,h,t Indicates whether the distribution network line (i, j) belongs to the dynamic island h at time t; α ht Indicates whether the dynamic island h exists at time t; Indicates whether the dynamic island h contains distributed units at time t;

[0078] 2) Frequency reserve constraints:

[0079]

[0080]

[0081] In the formula, Ω h Represents the set of devices connected to the dynamic island h; represents the power disturbance of distribution network node j at time t; H h is the inertia of the dynamic island h; t db and t nad The frequency adjustment dead time and the frequency minimum point time; f(0) and f(t nad ) represents the initial time frequency and at t nad The frequency of 0 、f nad and f db They represent the reference frequency, the frequency at the lowest frequency point, and the frequency at the end of the dead time respectively; represents the upper reserve of distributed unit c at time t, represents the maximum value of the reserve on the distributed unit c; J c represents the time constant of the distributed unit c; γ represents the frequency change rate, γ max Indicates the maximum frequency change rate; UR c is the climbing rate of distributed unit c.

[0082] Furthermore, 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] In the formula, Ω RL is a set of replaceable load nodes; and They represent the curtailable, transferable and replaceable electric load demand responses of distribution network node j at time t respectively; They represent curtailable, shiftable, and replaceable gas load demand responses, respectively; and represent the demand response coefficients of electricity load and gas load respectively; It indicates the maximum value of the load demand response that can be reduced by the distribution network node j; It indicates the maximum value of gas load demand response that can be reduced by gas distribution network node n; and They represent the outgoing and incoming demand responses of the electric load at the distribution network node j at time t respectively; and They represent the outgoing and incoming demand responses of gas load at distribution network node n at time t respectively; and They represent the load transfer-out and load transfer-in states of distribution network node j at time t respectively; and They represent the outgoing and incoming states of gas load at the gas distribution network node n at time t respectively; and They represent the minimum and maximum values ​​of the load transfer demand response of the distribution network node j respectively; and They represent the minimum and maximum values ​​of the gas load transfer-out demand response of the gas distribution network node n, respectively; and They represent the minimum and maximum values ​​of the electrical load transferred to the demand response at the distribution network node j respectively; and They represent the minimum and maximum values ​​of gas load transferred to demand response at node n of the gas distribution network respectively; It represents the maximum value of the transferable 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 the alternative load factor; α e and α g is the unit calorific value of electricity and the unit calorific value of gas; η e and η g It is the electricity energy conversion efficiency and gas energy conversion efficiency.

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

[0088]

[0089] Where d is the fault stage index; δ and θ are the fault scenario indexes; and σ are wind power scenario indexes; S is the wind power scenario set; p dδ is the probability of failure condition δ in stage d; For wind power scenarios The probability of the failure condition δ in stage d; ξ represents the staged realization of the failure uncertainty; For the fault condition δ wind power scenario in stage d Continuous variables under ; For the fault condition δ wind power scenario in stage d Under load loss; a dδ 、b dδ 、c dδ , A, B, C, D d 、E d and l dδFor abstract matrices and vectors; and They represent the fault uncertainty ξ dδ and dθ Decisions under influence; dδσ is the decision-making under the fault condition δ wind power scenario σ in stage d, In the fault situation of stage d, wind power scenario The following decision.

[0090] Furthermore, in step 6, an improved step-by-step hedging algorithm is used to solve the multi-stage gas-electricity distribution network coordination recovery model, as follows:

[0091] Step 6.1: Parameter initialization; let the number of iterations v←0, parameter And calculate the decision under each failure scenario: Among them, u d is the decision tree node of stage d; Indicates u d The corresponding iterative multiplier is is the decision of the fault scenario δ under the iteration number v+1;

[0092] Step 6.2: Update the number of iterations v←v+1;

[0093] Step 6.3: Aggregate d-stage decision tree node u d Decision-making, obtain the reference decision coefficient:

[0094] in, for u d The corresponding reference decision, is the decision tree node set of the uncertainty ξ in stage d, for u d The corresponding probability is for u d The corresponding solution decision;

[0095] Step 6.4: For each failure scenario, update the parameters: Among them, ζ is the penalty coefficient;

[0096] Step 6.5: Decouple the calculations for each failure scenario decision:

[0097]

[0098] Step 6.6: Iteration exit condition: If each scene tree node corresponds to a decision If they are equal, exit the iteration; otherwise, the corresponding decisions of the scene tree nodes that are equal to the fixed part are constants, and return to step 6.2.

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

[0100] (1) The present invention discloses a multi-stage gas-electricity combined distribution network coordinated recovery method that takes into account unexpected conditions and dynamic island frequency adjustment. Compared with the prior art, this strategy not only coordinates the repair of faults in the gas-electricity combined distribution network, but also comprehensively considers the positive effects of the distributed generator sets, energy storage equipment, network reconstruction, emergency resources, etc. of the gas-electricity combined distribution network on system recovery, as well as the gas-electricity load demand response and the frequency backup recovery capability of the distributed synchronous units in the gas-electricity combined island. It can more effectively recover the load loss 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 proposed in the present invention that takes into account unexpected conditions and dynamic island frequency adjustment can take into account the uncertainty of the staged development of faults and the output of distributed new energy units, thereby improving the gas-electricity combined distribution network's ability to respond to actual conditions and enhancing the efficiency of system recovery.

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

[0103] Figure 1 This is a schematic diagram of the gas-electricity combined distribution network of the present invention.

[0104] Figure 2 Schematic diagram of island division according to an embodiment of the present invention.

[0105] Figure 3 This is a demand response analysis diagram of an embodiment of the present invention.

[0106] Figure 4 A diagram of a fault scenario setting according to an embodiment of the present invention. DETAILED DESCRIPTION

[0107] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0108] The present invention considers unexpected conditions and dynamic island frequency adjustment of the multi-stage gas-electricity distribution network coordination recovery method, comprehensively considers the positive role of the distributed generator sets, energy storage equipment, network reconstruction, emergency resources, etc. of the gas-electricity distribution network on system recovery, as well as the gas-electricity load demand response, the frequency backup recovery capability of the distributed synchronous units in the gas-electricity combined island, and considers the extreme conditions of distributed new energy output and the randomness of the staged propagation of gas-electricity distribution network faults, proposes a multi-stage gas-electricity distribution network coordination recovery method considering unexpected conditions and dynamic island frequency adjustment, and adopts an improved step-by-step hedging algorithm to solve. The construction method includes the following steps:

[0109] Step 1: With the goal of minimizing the total cost of the gas-electricity combined distribution network, a model is established that takes into account the various equipment in the distribution network and the gas distribution network and their coupling relationships. At the same time, a gas-electricity combined distribution network system model is established by considering the distribution and scheduling of maintenance personnel;

[0110] The objective function of the gas-electricity combined distribution network system model established is to minimize the total cost of the gas-electricity combined distribution network, while ensuring the stability of the system:

[0111]

[0112] Where t is the time index; j is the distribution network node index; n is the gas distribution network node index; c is the distributed gas / coal-fired generator group index; e is the curve segment index; C j is the penalty cost of unit load loss at node j in the distribution network; C n is the penalty cost of unit load loss of n nodes in the gas distribution network; They are the unit cost of electricity / gas purchased by the distribution network / gas distribution network from the upper-level power grid / gas network; is the fuel cost of distributed unit c; C ce is the cost coefficient of distributed unit c segment e; is the load loss power at node j of the distribution network at time t; is the load loss volume of node n of the gas distribution network at time t; The amount of electricity / gas purchased by the distribution network / gas distribution network from the upper power grid / gas network; P cet is the power of distributed unit c on segment e at time t; SU ct , SD ct are the start / stop fuel consumption of distributed unit c at time t respectively.

[0113] The constraints 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.

[0114] Among them, the operation constraints of the gas-electricity combined distribution network include power balance constraints of distribution network nodes, distribution network flow constraints, distributed unit constraints, gas distribution network node balance constraints, gas distribution network flow constraints, energy storage constraints, and gas-electricity combined load loss constraints; coupling constraints include distributed unit coupling constraints and power-to-gas equipment constraints; maintenance constraints of the gas-electricity combined distribution network include maintenance personnel constraints and maintenance time constraints.

[0115] (1) Constraints on the operation of gas-electricity combined distribution network

[0116] 1) Power balance constraints of distribution network nodes

[0117]

[0118] Where g is the power-to-gas equipment index; k is the distribution network node index; w is the distributed wind turbine index; ij and jk are line indexes, representing lines (i, j) and (j, k) respectively; Ω j Access device set for distribution network node j; is the set of child nodes of distribution network node j; They represent the active load and reactive load of the distribution network node j at time t respectively; ρ jt is the active / reactive coefficient of distribution network node j at time t; The frequency adjustment power deficit of distribution network node j at time t; is the demand response of distribution network node j at time t; P gt P is the power consumption of the power-to-gas device g at time t; ij,t , P jk,t is the active power transmitted by distribution network lines (i, j) and (j, k) at time t; Q ij,t , Q jk,t P is the reactive power transmitted by distribution network lines (i, j) and (j, k) at time t; ct , Q ct is the active / reactive power output by the distributed generator set 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 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] In the formula, (·) min / max Indicates the minimum / maximum value; M is a sufficiently large real number; a ij,t represents the state of line (i, j) at time t; v it 、v jt is the voltage value of nodes i and j at time t; r ij 、x ij are the resistance and reactance values ​​of line (i, j) respectively. and are the maximum active power and reactive power of the distribution network line (i, j), is the maximum amount of electricity that the distribution network can purchase from the upper grid. For reactive power exchange between distribution network and upper grid, is the maximum value of reactive power exchange between the distribution network and the upper grid, and are the minimum and maximum voltages at node j, respectively.

[0123] 3) Distributed unit 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] In the formula, I ct Indicates the start and stop status of distributed unit c at time t; UR c ,DR c is the up / down ramp rate of distributed unit c; is the startup and shutdown counting time of distributed unit c at time t; is the minimum startup / shutdown time of distributed unit c at time t; su c 、sd c is the start-stop fuel consumption parameter of distributed unit c; (·) f Represents the predicted value.

[0131] 4) Gas distribution network node balance constraints:

[0132]

[0133] Where s is the gas storage equipment index; o is the gas distribution network node index; mn, no are the gas distribution network pipeline indexes, representing pipelines (m,n), (n,o); Ω n Represents the set of devices connected to the gas distribution network node n; is the sub-node set of gas distribution network node n; G gt is the amount of natural gas produced by the power-to-gas equipment g at time t; is the outflow and inflow of natural gas from gas storage equipment s at time t; is the demand response of 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) and (n,o) at time t; G ct is the amount of natural gas consumed by distributed unit c at time t.

[0134] 5) Gas distribution network flow constraints:

[0135]

[0136] In the formula, a mn,t Indicates the status 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 at nodes m and n of the gas distribution network.

[0137] 6) Energy storage constraints:

[0138]

[0139] In the formula, E st represents the capacity of gas storage equipment s at time t; Indicates the efficiency of natural gas flowing into / out of gas storage equipment.

[0140] 7) Load loss constraint:

[0141]

[0142] (2) Coupling constraints

[0143] 1) Distributed unit coupling constraints:

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

[0145] Where HHV is the high heating value coefficient of natural gas; Ω GU For gas unit assembly.

[0146] 2) Coupling constraints of power-to-gas equipment:

[0147] Ggt =(φ·P gt ·η g ) / HHV

[0148]

[0149] Where φ is the energy conversion coefficient; η g is the energy conversion efficiency of the power-to-gas device g.

[0150] (3) Constraints on fault maintenance of gas-electricity combined distribution network

[0151] 1) Maintenance personnel scheduling constraints:

[0152]

[0153]

[0154] Where p represents the maintenance personnel index; μ e , μ g Respectively represent the location of the maintenance station of the distribution network / gas distribution network; Ω AN ,Ω GN Respectively represent the fault set of distribution network / gas distribution network; Λ ij,jk,p represents the maintenance personnel p path. If it is from the faulty line (i, j) to the faulty line (j, k), then Λ ij,jk,p =1; N A 、N G Respectively represent the number of faults in the power distribution network / gas distribution network; and They represent the node potential of the faulty distribution network lines (i, j) and (j, k), respectively; and They represent the node potential energy of the faulty gas distribution network lines (m,n) and (n,o) respectively.

[0155] 2) Maintenance time constraints:

[0156]

[0157] Where d is the fault stage index; They represent the set of faults in stage d respectively; denote the time when maintenance personnel p arrives at faults (i, j) and (m, n), respectively; They represent the maintenance time of maintenance personnel p for faults (i, j) and (m, n) respectively; They represent the travel time of maintenance personnel p from (i,j) to (j,k) and from (m,n) to (n,o); T d Indicates the time when the fault occurs in stage d; F ij,p 、F mn,pRespectively indicate whether maintenance personnel p has arrived at (i, j) and (m, n); It is a 0-1 variable, indicating whether the faults (i, j) and (m, n) have been repaired at time t; ε is a very small real number.

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

[0159] The mathematical model corresponding to the network reconstruction, that is, the network reconstruction constraint is expressed as follows:

[0160]

[0161] -M·a ij,t ≤P′ ij,t ≤M·a ij,t

[0162]

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

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

[0165] The mathematical expressions of the dynamic island partition model and frequency reserve model considering the frequency adjustment characteristics are 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 an island set; Ω DG is the set of distributed unit nodes; jht Indicates whether node j belongs to dynamic island h at time t; y ij,h,t Indicates whether the line (i, j) belongs to the dynamic island h at time t; α ht Indicates whether the dynamic island h exists at time t; Indicates whether the dynamic island h contains distributed units at time t.

[0177] 2) Frequency reserve constraints:

[0178]

[0179] In the formula, Ω h Represents the set of devices connected to the dynamic island h; represents the power disturbance of node j at time t; H h is the inertia of the dynamic island h; t db ,t nad The frequency adjustment dead time and the frequency minimum point time; f(0), f(t nad ) represents the initial time and at t nad The frequency of 0 、f nad 、f db They represent the reference frequency, the frequency at the lowest frequency point, and the frequency at the end of the dead time respectively; represents the upper reserve of distributed unit c at time t; J c represents the time constant of the distributed unit c; γ represents 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 curtailable, transferable, and replaceable demand response.

[0181] The demand response constraints are expressed as follows:

[0182]

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

[0184] In the formula, Ω RL is a set of replaceable load nodes; and They represent the curtailable, transferable and replaceable electric load demand responses of distribution network node j at time t respectively; They represent curtailable, shiftable, and replaceable gas load demand responses, respectively; and represent the demand response coefficients of electricity load and gas load respectively; It indicates the maximum value of the load demand response that can be reduced by the distribution network node j; It indicates the maximum value of gas load demand response that can be reduced by gas distribution network node n; and They represent the outgoing and incoming demand responses of the electric load at the distribution network node j at time t respectively; and They represent the outgoing and incoming demand responses of gas load at distribution network node n at time t respectively; and They represent the load transfer-out and load transfer-in states of distribution network node j at time t respectively; and They represent the outgoing and incoming states of gas load at the gas distribution network node n at time t respectively; and They represent the minimum and maximum values ​​of the load transfer demand response of the distribution network node j respectively; and They represent the minimum and maximum values ​​of the gas load transfer-out demand response of the gas distribution network node n, respectively; and They represent the minimum and maximum values ​​of the electrical load transferred to the demand response at the distribution network node j respectively; and They represent the minimum and maximum values ​​of gas load transferred to demand response at node n of the gas distribution network respectively; It represents the maximum value of the transferable 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 the alternative load factor; α e and α g is the unit calorific value of electricity and the unit calorific value of gas; η e and η gIt is the electricity energy conversion efficiency and gas energy conversion efficiency.

[0185] Step 5: On the basis of step 4, the unexpected nature of the staged development of faults and the extreme output scenarios of distributed renewable energy units are considered to form a multi-stage gas-electricity distribution network coordinated recovery model that considers unexpected conditions and dynamic island frequency adjustment.

[0186] Preferably, the unexpectedness of the staged development of faults and the extreme output scenarios of distributed renewable energy units are considered to form a multi-stage gas-electricity distribution network coordination recovery model that considers unexpected conditions and dynamic island frequency adjustment, ensuring the robustness of decision-making in response to faults and uncertainty in renewable energy basic output. The corresponding mathematical model is expressed as follows:

[0187]

[0188] In the formula, p dδ is the probability of failure condition δ in stage d; For wind power scenarios The probability of failure condition δ in stage d; ξ represents the staged realization of failure uncertainty.

[0189] Step 6: Use the improved step-by-step hedging algorithm to solve the model proposed in step 5, apply the proposed method to the actual scenario, and form a decision tree result that meets the unexpected conditions to ensure the effectiveness and robustness of the recovery strategy.

[0190] The multi-stage gas-electricity distribution network coordination restoration model proposed in step 5 is difficult to solve. In order to ensure the solution efficiency of the proposed model, an improved step-by-step hedging algorithm is proposed for solution. The specific model is as follows:

[0191] Step 6.1: Parameter initialization. Let the number of iterations v←0, the parameters And calculate the decision under each failure scenario:

[0192] Among them, u d is the decision tree node of stage d; Indicates u d The corresponding iterative multiplier is is the decision of the fault scenario δ under the iteration number v+1.

[0193] Step 6.2: Update the number of iterations v←v+1.

[0194] Step 6.3: Aggregate d-stage decision tree node u d Decision-making, obtain the reference decision coefficient:

[0195] in, for u d The corresponding reference decision, is the decision tree node set of the uncertainty ξ in stage d, for u d The corresponding probability is for u d The corresponding solution decision.

[0196] Step 6.4: For each failure scenario, update the parameters: Among them, ζ is the penalty coefficient.

[0197] Step 6.5: Decouple the calculations for each failure scenario decision:

[0198]

[0199] Step 6.6: Iteration exit condition: If each scene tree node corresponds to a decision If they are equal, exit the iteration. Otherwise, the corresponding decisions of the scene tree nodes that are equal to the fixed part are constants, and return to step 6.2.

[0200] Example analysis:

[0201] The schematic diagram of the system is as follows Figure 1 As shown in the figure, the system includes 2 distributed wind turbines, 3 distributed coal-fired units, 2 distributed gas-fired units, 5 tie switches, 1 gas storage device, and 1 power-to-gas device. It is assumed that the system failure propagates in three stages under extreme disasters.

[0202] The present invention adopts five scenarios to solve the deterministic gas-electricity joint distribution network coordinated restoration strategy, and the factors considered in each scheme are shown in Table 1. The total cost and load loss results of the above five schemes are shown in Table 2.

[0203] Table 1. Elements included in each plan

[0204]

[0205]

[0206] Table 2 shows the price parameter settings for this example.

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

[0208]

[0209] According to step 1: setting up Scheme 1, it can be seen that after an extreme disaster occurs, if only the gas-electricity combined distribution network failure maintenance is considered, the system will lose a total load of 15.70MWh and 503.27kcf during the dispatch period, causing economic losses of 19.22 million yuan. Based on Scheme 1, considering the role of power-to-gas equipment and gas storage equipment, the overall system cost is reduced and the loss of load is reduced.

[0210] According to step 2: Add network reconstruction as an emergency resource on the basis of solution 2. While the gas-electricity joint distribution network is being repaired, the island topology of the gas-electricity joint distribution network can be adjusted through network reconstruction, thereby achieving partial load recovery.

[0211] According to step 3: Based on Scheme 2, the frequency adjustment characteristics of the gas-electricity combined distribution network system are added, so that the frequency reserve can be used to partially restore the load under extreme faults. The dynamic island division results are as follows: Figure 2 As shown, actual simulation verifies that the frequency stability is met under the frequency adjustment characteristics. Compared with Scheme 3, Scheme 4 can reduce the electric load loss by 0.31MWh.

[0212] According to step 4: based on scheme 4, add the demand response of gas-electricity combined distribution network load, including curtailable, transferable and replaceable demand response. And analyze the three types of demand response, the parameter settings and results are shown in Table 3, Figure 3 shown.

[0213] Table 3. Setting coefficients of various demand response schemes

[0214]

[0215] According to step 5 and step 6: Based on scheme 5, consider adding the unexpected staged development of faults and the extreme output scenario of distributed new energy units, where the fault scenario is set as follows: Figure 4 As shown, the improved step-by-step hedging algorithm is used to solve it. To more clearly illustrate the effectiveness of the method, Schemes 6-7 are set up based on Scheme 5, as shown in Table 4. The calculation results are shown in Table 5.

[0216] Table 4. Elements included in each plan

[0217]

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

[0219]

[0220] It can be seen that the total cost of Solution 8 is significantly lower than that of Solution 6. The result of the solution is a decision tree, and the ability to cope with fault scenarios is improved. Compared with Solution 7, the cost of Solution 8 is slightly higher, but it ensures a smaller load loss in the worst scenario and has higher robustness.

Claims

1. A multi-stage gas-electricity joint distribution network coordinated restoration method, characterized in that: The specific steps include: Step 1: With the goal of minimizing the total cost of the gas-electricity combined distribution network, a model is established that takes into account the various equipment in the distribution network and the gas distribution network and their coupling relationships. At the same time, a gas-electricity combined distribution network system model is established by considering the distribution and scheduling of maintenance personnel; Step 2: Based on the gas-electricity combined distribution network system model, adding distribution network reconstruction as an emergency resource; Step 3: Based on step 2, considering the system frequency adjustment characteristics, a dynamic island division model and a frequency reserve model are established; Step 4: Based on the dynamic island division model and the frequency reserve model, the demand response capability of the gas-electricity combined distribution network is considered, including curtailable demand response, transferable demand response and replaceable demand response; Step 5: Based on step 4, the unexpected nature of the staged development of faults and the extreme output scenarios of distributed renewable energy units are considered to form a multi-stage gas-electricity joint distribution network coordinated recovery model; Step 6: Use the improved step-by-step hedging algorithm to solve the multi-stage gas-electricity distribution network coordinated restoration model, apply the proposed method to the actual scenario of gas-electricity distribution network coordinated restoration, and form a decision tree result that meets unexpected conditions.

2. The multi-stage gas-electricity distribution network coordinated restoration method according to claim 1 is characterized in that: In step 1, the objective function of the gas-electricity combined distribution network system model established is to minimize the total cost of the gas-electricity combined distribution network. The objective function is as follows: Where t is the time index; j is the distribution network node index; n is the gas distribution network node index; c is the distributed gas / coal-fired generator group index; e is the curve segment index; C j is the penalty cost of unit load loss at node j in the distribution network; C n is the penalty cost of unit load loss of n nodes in the gas distribution network; The unit cost of the distribution network purchasing electricity from the upper grid, The unit cost of purchasing gas from the upper gas grid for the gas distribution network; is the fuel cost of distributed unit c; C ce is the cost coefficient of distributed unit c segment e; is the load loss power at node j of the distribution network at time t; is the load loss volume of node n of the gas distribution network at time t; Purchase electricity from the upper power grid for the distribution network. The gas volume purchased by the gas distribution network from the upper gas network; P cet is the power of distributed unit c on segment e at time t; SU ct and SD ct are the startup fuel consumption and shutdown fuel consumption of distributed unit c at time t respectively.

3. The multi-stage gas-electricity distribution network coordinated restoration method according to claim 2 is characterized in that: The constraints 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; The gas-electricity combined distribution network operation constraints include distribution network node power balance constraints, distribution network flow constraints, distributed unit constraints, gas distribution network node balance constraints, gas distribution network flow constraints, energy storage constraints and gas-electricity combined load loss constraints; the details are as follows: 1) Power balance constraints of distribution network nodes: Where g is the power-to-gas equipment index; k is the distribution network node index; w is the distributed wind turbine index; ij and jk are line indexes, representing distribution network line (i, j) and distribution network line (j, k) respectively; Ω j Access device set for distribution network node j; is the set of child nodes of distribution network node j; and They represent the active load and reactive load of the distribution network node j at time t respectively; ρ jt is the active / reactive coefficient of distribution network node j at time t; The frequency adjustment power deficit of distribution network node j at time t; is the demand response of distribution network node j at time t; P gt P is the power consumption of the power-to-gas device g at time t; ij,t and P jk,t is the active power transmitted by distribution network lines (i, j) and (j, k) at time t; Q ij,t and Q jk,t P is the reactive power transmitted by distribution network lines (i, j) and (j, k) at time t; ct and Q ct is the active power and reactive power output by the distributed generator set c at time t; P wt and Q wt is the active power and reactive power output by the distributed wind turbine w at time t; 2) Distribution network flow constraints: In the formula, (·) min / max Indicates the minimum / maximum value; M is a sufficiently large real number; a ij,t represents 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 maximum active power and reactive power of the distribution network line (i, j), is the maximum amount of electricity that the distribution network can purchase from the upper grid. For reactive power exchange between distribution network and upper grid, It is the maximum value of reactive power exchange between the distribution network and the upper grid; and are the minimum and maximum voltages at node j respectively; 3) Distributed unit constraints: ARE ct =are c ·(AND ct -AND c,t-1 ),SU ct ≥0 SD ct =sd c ·(I c,t-1 -I ct ),SD ct ≥0 P ct =∑ e P cet In the formula, I ct Indicates the start and stop status of distributed unit c at time t; and are the minimum and maximum values ​​of the active power output by the distributed generator set c respectively; and are the minimum and maximum values ​​of reactive power output by distributed generator set c; UR c and DR c is the ramp-up rate and ramp-down rate of distributed unit c; and is the startup count time and shutdown count time of distributed unit c at time t; and is the minimum startup time and minimum shutdown time of distributed unit c at time t; su c and sd c are the startup fuel consumption parameters and shutdown fuel consumption parameters of distributed unit c; (·) f represents the predicted value; is the maximum power of distributed unit c in segment e at time t, is the maximum reactive power of the distributed wind turbine w; 4) Gas distribution network node balance constraints: Where s is the gas storage equipment index; o is the gas distribution network node index; mn and no are the gas distribution network pipeline indexes, 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 sub-node set of gas distribution network node n; G gt is the amount of natural gas produced by the power-to-gas equipment g at time t; and are the outflow and inflow of natural gas from gas storage equipment s at time t, respectively; is the demand response of gas distribution network node n at time t; G mn,t and G no,t is the amount of natural gas transmitted by gas distribution network pipelines (m,n) and (n,o) at time t; G ct is the amount of natural gas consumed by distributed unit c at time t; is the predicted value of natural gas load at gas distribution network node n at time t; is the load loss volume of gas distribution network node n at time t; 5) Gas distribution network flow constraints: In the formula, a mn,t Indicates the status of the gas distribution network pipeline (m,n); K mn is the Weymouth coefficient of the gas distribution network pipeline (m,n); π mt and π nt They represent the gas pressures at nodes m and n of the gas distribution network respectively; and They represent the minimum and maximum values ​​of the gas pressure at node n of the gas distribution network respectively; is the maximum value of gas distribution network pipelines (m, n) and the amount of natural gas transmitted; 6) Energy storage constraints: In the formula, E st represents the capacity of gas storage equipment s at time t; and They represent the efficiency of natural gas flowing into and out of the gas storage equipment s respectively; and They represent the minimum and maximum values ​​of the capacity of the gas storage device s respectively; and are the minimum and maximum values ​​of the natural gas outflow or inflow of gas storage equipment s, respectively; 7) Gas-electricity joint load loss constraints: The coupling constraints include the coupling constraints of distributed units and the power-to-gas equipment constraints, which are as follows: 1) Distributed unit coupling constraints: G ct =(∑ e C ce ·P cet +SU ct +SD ct ) / HHV,c∈Ω GU Where HHV is the high heating value coefficient of natural gas; Ω GU Assemble for gas units; 2) Coupling constraints of power-to-gas equipment: G gt =(φ·P gt ·or g ) / HHV Where, φ is the energy conversion coefficient; η g is the energy conversion efficiency of the power-to-gas device g; is the maximum power consumption of the power-to-gas device g; The gas-electricity combined distribution network fault maintenance constraints include maintenance personnel scheduling constraints and maintenance time constraints, which are as follows: 1) Maintenance personnel scheduling constraints: Where p represents the maintenance personnel index; μ e and μ g Respectively represent the locations of the maintenance stations for the distribution network and gas distribution network; Ω AN and Ω GN They represent the distribution network fault set and the gas distribution network fault set respectively; Λ ij,jk,p represents the path of maintenance personnel p. If it is from the faulty distribution network line (i, j) to the faulty distribution network line (j, k), then Λ ij,jk,p =1, otherwise Λ ij,jk,p =0; N A and N G represent the number of faults in the power distribution network and the gas distribution network respectively; and They represent the node potential of the faulty distribution network lines (i, j) and (j, k), respectively; and Respectively represent the node potential energy of the faulty gas distribution network lines (m,n) and (n,o); Λ mn,no,p represents the path of maintenance personnel p. If it is from the faulty gas distribution network line (m,n) to the faulty gas distribution network line (n,o), then Λ mn,no,p =1, otherwise It indicates that maintenance personnel p departs from the maintenance station to the faulty distribution network line (i, j); It represents the route (m,n) from the maintenance station to the faulty gas distribution network where maintenance personnel p departs; 2) Maintenance time constraints: Where d is the fault stage index; Ω AN and Ω GN represent the fault sets of the power distribution network and the gas distribution network respectively; and They represent the fault sets of the distribution network and gas distribution network in stage d respectively; and They represent the time when maintenance personnel p arrives at the faulty distribution network lines (i, j) and (j, k), respectively; and They represent the time when maintenance personnel p arrives at the faulty gas distribution network lines (m,n) and (n,o), respectively; represents the maintenance time of maintenance personnel p for the faulty distribution network line (i, j), It represents the maintenance time of maintenance personnel p on the faulty gas distribution network line (m,n); represents the travel time of maintenance personnel p from the faulty distribution network line (i, j) to (j, k); T represents the travel time of maintenance personnel p from the faulty gas distribution network line (m,n) to (n,o); d Indicates the time when the fault occurred in stage d; F ij,p and F mn,p Respectively indicate whether maintenance personnel p has arrived at (i, j) and (m, n); and It is a 0-1 variable, indicating whether the maintenance of (i, j) and (m, n) is completed at time t; ε is a very small real number.

4. The multi-stage gas-electricity distribution network coordinated restoration method according to claim 1 is characterized in that: The mathematical model corresponding to the network reconstruction in step 2 is expressed as follows: Network Reconfiguration Constraints: In the formula, Ω L is the distribution network line set; Ω Γ is the set of reconstructed tie switches; N is the number of distribution network nodes; β jt Indicates whether the distribution network node j is the root node at time t; P' ij,t and P′ jk,t They are the virtual power flows of distribution network lines (i, j) and (j, k) respectively; Indicates whether the state of the tie switch on the distribution network line (i, j) changes at time t; N total,max The maximum number of actions allowed for the reconstruction in the entire period.

5. The multi-stage gas-electricity joint distribution network coordinated restoration method according to claim 1 is characterized in that: The dynamic island division model and frequency reserve model considering the frequency adjustment characteristics in step 3 are mathematically expressed as follows: 1) Dynamic island division: l iht ·l jht =a ij,t and ij,h,t ≤λ iht and ij,h,t ≤λ jht y ij,h,t ≥λ iht -l jht +1 y ij,h,t ≥λ iht +λ jht -1 a ht ≤∑ j l jht Where h is the dynamic island index; Ω H is an island set; Ω DG is the set of distributed unit nodes; jht and λ iht They respectively indicate whether the distribution network nodes j and i belong to the dynamic island h at time t; y ij,h,t Indicates whether the distribution network line (i, j) belongs to the dynamic island h at time t; α ht Indicates whether the dynamic island h exists at time t; Indicates whether the dynamic island h contains distributed units at time t; 2) Frequency reserve constraints: In the formula, Ω h Represents the set of devices connected to the dynamic island h; represents the power disturbance of distribution network node j at time t; H h is the inertia of the dynamic island h; t db and t nad The frequency adjustment dead time and the frequency minimum point time; f(0) and f(t nad ) represents the initial time frequency and at t nad The frequency of 0 、f nad and f db They represent the reference frequency, the frequency at the lowest frequency point, and the frequency at the end of the dead time respectively; represents the upper reserve of distributed unit c at time t, represents the maximum value of the reserve on the distributed unit c; J c represents the time constant of the distributed unit c; γ represents the frequency change rate, γ max Indicates the maximum frequency change rate; UR c is the climbing rate of distributed unit c.

6. The multi-stage gas-electricity distribution network coordinated restoration method according to claim 1 is characterized in that: The demand response constraint in step 4 is expressed as follows: a rl =(a e ·or e ) / (a g ·or g ) In the formula, Ω RL is a set of replaceable load nodes; and They represent the curtailable, transferable and replaceable electric load demand responses of distribution network node j at time t respectively; They represent curtailable, shiftable, and replaceable gas load demand responses, respectively; and represent the demand response coefficients of electricity load and gas load respectively; It indicates the maximum value of the load demand response that can be reduced by the distribution network node j; It indicates the maximum value of gas load demand response that can be reduced by gas distribution network node n; and They represent the outgoing and incoming demand responses of the electric load at the distribution network node j at time t respectively; and They represent the outgoing and incoming demand responses of gas load at distribution network node n at time t respectively; and They represent the load transfer-out and load transfer-in states of distribution network node j at time t respectively; and They represent the outgoing and incoming states of gas load at the gas distribution network node n at time t respectively; and They represent the minimum and maximum values ​​of the load transfer demand response of the distribution network node j respectively; and They represent the minimum and maximum values ​​of the gas load transfer-out demand response of the gas distribution network node n, respectively; and They represent the minimum and maximum values ​​of the electrical load transferred to the demand response at the distribution network node j respectively; and They represent the minimum and maximum values ​​of gas load transferred to demand response at node n of the gas distribution network respectively; It represents the maximum value of the transferable 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 the alternative load factor; α e and α g It is the unit calorific value of electricity and the unit calorific value of gas; η e and η g It is the electricity energy conversion efficiency and gas energy conversion efficiency.

7. The multi-stage gas-electricity distribution network coordinated restoration method according to claim 1 is characterized in that: In step 5, the abstract mathematical model corresponding to the multi-stage gas-electricity joint distribution network coordinated restoration model is expressed as follows: Where d is the fault stage index; δ and θ are the fault scenario indexes; and σ are wind power scenario indexes; S is the wind power scenario set; p dδ is the probability of failure condition δ in stage d; For wind power scenarios The probability of the failure condition δ in stage d; ξ represents the staged realization of the failure uncertainty; For the fault condition δ wind power scenario in stage d Continuous variables under ; For the fault condition δ wind power scenario in stage d Under load loss; a dδ 、b dδ 、c dδ , A, B, C, D d 、E d and l dδ For abstract matrices and vectors; and They represent the fault uncertainty ξ dδ and dθ Decisions under influence; dδσ is the decision-making under the fault condition δ wind power scenario σ in stage d, In the fault situation of stage d, wind power scenario The following decision.

8. The multi-stage gas-electricity joint distribution network coordinated restoration method according to claim 7 is characterized in that: In step 6, an improved step-by-step hedging algorithm is used to solve the multi-stage gas-electricity distribution network coordination recovery model, as follows: Step 6.1: Parameter initialization; let the number of iterations v←0, parameter And calculate the decision under each failure scenario: Among them, u d is the decision tree node of stage d; Indicates u d The corresponding iterative multiplier is is the decision of the fault scenario δ under the iteration number v+1; Step 6.2: Update the number of iterations v←v+1; Step 6.3: Aggregate d-stage decision tree node u d Decision-making, obtain the reference decision coefficient: in, for u d The corresponding reference decision, is the decision tree node set of the uncertainty ξ in stage d, for u d The corresponding probability is for u d The corresponding solution decision; Step 6.4: For each failure scenario, update the parameters: Among them, ζ is the penalty coefficient; Step 6.5: Decouple the calculations for each failure scenario decision: Step 6.6: Iteration exit condition: If each scene tree node corresponds to a decision If they are equal, exit the iteration; otherwise, the corresponding decisions of the scene tree nodes that are equal to the fixed part are constants, and return to step 6.2.

Images