Homogenization dimensionality reduction decoupling method for coordinated restoration of large-scale heterogeneous non-constant multi-energy systems

Abstract

The present invention discloses a homogenization dimensionality reduction decoupling method for coordinated recovery of large-scale heterogeneous non-constant multi-energy systems, comprising: constructing a two-layer optimization model for post-disaster load recovery timing decision of electricity-gas-water multi-energy under multiple coupled non-constant partial differential constraints based on a dynamic reconstruction model of a power grid, a compressible dynamic energy flow model of a gas grid and a non-constant hydrodynamic energy flow model of a water grid; discretizing the dynamic reconstruction model of the power grid, the compressible dynamic energy flow model of the gas grid and the non-constant hydrodynamic energy flow model of the water grid into a coupled algebraic equation group in time and space respectively; constructing an optimized dimensionality reduction model for post-disaster load recovery timing decision of electricity-gas-water multi-energy in modal space based on the coupled algebraic equation group of the power grid, the gas grid and the water grid; decoupling the optimized dimensionality reduction model for post-disaster load recovery timing decision of electricity-gas-water multi-energy into three independent scheduling sub-models with different time scales to solve and obtain the optimal solution of the original optimized dimensionality reduction model for post-disaster load recovery timing decision of electricity-gas-water multi-energy.

Description

Technical Field

[0001] The present invention relates to the technical field of power systems, and in particular to a homogenization dimensionality reduction decoupling method for collaborative restoration of large-scale heterogeneous non-constant multi-energy systems. Background Art

[0002] The main technical difficulty of multi-energy system emergency linkage technology in engineering applications is that the disaster prevention and emergency measures of each system and department are independently decided, and the emergency response time scale and dynamic characteristics of different energy systems are significantly different, making it difficult to achieve effective coordination. The multi-energy emergency coordinated recovery decision-making problem involves high-dimensional spatiotemporal partial differential constraint optimization solution, especially the dynamic characteristics of open and non-constant multi-energy flow networks, which leads to its technical bottleneck that the simultaneous solution process of multi-energy coordinated decision-making is extremely difficult. In addition, when analyzing the dynamic characteristics of multi-energy networks, its energy flow characteristics need to be represented by hyperbolic dynamic partial differential equations, while nonlinear dynamic partial differential equations are difficult to directly apply to optimization calculations. To solve this problem, existing studies usually use finite difference methods to realize approximate discrete processing of dynamic partial differential equations in two dimensions of time and space. However, high-precision differential discretization requires the selection of appropriate difference formats and smaller difference steps, resulting in the explosive growth of the spatiotemporal grid node state variables of the non-constant partial differential numerical solution as the accuracy requirements increase, increasing the difficulty of solving multi-energy linkage decisions and reducing the solution speed, resulting in extremely difficult decision optimization models.

[0003] At present, most of the research on dimensionality reduction modeling of multi-energy systems usually adopts two-port network modeling, which highly ignores the partial differential characteristic terms of the original energy flow model, resulting in a large truncation error of the dimensionality reduction model. Homogenization dimensionality reduction of large-scale heterogeneous and non-constant multi-energy networks is still in a technical gap. It is difficult to shorten the solution time while ensuring high model accuracy. The significant differences in the scheduling time scales of different energy networks make it difficult to make decisions simultaneously, resulting in a long recovery time for multi-energy loads. Summary of the invention

[0004] In view of this, the present invention provides a homogeneous dimensionality reduction decoupling method for coordinated recovery of large-scale heterogeneous non-constant multi-energy systems, which is used to at least solve the problem in the prior art that it is difficult to accurately and quickly realize emergency decision-making for coordinated recovery of power outages in large-scale heterogeneous non-constant multi-energy systems under extreme disasters.

[0005] In order to achieve the above object, the present invention adopts the following technical solution:

[0006] The homogenization dimensionality reduction decoupling method for coordinated recovery of large-scale heterogeneous non-constant multi-energy systems includes the following steps:

[0007] S1. Based on the uniform transmission line characteristics of the power grid, the compressible fluid dynamics characteristics of the gas grid, and the hydrodynamic energy flow characteristics of the water grid, a dynamic reconstruction model of the power grid, a compressible dynamic energy flow model of the gas grid, and a non-constant hydrodynamic energy flow model of the water grid are constructed respectively. Based on the dynamic reconstruction model of the power grid, the compressible dynamic energy flow model of the gas grid, and the non-constant hydrodynamic energy flow model of the water grid, a two-layer optimization model for the timing decision of post-disaster load recovery of multiple energy sources of electricity, gas, and water under multiple coupling non-constant partial differential constraints is constructed, including: an upper-layer load emergency power supply decision model is used to obtain the load emergency power supply decision of the dynamic coordinated reconstruction of the electricity-gas-water multi-energy network, a lower-layer mobile emergency resource scheduling optimization model is used to obtain multi-type mobile emergency resource scheduling considering the multi-energy load repair path planning, and the upper-layer load emergency power supply decision model and the lower-layer mobile emergency resource scheduling optimization model interact iteratively to roll over the electricity-gas-water multi-energy network and the repair path strategy;

[0008] S2. Discretize the dynamic reconstruction model of the power grid, the compressible dynamic energy flow model of the gas grid and the non-steady hydrodynamic energy flow model of the water grid into a system of coupled algebraic equations through time and space grids respectively;

[0009] S3. Based on the coupled algebraic equations of the power grid, gas grid and water grid, the discrete state data of the spatiotemporal grid of electricity, gas and water energy are extracted to form a snapshot matrix, and its intrinsic mode is decomposed to obtain the optimal orthogonal characteristic basis that characterizes the characteristics of electric energy flow, compressible gas energy flow and hydraulic energy flow. The equivalent linear modal space equations of the dynamic reconstruction model of the power grid, the compressible dynamic energy flow model of the gas grid and the non-constant hydrodynamic energy flow model of the water grid are further derived to obtain the homogenization and dimensionality reduction of the equivalent linear modal space equations, thereby constructing the optimization dimensionality reduction model of the post-disaster load recovery timing decision of electricity, gas and water multi-energy in the modal space;

[0010] S4. Considering the asynchronous interaction of coupling information caused by the differences in emergency response time scales of different energy systems, the Lagrangian relaxation decomposition method is used to decouple the electricity-gas-water multi-energy post-disaster load recovery timing decision optimization and reduction model into three independent scheduling sub-models with different time scales: power grid scheduling sub-model, water network scheduling sub-model and gas network scheduling sub-model. The scheduling decisions of each scheduling sub-model are optimized in parallel through the coordinated decision variables among the asynchronously interacting scheduling sub-models, and the optimization results and boundary information of each scheduling sub-model are fed back to its associated sub-model respectively. After updating the coordination variables, each scheduling sub-model is optimized in turn, and the interactive iteration is repeated until the optimal solution of the original electricity-gas-water multi-energy post-disaster load recovery timing decision optimization and reduction model is obtained.

[0011] Preferably, the iterative interaction between the upper load emergency power supply decision model and the lower mobile emergency resource scheduling optimization model in S1 to roll over the electricity-gas-water multi-energy network and the repair path strategy includes:

[0012] (1) Input the parameters of the power grid, gas grid, and water grid, and set the number of iterations and convergence threshold;

[0013] (2) Solve the upper-level main problem to obtain the emergency power supply decision of important load nodes, and pass the load restoration decision and network topology update information to the lower-level sub-problems;

[0014] (3) The lower-level sub-problem determines the water-blocking status of the fault area according to the water level in the fault area, solves the emergency repair resource configuration, and transmits the equipment recovery status of the fault area to the upper-level main problem to update the multi-energy network topology;

[0015] (4) Calculate the convergence criterion. If the solution of the current iteration meets the preset convergence condition, the iteration ends and the optimal solution is output; otherwise, jump to step (2) and continue iterating until the convergence criterion is met.

[0016] Preferably, the specific content of S3 includes:

[0017] (1) Multi-energy flow spatial intrinsic reconstruction

[0018] The number of river channel space segments is , the number of scheduling time segments is , before extraction The spatiotemporal discrete state data of river water level and flow in each period constitutes a snapshot matrix of hydraulic energy flow distribution. :

[0019] ,

[0020] In the formula, and For the Period Water level and flow at each spatial segment of the river;

[0021] Extracting the snapshot matrix of hydraulic energy flow distribution through eigenmode decomposition Key hydraulic energy flow characteristics:

[0022] ,

[0023] ,

[0024] ,

[0025] ,

[0026] In the formula, for In descending order non-zero eigenvalues ​​of the hydraulic energy flow space; for Arrange the non-zero eigenvalues ​​in descending order orthogonal eigenvectors; for Arrange the non-zero eigenvalues ​​in descending order orthogonal eigenvectors; for OK zero matrix of columns; and They are , Composition , Orthogonal matrix:

[0027] ,

[0028] Pick Before Column vectors :

[0029] ,

[0030] make , ,express Column vector of exist Projection Records on :

[0031] ,

[0032] In the formula, Representation vector and The inner product of For the A unit column vector with 1 components and the rest 0. According to the relationship between the matrix norm and the spectral radius, we can calculate and The truncation error is:

[0033] ,

[0034] but The optimal orthogonal characteristic basis for characterizing key hydraulic energy flow characteristics;

[0035] (2) Dimensionality reduction and extrapolation of spatiotemporal differential projection

[0036] make , , using the rolling optimization solution method, assuming that the rolling time, then When all variables are known at a certain moment, the coupled algebraic equations of the water network can be written in vector form:

[0037] ,

[0038] In the formula, and The time and space steps are respectively, , For the In the period Rainfall intensity at each river section; and For two matrix:

[0039] ,

[0040] ,

[0041] when season The corresponding dimensionality reduction solution ,when season , then the equivalent linear modal space equation of the homogenization and dimensionality reduction of the water network unsteady hydrodynamic energy flow model is obtained as follows:

[0042] ,

[0043] In the formula, The modal space state vector representing the projection of the time-domain discrete variables of the hydraulic energy flow onto the optimal orthogonal eigenbasis;

[0044] Then the dimensionality reduction solution of the non-steady hydrodynamic energy flow model of the water network is obtained after homogenization dimensionality reduction:

[0045] ,

[0046] Therefore, the equivalent linear modal space equations of the power grid dynamic reconstruction model and the gas grid compressible dynamic energy flow model are simplified through homogenization and dimensionality reduction processing:

[0047] ,

[0048] ,

[0049] In the formula, The modal space state vector representing the projection of the discrete variables of the electric energy flow in the time domain onto the optimal orthogonal eigenbasis; The optimal orthogonal characteristic basis for characterizing key power flow characteristics; Represents the column vector of the instantaneous matrix of power flow distribution; and For the Period Voltage and current at each transmission line segment; and They represent the vector form of the power grid dynamic reconstruction model and The coefficient matrix of A modal space state vector representing the projection of time-domain discrete variables of electric energy flow and compressible gas energy flow onto an optimal orthogonal eigenbasis; The optimal orthogonal characteristic basis for characterizing the key compressible gas energy flow characteristics; Represents the column vector of the instantaneous matrix of compressible gas energy flow distribution; and For the Period Gas pressure and mass flow at each gas pipeline section; and They represent the isothermal Euler partial differential equation of the gas network compressible fluid in vector form. and The coefficient matrix of

[0050] The previous results of rolling optimization are transformed into The original solution for the time period Project to the optimal orthogonal eigenvalue basis to obtain the previous Step dimensionality reduction solution , and then by the orthogonal characteristic basis and the The dimension reduction solution of all time periods is recursively obtained by step-by-step dimension reduction solution;

[0051] (3) High-fidelity dynamic screening feature base

[0052] The number of orthogonal characteristic basis vectors representing hydraulic energy flow characteristics, electric energy flow characteristics and compressible gas flow characteristics is calculated using the instantaneous image feature high-fidelity dynamic screening method. , thereby constructing a set of optimal orthogonal eigenbases;

[0053] For the reduced-dimensional solution component obtained by reduced-order extrapolation difference, the truncation error between it and the original solution is:

[0054] ,

[0055] In the formula, ,and ;

[0056] For preset model accuracy , make sure to satisfy Minimum accuracy required ; At the same time, in the process of reduced-order extrapolation, if , then re-extract the spatiotemporal discrete state data to form a new multi-energy energy flow instantaneous image matrix , and construct a new optimal orthogonal eigenbase until the dimensionality reduction solution on all time layers is obtained;

[0057] .

[0058] Preferably, the two-layer optimization model for post-disaster load restoration timing decision of electricity, gas and water multi-energy is specifically:

[0059] The upper load emergency power supply decision model includes:

[0060] The objective function is to maximize the weighted power failure load recovery:

[0061] ,

[0062] In the formula, for At any time, is a set of discrete time points; is the set of power-off nodes in the distribution network; To characterize Time Node A 0-1 variable indicating the load operating state; for Time Node Active power supplied by the system required by other loads except the drainage pump station; For Node The weight coefficient of the load at the location; express Time Node Drainage pump station 0-1 variable of running status; For Node Drainage pump station The load weight factor; for Time Node Drainage pump station Active power of

[0063] The constraints include: the dynamic reconstruction model of the power grid and its constraints, the compressible dynamic energy flow model of the gas grid and its constraints, and the non-steady hydrodynamic energy flow model of the water grid and its constraints;

[0064] The lower-level mobile emergency resource scheduling optimization model includes:

[0065] The scheduling objective function is to minimize the total repair time:

[0066] ,

[0067] In the formula, The order of emergency repairs for the faulty area; For the repair team involved in the dispatch A collection of; For the repair team Total repair time; is the set of fault areas, and They are Any fault area in ; For the repair team From the fault area arrive 0-1 variable, if the repair team The path contains the fault area arrive , then the value is 1, otherwise it is 0; For the repair team From the fault area Rushing to the fault area The travel time; For the repair team Repair the faulty area the time required;

[0068] Constraints include: mobile emergency resource scheduling constraints.

[0069] Preferably, the power grid dynamic reconstruction model and its constraints include:

[0070] The electric power dynamic network is modeled using the telegraph partial differential equation that characterizes the characteristics of uniform transmission lines. The dynamic reconstruction model of the power grid is:

[0071] ,

[0072] In the formula, and Respectively Transmit online position at all times The voltage and corresponding current at and Respectively represent the time and the coordinates along the transmission line direction; and are the resistance and inductance per unit length of the transmission line, respectively. and They represent the conductance and capacitance per unit length of the transmission line, respectively;

[0073] The constraints of the power grid dynamic reconstruction model include:

[0074] ,

[0075] ,

[0076] ,

[0077] ,

[0078] ,

[0079] ,

[0080] ,

[0081] In the formula, express Timeline Connectivity state variables, Indicates line closure, Indicates that the line is disconnected; is a 0-1 state variable, where Indicates that the line is closed. Indicates that the line is disconnected; is a 0-1 state variable, where Representation Node Is a node The parent node of is a collection of lines; is a set of power grid nodes; For the node A collection of connected nodes; To express Timeline A 0-1 variable for the switch state change, where Indicates that the circuit breaker is closed. Indicates that the line switch is disconnected; and for Mobile power supply vehicle injects power into nodes at any time Active and reactive power; and for Time Node Active and reactive power generated by the gas turbine; and They are Timeline Active and reactive power flowing through; and They are Timeline Active and reactive power flowing through; for Time Node Reactive power supplied by the system required by other loads except the drainage pump station; for Time Node Drainage pump station Reactive power;

[0082] The compressible dynamic energy flow model of the gas grid and its constraints include:

[0083] When the gas flows isothermally in the pipeline, it is characterized by a one-dimensional isothermal Euler partial differential equation. The compressible dynamic energy flow model of the gas network is:

[0084] ,

[0085] In the formula, and Respectively Position on pipeline at the moment Gas pressure and mass flow rate at ; is the speed of sound; is the cross-sectional area of ​​the pipe; Indicates the pipe friction coefficient; is the inner diameter of the pipe;

[0086] The gas grid and the power grid are coupled through a gas turbine, and the coupled device constraints are:

[0087] ,

[0088] In the formula, For the operating efficiency of the gas turbine; for The gas mass flow rate input to the gas turbine at all times; is the specific enthalpy of the gas turbine;

[0089] The gas network operation constraints are:

[0090] ,

[0091] ,

[0092] ,

[0093] ,

[0094] In the formula, for Time Node Gas pressure at and They are End time node and the first node Gas pressure at is the node set of the gas network; and Respectively represent the nodes The gas network pipeline set of the first node and the last node; for Time Node Injected gas mass flow rate; and They are Time outflow end node and the inflow node Gas mass flow rate; and Node Upper and lower limits of pressure; and Node Upper and lower limits of mass flow rate;

[0095] The unsteady hydrodynamic energy flow model of the water network and its constraints include:

[0096] Assuming the cross section of the river is a rectangle, the relationship between the water level and flow in the river satisfies the non-steady Saint-Venant hydrodynamic partial differential equation:

[0097] ,

[0098] ,

[0099] ,

[0100] In the formula, and Respectively Current river position Water level and flow at the site; It indicates the amount of water flowing into the river side per unit length; is the acceleration due to gravity; and They represent the riverbed slope and the equivalent friction of the river channel respectively; is the Manning coefficient; is the width of the river;

[0101] For drainage pumping stations connected to rivers and lakes, the power-flow relationship is:

[0102] ,

[0103] ,

[0104] In the formula, is the density of water; For Node Drainage pump station Static head; for Time Node Drainage pump station Traffic volume; For Node Drainage pump station operational efficiency; For Node Drainage pump station Power factor; Assemble for the drainage pump station;

[0105] When the water level in the drainage channel is low, the water flow is regarded as a pressureless non-steady flow, and the one-dimensional Saint-Venant partial differential equation is used to describe the change of hydraulic elements along the channel:

[0106] ,

[0107] ,

[0108] ,

[0109] ,

[0110] In the formula, for Time Channel Cross-sectional area of ​​water flow; for Time Channel Confluence flow; for Time Channel water depth; for Time Channel The hydraulic slope of for Time Channel The channel bottom slope; is the width of the pipe; is the cross-sectional area of ​​the conduit; is the hydraulic radius; For pipe and channel collection;

[0111] Simultaneous fault area In the period The water depth, rainfall intensity, drainage capacity of the drainage truck and the amount of water discharged into the pipe network meet the water balance constraints:

[0112] ,

[0113] In the formula, Fault area Flooded area; Fault area In the period The depth of waterlogging; It is a collection of flooded sub-areas; For the period area The rainfall intensity within Fault area rainfall area; Assemble emergency drainage vehicles located in flooded areas; and The time periods Emergency drainage vehicle Pumping and drainage volume and inflow into the canal of rainfall; A collection of drainage canals for flooded areas; is the set of fault areas; is the time period length;

[0114] Mobile emergency resource scheduling constraints include:

[0115] Path constraints, resource limitation constraints, and time scheduling constraints:

[0116] ,

[0117] ,

[0118] In the formula, Indicates the repair team Upon reaching the fault area moment; The time when all faulty areas are repaired; is a maximum positive real number; and are the starting point and end point sets respectively; It is a 0-1 variable. If the fault area exist If the moment is repaired, the value is 1, otherwise it is 0; Fault area Fix the 0-1 variable of the status, if the fault area The repair team If repaired, the value is 1, otherwise it is 0;

[0119] At the same time, considering the impact of water accumulation in the fault area on the flooding of power equipment, in order to ensure that the power equipment can resume operation safely and reliably after the emergency repair is completed, the flooding blocking constraint in the fault area is introduced:

[0120] ,

[0121] ,

[0122] In the formula, Indicates the fault area exist The flood blocking state at the moment, if the water level in the fault area is higher than the specified height, the value is 1, otherwise it is 0; Indicates the allowable flooding depth of electrical equipment in the fault area.

[0123] Preferably, the specific content of S2 includes:

[0124] The central difference method and Implicit Cell Centered linear difference method are used to discretize the space-time grids of the power grid dynamic reconstruction model and the gas grid compressible dynamic energy flow model into a set of coupled algebraic equations:

[0125] ,

[0126] ,

[0127] In the formula, For the Period The voltage at each transmission line segment; For the Period The current at each transmission line segment; Respectively Period The pressure and mass flow rate at each gas network segment; and are the resistance and inductance per unit length of the transmission line, respectively. and They represent the conductance and capacitance per unit length of the transmission line, respectively; is the speed of sound; is the cross-sectional area of ​​the pipe; Indicates the pipe friction coefficient; is the inner diameter of the pipe;

[0128] The Preissmann four-point implicit difference method is used to discretize the unsteady hydrodynamic energy flow model of the water network into a set of coupled algebraic equations:

[0129] ,

[0130] In the formula, and and space step length, respectively; and For the Period Water level and flow at each river section; and For the In the period and Rainfall intensity at each river section; is the acceleration due to gravity; is the Manning coefficient; is the width of the river.

[0131] Preferably, the specific content of S4 includes:

[0132] The Lagrangian relaxation decomposition method is used to decouple the multi-energy post-disaster load restoration timing decision optimization dimensionality reduction model of electricity, gas and water into three independent scheduling sub-models with different time scales. Each scheduling sub-model includes a power grid scheduling sub-model , Water network dispatch sub-model And the gas grid dispatch sub-model ,Will Represents a set of scheduling sub-models, where any scheduling sub-model is denoted as , The associated submodel is denoted as , express The associated submodel A collection of;

[0133] The original electricity-gas-water multi-energy post-disaster load restoration timing decision optimization dimensionality reduction model is expressed as:

[0134] ,

[0135] ,

[0136] In the formula, express The load recovery function, and Respectively represent the local decision variables and coordination decision variables of each scheduling sub-model; and Respectively Passed to its associated child model And sub-models Pass it to its associated The coordination decision variables of

[0137] By introducing the dual multiplier Eliminate the coupling variable constraints and further express the original electricity-gas-water multi-energy post-disaster load restoration timing decision optimization dimensionality reduction model as an augmented Lagrangian function :

[0138] ,

[0139] In the formula, and They are Passed to its associated child model and its associated sub-models Pass to The dual multiplier of ;

[0140] The augmented Lagrangian function is decoupled into different scheduling sub-models:

[0141] 1) Power grid dispatch sub-model The objective function is:

[0142] ,

[0143] In the formula, It is the local decision variable of the power grid dispatch sub-model; It is the coordination decision variable between the power grid dispatch submodel and the water grid and gas grid dispatch submodel; and The power grid dispatch sub-model is passed to its associated sub-model and its associated sub-models The dual multiplier passed to the power grid submodel; and The power grid dispatch sub-model is passed to its associated sub-model and its associated sub-models coordination decision variables passed to the grid sub-model; represents the load recovery function of the power grid dispatch submodel;

[0144] 2) Water network scheduling sub-model The objective function is:

[0145] ,

[0146] In the formula, It is the local decision variable of the water network scheduling sub-model; It is the coordination decision variable between the water network dispatch sub-model and the power grid and gas grid sub-models; and The water network scheduling sub-model is passed to its associated sub-model and its associated sub-models The dual multiplier passed to the water grid model; and The water network scheduling sub-model is passed to its associated sub-model and its associated sub-models coordination decision variables passed to the water grid sub-model; represents the load recovery function of the water network dispatch submodel;

[0147] 3) Gas network dispatch sub-model The objective function is:

[0148] ,

[0149] In the formula, It is the local decision variable of the gas grid dispatch sub-model; Includes coordination decision variables between the gas grid dispatch sub-model and the power grid and gas grid sub-models; and The gas grid dispatch sub-model is passed to its associated sub-model and its associated sub-models The dual multiplier passed to the gas grid sub-model; and The gas grid dispatch sub-model is passed to its associated sub-model and its associated sub-models coordination decision variables passed to the gas-grid sub-model; represents the load recovery function of the gas grid dispatch submodel;

[0150] At the same time, considering the asynchronous interaction of coupled information caused by the differences in emergency response time scales of different energy systems, an asynchronous mutual feedback method is adopted to interact with multi-energy network coordination decision variables, and auxiliary decision variables are introduced and auxiliary multipliers Coordination decision variables used to track asynchronous interactions and the dual multiplier ;

[0151] The Lagrangian relaxation decomposition method specifically includes the following contents:

[0152] (1) Initialize the coordination decision variables, dual multipliers, auxiliary decision variables, and auxiliary multipliers of each scheduling sub-model;

[0153] (2) Parallel optimization of the scheduling decisions of each scheduling sub-model to update the local decision variables and intermediate variables that coordinate decision variables , and its update formula is:

[0154] ,

[0155] In the formula, and Respectively represent In iteration Passed to its associated child model The dual multiplier, auxiliary multiplier, auxiliary decision variable and intermediate variable of the coordinated decision variable;

[0156] (3) Update Coordination decision variables between its associated sub-models ; If in the In the iteration, the associated submodel and To exchange information, use and the previous iteration value Convex combination of updated coordinated interaction variables , which is of the form:

[0157] ,

[0158] In the formula, represents the weight coefficient of the convex combination;

[0159] Otherwise, keep The value of the previous iteration constant;

[0160] The updated coordinated interaction variable Send to associated child model and accepts the associated child model The coordinated interaction variable ;

[0161] (4) Update auxiliary decision variables and the dual multiplier ; If in the In the iteration, Receive its associated sub-model The coordinated interaction variable and dual multiplier , then update the auxiliary decision variables respectively and the dual multiplier Otherwise, keep and The value of the previous iteration and ;

[0162] ,

[0163] ,

[0164] The updated dual multiplier Send to associated child model and accepts the associated child model The dual multiplier of ;

[0165] (5) Update auxiliary multiplier variables ; If in the In the iteration, Receive its associated sub-model Updated dual multiplier , then assign it to ,Right now Otherwise, keep is the auxiliary multiplier variable value of the previous iteration ;

[0166] (6) For The scheduling sub-model that does not exchange information in the iteration is kept , , and is the value of the previous iteration, that is , , , ;

[0167] (7) Determine the convergence conditions; interactively and repeatedly iterate and calculate the original residual until the convergence criteria are met, thereby obtaining the optimal solution of the original electricity-gas-water multi-energy post-disaster load restoration timing decision optimization dimensionality reduction model;

[0168] ,

[0169] In the formula, Indicates The original residual after iterations; is the convergence accuracy of the original residual.

[0170] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a homogenization dimensionality reduction decoupling method for collaborative recovery of large-scale heterogeneous non-constant multi-energy systems, which has the following beneficial effects:

[0171] Compared with the existing emergency drainage scheduling method of the water conservancy network under heavy rain disasters, the electricity-gas-water multi-energy emergency collaborative recovery decision proposed in the present invention effectively ensures the rapid power supply restoration of the power grid by dynamically coordinating the reconstruction of multiple energy sources and scheduling multiple types of emergency resources to provide emergency power supply to key multi-energy loads. At the same time, the homogenization dimensionality reduction technology is used to greatly reduce the dimension of the multi-energy flow optimization constraint vector, thereby reducing the difficulty of solving the optimization model of the post-disaster load recovery timing decision of electricity-gas-water multi-energy; on this basis, the dimensionality reduction model is decoupled into three scheduling sub-models for parallel optimization and solution in combination with the Lagrangian relaxation decomposition method. Compared with solver solution methods such as ADCME and Moose + Gurobi, the present invention reduces the decision calculation time by more than two orders of magnitude while ensuring the solution accuracy, greatly improving the solution efficiency of large-scale multi-energy collaborative recovery models. BRIEF DESCRIPTION OF THE DRAWINGS

[0172] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0173] Figure 1 This is a flow chart of the homogenization dimensionality reduction decoupling method for collaborative recovery of large-scale heterogeneous non-constant multi-energy systems proposed in the present invention. DETAILED DESCRIPTION

[0174] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0175] The present invention provides a homogenization dimensionality reduction decoupling method for coordinated recovery of large-scale heterogeneous non-constant multi-energy systems, comprising the following steps:

[0176] S1. Based on the uniform transmission line characteristics of the power grid, the compressible fluid dynamics characteristics of the gas grid, and the hydrodynamic energy flow characteristics of the water grid, a dynamic reconstruction model of the power grid, a compressible dynamic energy flow model of the gas grid, and a non-constant hydrodynamic energy flow model of the water grid are constructed respectively. Based on the dynamic reconstruction model of the power grid, the compressible dynamic energy flow model of the gas grid, and the non-constant hydrodynamic energy flow model of the water grid, a two-layer optimization model for the timing decision of post-disaster load recovery of multiple energy sources of electricity, gas, and water under multiple coupling non-constant partial differential constraints is constructed, including: an upper-layer load emergency power supply decision model is used to obtain the load emergency power supply decision of the dynamic coordinated reconstruction of the electricity-gas-water multi-energy network, a lower-layer mobile emergency resource scheduling optimization model is used to obtain multi-type mobile emergency resource scheduling considering the multi-energy load repair path planning, and the upper-layer load emergency power supply decision model and the lower-layer mobile emergency resource scheduling optimization model interact iteratively to roll over the electricity-gas-water multi-energy network and the repair path strategy;

[0177] S2. Discretize the dynamic reconstruction model of the power grid, the compressible dynamic energy flow model of the gas grid and the non-steady hydrodynamic energy flow model of the water grid into a system of coupled algebraic equations through time and space grids respectively;

[0178] S3. Based on the coupled algebraic equations of the power grid, gas grid and water grid, the discrete state data of the spatiotemporal grid of electricity, gas and water energy are extracted to form a snapshot matrix, and its intrinsic mode is decomposed to obtain the optimal orthogonal characteristic basis that characterizes the characteristics of electric energy flow, compressible gas energy flow and hydraulic energy flow. The equivalent linear modal space equations of the dynamic reconstruction model of the power grid, the compressible dynamic energy flow model of the gas grid and the non-constant hydrodynamic energy flow model of the water grid are further derived to obtain the homogenization and dimensionality reduction of the equivalent linear modal space equations, thereby constructing the optimization dimensionality reduction model of the post-disaster load recovery timing decision of electricity, gas and water multi-energy in the modal space;

[0179] S4. Considering the asynchronous interaction of coupling information caused by the differences in emergency response time scales of different energy systems, the Lagrangian relaxation decomposition method is used to decouple the electricity-gas-water multi-energy post-disaster load recovery timing decision optimization and reduction model into three independent scheduling sub-models with different time scales: power grid scheduling sub-model, water network scheduling sub-model and gas network scheduling sub-model. The scheduling decisions of each scheduling sub-model are optimized in parallel through the coordinated decision variables among the asynchronously interacting scheduling sub-models, and the optimization results and boundary information of each scheduling sub-model are fed back to its associated sub-model respectively. After updating the coordination variables, each scheduling sub-model is optimized in turn, and the interactive iteration is repeated until the optimal solution of the original electricity-gas-water multi-energy post-disaster load recovery timing decision optimization and reduction model is obtained.

[0180] In order to further implement the above technical solutions, the two-layer optimization model for post-disaster load restoration timing decision of electricity, gas and water multi-energy is as follows:

[0181] Based on the multi-energy coordinated restoration strategy for the time sequence restoration of important loads, an optimization model for the time sequence decision of post-disaster load restoration of electricity, gas and water multi-energy under multiple coupled non-constant partial differential constraints is constructed. The model fully considers the hydrodynamic energy flow characteristics represented by the Saint-Venant partial differential equation of the water network, the uniform transmission line characteristics represented by the telegraph partial differential equation of the power grid, and the compressible fluid dynamics characteristics represented by the isothermal Euler partial differential equation of the gas network. The upper main problem is the load emergency power supply decision of the dynamic coordinated reconstruction of the electricity, gas and water multi-energy network. Considering the maximum weighted power loss load recovery as the goal, the upper load emergency power supply decision model can be expressed as:

[0182] ,

[0183] In the formula, for At any time, is a set of discrete time points; is the set of power-off nodes in the distribution network; To characterize Time Node A 0-1 variable indicating the load operating state; for Time Node Active power supplied by the system required by other loads except the drainage pump station; For Node The weight coefficient of the load at the location; express Time Node Drainage pump station 0-1 variable of running status; For Node Drainage pump station The load weight factor; for Time Node Drainage pump station Active power of

[0184] The constraints include: the dynamic reconstruction model of the power grid and its constraints, the compressible dynamic energy flow model of the gas grid and its constraints, and the non-steady hydrodynamic energy flow model of the water grid and its constraints;

[0185] The lower-level sub-problem is the scheduling of multi-type mobile emergency resources considering the emergency repair path planning of multiple energy loads, with the shortest total repair time as the scheduling goal. The lower-level mobile emergency resource scheduling optimization model can be expressed as:

[0186] ,

[0187] In the formula, The order of emergency repairs for the faulty area; For the repair team involved in the dispatch A collection of; For the repair team Total repair time; is the set of fault areas, and They are Any fault area in ; For the repair team From the fault area arrive 0-1 variable, if the repair team The path contains the fault area arrive , then the value is 1, otherwise it is 0; For the repair team From the fault area Rushing to the fault area The travel time; For the repair team Repair the faulty area the time required;

[0188] Constraints include: mobile emergency resource scheduling constraints.

[0189] In order to further implement the above technical solutions, the iterative interaction between the upper load emergency power supply decision model and the lower mobile emergency resource scheduling optimization model in S1 to roll over the electricity-gas-water multi-energy network and the emergency repair path strategy includes:

[0190] (1) Input the parameters of the power grid, gas grid, and water grid, and set the number of iterations and convergence threshold;

[0191] (2) Solve the upper-level main problem to obtain the emergency power supply decision of important load nodes, and pass the load restoration decision and network topology update information to the lower-level sub-problems;

[0192] (3) The lower-level sub-problem determines the water-blocking status of the fault area according to the water level in the fault area, solves the emergency repair resource configuration, and transmits the equipment recovery status of the fault area to the upper-level main problem to update the multi-energy network topology;

[0193] (4) Calculate the convergence criterion. If the solution of the current iteration meets the preset convergence condition, the iteration ends and the optimal solution is output; otherwise, jump to step (2) and continue iterating until the convergence criterion is met.

[0194] In order to further implement the above technical solutions, the power grid dynamic reconstruction model and its constraints include:

[0195] The electric power dynamic network is modeled using the telegraph partial differential equation that characterizes the characteristics of uniform transmission lines. The dynamic reconstruction model of the power grid is:

[0196] ,

[0197] In the formula, and Respectively Transmit online position at all times The voltage and corresponding current at and Respectively represent the time and the coordinates along the transmission line direction; and are the resistance and inductance per unit length of the transmission line, respectively. and They represent the conductance and capacitance per unit length of the transmission line, respectively;

[0198] The constraints of the power grid dynamic reconstruction model include:

[0199] ,

[0200] ,

[0201] ,

[0202] ,

[0203] ,

[0204] ,

[0205] ,

[0206] In the formula, express Timeline Connectivity state variables, Indicates line closure, Indicates that the line is disconnected; is a 0-1 state variable, where Indicates that the line is closed. Indicates that the line is disconnected; is a 0-1 state variable, where Representation Node Is a node The parent node of is a collection of lines; is a set of power grid nodes; For the node A collection of connected nodes; To express Timeline A 0-1 variable for the switch state change, where Indicates that the circuit breaker is closed. Indicates that the line switch is disconnected; and for Mobile power supply vehicle injects power into nodes at any time Active and reactive power; and for Time Node Active and reactive power generated by the gas turbine; and They are Timeline Active and reactive power flowing through; and They are Timeline Active and reactive power flowing through; for Time Node Reactive power supplied by the system required by other loads except the drainage pump station; for Time Node Drainage pump station Reactive power;

[0207] The compressible dynamic energy flow model of the gas grid and its constraints include:

[0208] When the gas flows isothermally in the pipeline, it is characterized by a one-dimensional isothermal Euler partial differential equation. The compressible dynamic energy flow model of the gas network is:

[0209] ,

[0210] In the formula, and Respectively Position on pipeline at the moment Gas pressure and mass flow rate at ; is the speed of sound; is the cross-sectional area of ​​the pipe; Indicates the pipe friction coefficient; is the inner diameter of the pipe;

[0211] The gas grid and the power grid are coupled through a gas turbine, and the coupled device constraints are:

[0212] ,

[0213] In the formula, For the operating efficiency of the gas turbine; for The gas mass flow rate input to the gas turbine at all times; is the specific enthalpy of the gas turbine;

[0214] The gas network operation constraints are:

[0215] ,

[0216] ,

[0217] ,

[0218] ,

[0219] In the formula, for Time Node Gas pressure at and They are End time node and the first node Gas pressure at is the node set of the gas network; and Respectively represent the nodes The gas network pipeline set of the first node and the last node; for Time Node Injected gas mass flow rate; and They are Time outflow end node and the inflow node Gas mass flow rate; and Node Upper and lower limits of pressure; and Node Upper and lower limits of mass flow rate;

[0220] The unsteady hydrodynamic energy flow model of the water network and its constraints include:

[0221] The flood drainage emergency resource scheduling model satisfies the dynamic energy flow constraints of the flood drainage network. In order to reduce the complexity of the dynamic energy flow constraints and avoid large errors, the river section is set to a rectangular shape, and the relationship between the river water level and flow satisfies the non-constant Saint-Venant hydrodynamic partial differential equation:

[0222] ,

[0223] ,

[0224] ,

[0225] In the formula, and Respectively Current river position Water level and flow at the site; It indicates the amount of water flowing into the river side per unit length; is the acceleration due to gravity; and They represent the riverbed slope and the equivalent friction of the river channel respectively; is the Manning coefficient; is the width of the river;

[0226] For drainage pumping stations connected to rivers and lakes, the power-flow relationship is:

[0227] ,

[0228] ,

[0229] In the formula, is the density of water; For Node Drainage pump station Static head; for Time Node Drainage pump station Traffic volume; For Node Drainage pump station operational efficiency; For Node Drainage pump station Power factor; Assemble for the drainage pump station;

[0230] When the water level in the drainage channel is low, the water flow is regarded as a pressureless and unsteady flow, and the one-dimensional Saint-Venant partial differential equation is used to describe the change of hydraulic elements along the channel:

[0231] ,

[0232] ,

[0233] ,

[0234] ,

[0235] In the formula, for Time Channel Cross-sectional area of ​​water flow; for Time Channel Confluence flow; for Time Channel water depth; for Time Channel The hydraulic slope of for Time Channel The channel bottom slope; is the width of the pipe; is the cross-sectional area of ​​the conduit; is the hydraulic radius; For pipe and channel collection;

[0236] Simultaneous fault area In the period The water depth, rainfall intensity, drainage capacity of the drainage truck and the amount of water discharged into the pipe network meet the water balance constraints:

[0237] ,

[0238] In the formula, Fault area Flooded area; Fault area In the period The depth of waterlogging; It is a collection of flooded sub-areas; For the period area The rainfall intensity within Fault area rainfall area; Assemble emergency drainage vehicles located in flooded areas; and The time periods Emergency drainage vehicle Pumping and drainage volume and inflow into the canal of rainfall; A collection of drainage canals for flooded areas; is the set of fault areas; is the time period length;

[0239] Mobile emergency resource scheduling constraints include:

[0240] Path constraints, resource limitation constraints, and time scheduling constraints:

[0241] ,

[0242] ,

[0243] In the formula, Indicates the repair team Upon reaching the fault area moment; The time when all faulty areas are repaired; is a maximum positive real number; and are the starting point and end point sets respectively; It is a 0-1 variable. If the fault area exist If the moment is repaired, the value is 1, otherwise it is 0; Fault area Fix the 0-1 variable of the status, if the fault area The repair team If repaired, the value is 1, otherwise it is 0;

[0244] At the same time, considering the impact of water accumulation in the fault area on the flooding of power equipment, in order to ensure that the power equipment can resume operation safely and reliably after the emergency repair is completed, the flooding blocking constraint in the fault area is introduced:

[0245] ,

[0246] ,

[0247] In the formula, Indicates the fault area exist The flood blocking state at the moment, if the water level in the fault area is higher than the specified height, the value is 1, otherwise it is 0; Indicates the allowable flooding depth of electrical equipment in the fault area.

[0248] In order to further implement the above technical solution, the specific contents of S2 include:

[0249] The central difference method and Implicit Cell Centered linear difference method are used to discretize the space-time grids of the power grid dynamic reconstruction model and the gas grid compressible dynamic energy flow model into a set of coupled algebraic equations:

[0250] ,

[0251] ,

[0252] In the formula, For the Period The voltage at each transmission line segment; For the Period The current at each transmission line segment; Respectively Period The pressure and mass flow rate at each gas network segment; and are the resistance and inductance per unit length of the transmission line, respectively. and They represent the conductance and capacitance per unit length of the transmission line, respectively; is the speed of sound; is the cross-sectional area of ​​the pipe; Indicates the pipe friction coefficient; is the inner diameter of the pipe;

[0253] For the non-steady hydrodynamic energy flow model of the water network, in order to reduce its complexity and avoid large errors, this application uses the Preissmann four-point implicit difference method to discretize the Saint-Venant hydrodynamic partial differential equations into a set of algebraic difference equations, which are shown below:

[0254] ,

[0255] In the formula, and and space step length, respectively; and For the Period Water level and flow at each river section; and For the In the period and Rainfall intensity at each river section; is the acceleration due to gravity; is the Manning coefficient; is the width of the river.

[0256] In order to further implement the above technical solutions, the specific contents of S3 include:

[0257] (1) Multi-energy flow spatial intrinsic reconstruction

[0258] The number of river channel space segments is , the number of scheduling time segments is , before extraction The spatiotemporal discrete state data of river water level and flow in each period constitutes a snapshot matrix of hydraulic energy flow distribution. :

[0259] ,

[0260] In the formula, and For the Period Water level and flow at each spatial segment of the river;

[0261] Extracting the snapshot matrix of hydraulic energy flow distribution through eigenmode decomposition Key hydraulic energy flow characteristics:

[0262] ,

[0263] ,

[0264] ,

[0265] ,

[0266] In the formula, for In descending order non-zero eigenvalues ​​of the hydraulic energy flow space; for Arrange the non-zero eigenvalues ​​in descending order orthogonal eigenvectors; for Arrange the non-zero eigenvalues ​​in descending order orthogonal eigenvectors; for OK zero matrix of columns; and They are , Composition , Orthogonal matrix:

[0267] ,

[0268] Pick Before Column vectors :

[0269] ,

[0270] make , ,express Column vector of exist Projection Records on :

[0271] ,

[0272] In the formula, Representation vector and The inner product of For the A unit column vector with 1 components and the rest 0. According to the relationship between the matrix norm and the spectral radius, we can calculate and The truncation error is:

[0273] ,

[0274] but The optimal orthogonal characteristic basis for characterizing key hydraulic energy flow characteristics;

[0275] (2) Dimensionality reduction and extrapolation of spatiotemporal differential projection

[0276] make , , using the rolling optimization solution method, assuming that the rolling time, then When all variables are known at a certain moment, the coupled algebraic equations of the water network can be written in vector form:

[0277] ,

[0278] In the formula, and The time and space steps are respectively, , For the In the period Rainfall intensity at each river section; and For two matrix:

[0279] ,

[0280] ,

[0281] when season The corresponding dimensionality reduction solution ,when season , then the equivalent linear modal space equation of the homogenization and dimensionality reduction of the water network unsteady hydrodynamic energy flow model is obtained as follows:

[0282] ,

[0283] In the formula, The modal space state vector representing the projection of the time-domain discrete variables of the hydraulic energy flow onto the optimal orthogonal eigenbasis;

[0284] Then the dimensionality reduction solution of the non-steady hydrodynamic energy flow model of the water network is obtained after homogenization dimensionality reduction:

[0285] ,

[0286] Therefore, the equivalent linear modal space equations of the power grid dynamic reconstruction model and the gas grid compressible dynamic energy flow model are simplified through homogenization and dimensionality reduction processing:

[0287] ,

[0288] ,

[0289] In the formula, The modal space state vector representing the projection of the discrete variables of the electric energy flow in the time domain onto the optimal orthogonal eigenbasis; The optimal orthogonal characteristic basis for characterizing key power flow characteristics; Represents the column vector of the instantaneous matrix of power flow distribution; and For the Period Voltage and current at each transmission line segment; and They represent the coefficient matrices in the vector form of the power grid dynamic reconstruction model respectively; A modal space state vector representing the projection of time-domain discrete variables of electric energy flow and compressible gas energy flow onto an optimal orthogonal eigenbasis; The optimal orthogonal characteristic basis for characterizing the key compressible gas energy flow characteristics; Represents the column vector of the instantaneous matrix of compressible gas energy flow distribution; and For the Period Gas pressure and mass flow at each gas pipeline section; and They represent the coefficient matrices in vector form of the isothermal Euler partial differential equation for compressible fluid in the gas grid;

[0290] The previous results of rolling optimization are transformed into The original solution for the time period Project to the optimal orthogonal eigenvalue basis to obtain the previous Step dimensionality reduction solution , and then by the orthogonal characteristic basis and the The dimension reduction solution of all time periods is recursively obtained by step-by-step dimension reduction solution;

[0291] (3) High-fidelity dynamic screening feature base

[0292] The number of orthogonal characteristic basis vectors representing hydraulic energy flow characteristics, electric energy flow characteristics and compressible gas flow characteristics is calculated using the instantaneous image feature high-fidelity dynamic screening method. , thereby constructing a set of optimal orthogonal eigenbases;

[0293] For the reduced-dimensional solution component obtained by reduced-order extrapolation difference, the truncation error between it and the original solution is:

[0294] ,

[0295] In the formula, ,and ;

[0296] For preset model accuracy , make sure to satisfy Minimum accuracy required ; At the same time, in the process of reduced-order extrapolation, if , then re-extract the spatiotemporal discrete state data to form a new multi-energy energy flow instantaneous image matrix , and construct a new optimal orthogonal eigenbase until the dimensionality reduction solution on all time layers is obtained;

[0297] .

[0298] In order to further implement the above technical solution, the specific contents of S4 include:

[0299] The Lagrangian relaxation decomposition method is used to decouple the multi-energy post-disaster load restoration timing decision optimization dimensionality reduction model of electricity, gas and water into three independent scheduling sub-models with different time scales. Each scheduling sub-model includes a power grid scheduling sub-model , Water network dispatch sub-model And the gas grid dispatch sub-model ,Will Represents a set of scheduling sub-models, where any scheduling sub-model is denoted as , The associated submodel is denoted as , representation and scheduling sub-model There are other scheduling sub-models that coordinate the interaction of decision variables; express The associated submodel A collection of;

[0300] The original electricity-gas-water multi-energy post-disaster load restoration timing decision optimization dimensionality reduction model is expressed as:

[0301] ,

[0302] ,

[0303] In the formula, express The load recovery function, and Respectively represent the local decision variables and coordination decision variables of each scheduling sub-model; and Respectively Passed to its associated child model And sub-models Pass it to its associated The coordination decision variables of

[0304] By introducing the dual multiplier Eliminate the coupling variable constraints and further express the original electricity-gas-water multi-energy post-disaster load restoration timing decision optimization dimensionality reduction model as an augmented Lagrangian function :

[0305] ,

[0306] In the formula, and They are Passed to its associated child model and its associated sub-models Pass to The dual multiplier of ;

[0307] The augmented Lagrangian function is decoupled into different scheduling sub-models:

[0308] 1) Power grid dispatch sub-model The objective function is:

[0309] ,

[0310] In the formula, It is the local decision variable of the power grid dispatch sub-model, including load power, line switch status and other variables; It is the coordination decision variable between the power grid dispatch submodel and the water network and gas network dispatch submodel, including decision interaction variables such as drainage pump station supply power, pump station operation status and gas turbine demand power; and The power grid dispatch sub-model is passed to its associated sub-model and its associated sub-models The dual multiplier passed to the power grid submodel; and The power grid dispatch sub-model is passed to its associated sub-model and its associated sub-models coordination decision variables passed to the grid sub-model; represents the load recovery function of the power grid dispatch submodel;

[0311] 2) Water network scheduling sub-model The objective function is:

[0312] ,

[0313] In the formula, It is the local decision variable of the water network dispatch sub-model, including river water level, flow and other decision variables; It is the coordination decision variable between the water network dispatch sub-model and the power grid and gas grid sub-model, including decision interaction variables such as the required power of drainage pumping stations and the depth of water accumulation at fault points; and The water network scheduling sub-model is passed to its associated sub-model and its associated sub-models The dual multiplier passed to the water grid model; and The water network scheduling sub-model is passed to its associated sub-model and its associated sub-models coordination decision variables passed to the water grid sub-model; represents the load recovery function of the water network dispatch submodel;

[0314] 3) Gas network dispatch sub-model The objective function is:

[0315] ,

[0316] In the formula, It is the local decision variable of the gas grid dispatch sub-model, including state variables such as gas pressure and mass flow rate; It includes the coordination decision variables of the gas grid dispatch submodel with the power grid and gas grid submodel, including decision variables such as gas turbine supply power that interact with the power grid subproblem; and The gas grid dispatch sub-model is passed to its associated sub-model and its associated sub-models The dual multiplier passed to the gas grid sub-model; and The gas grid dispatch sub-model is passed to its associated sub-model and its associated sub-models coordination decision variables passed to the gas-grid sub-model; represents the load recovery function of the gas grid dispatch submodel;

[0317] At the same time, considering the asynchronous interaction of coupled information caused by the differences in emergency response time scales of different energy systems, an asynchronous mutual feedback method is adopted to interact with multi-energy network coordination decision variables, and auxiliary decision variables are introduced and auxiliary multipliers Coordination decision variables used to track asynchronous interactions and the dual multiplier ;

[0318] The Lagrangian relaxation decomposition method specifically includes the following contents:

[0319] (1) Initialize the coordination decision variables, dual multipliers, auxiliary decision variables, and auxiliary multipliers of each scheduling sub-model; initialize the coordination decision variables as , , , initialize the dual multiplier to , , ,Will Associated sub-models The auxiliary decision variables and auxiliary multipliers between are initialized as ; The initial values ​​of the coordination decision variables and the dual multipliers are set by random initialization within the value range;

[0320] (2) Parallel optimization of the scheduling decisions of each scheduling sub-model to update the local decision variables and intermediate variables that coordinate decision variables , and its update formula is:

[0321] ,

[0322] In the formula, and Respectively represent In iteration Passed to its associated child model The dual multiplier, auxiliary multiplier, auxiliary decision variable and intermediate variable of the coordinated decision variable;

[0323] (3) Update Coordination decision variables between its associated sub-models ; If in the In the iteration, the associated submodel and To exchange information, use and the previous iteration value Convex combination of updated coordinated interaction variables , which is of the form:

[0324] ,

[0325] In the formula, represents the weight coefficient of the convex combination;

[0326] Otherwise, keep The value of the previous iteration constant;

[0327] The updated coordinated interaction variable Send to associated child model and accepts the associated child model The coordinated interaction variable ;

[0328] (4) Update auxiliary decision variables and the dual multiplier ; If in the In the iteration, Receive its associated sub-model The coordinated interaction variable and dual multiplier , then update the auxiliary decision variables respectively and the dual multiplier Otherwise, keep and The value of the previous iteration and ;

[0329] ,

[0330] ,

[0331] The updated dual multiplier Send to associated child model and accepts the associated child model The dual multiplier of ;

[0332] (5) Update auxiliary multiplier variables ; If in the In the iteration, Receive its associated sub-model Updated dual multiplier , then assign it to ,Right now Otherwise, keep is the auxiliary multiplier variable value of the previous iteration ;

[0333] (6) For The scheduling sub-model that does not exchange information in the iteration is kept , , and is the value of the previous iteration, that is , , , ;

[0334] (7) Determine the convergence conditions; interactively and repeatedly iterate and calculate the original residual until the convergence criteria are met, thereby obtaining the optimal solution of the original electricity-gas-water multi-energy post-disaster load restoration timing decision optimization dimensionality reduction model;

[0335] ,

[0336] In the formula, Indicates The original residual after iterations; is the convergence accuracy of the original residual.

[0337] The present invention will be further described below through specific examples:

[0338] Apply the model and method described in steps 1-4 to the coordinated restoration decision-making of the electricity-gas-water multi-energy system in a certain region. Figure 1 The process shown is implemented in Python. The optimization efficiency comparison of different solvers is shown in Table 1:

[0339] ,

[0340] Compared with the existing emergency drainage scheduling method of the water conservancy network under rainstorm disasters, the electricity-gas-water multi-energy emergency collaborative recovery decision proposed in the present invention effectively ensures the rapid power supply restoration of the power grid by dynamically coordinating the reconstruction of multiple energy sources and scheduling multiple types of emergency resources to ensure emergency power supply to key multi-energy loads. At the same time, the homogeneous dimensionality reduction technology and asynchronous distributed decoupling solution method are used to improve the solution efficiency of large-scale multi-energy models. It can be seen from Table 1 that compared with other solver solution methods, the present invention reduces the decision calculation time by more than two orders of magnitude while ensuring the solution accuracy, greatly improving the efficiency of multi-energy collaborative recovery decision-making.

[0341] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A homogeneous dimensionality reduction decoupling method for collaborative recovery of large-scale heterogeneous non-constant multi-energy systems, characterized by: The following steps are involved: S1. Based on the uniform transmission line characteristics of the power grid, the compressible fluid dynamics characteristics of the gas grid, and the hydrodynamic energy flow characteristics of the water grid, a dynamic reconstruction model of the power grid, a compressible dynamic energy flow model of the gas grid, and a non-constant hydrodynamic energy flow model of the water grid are constructed respectively. Based on the dynamic reconstruction model of the power grid, the compressible dynamic energy flow model of the gas grid, and the non-constant hydrodynamic energy flow model of the water grid, a two-layer optimization model for the timing decision of post-disaster load recovery of multiple energy sources of electricity, gas, and water under multiple coupling non-constant partial differential constraints is constructed, including: an upper-layer load emergency power supply decision model is used to obtain the load emergency power supply decision of the dynamic coordinated reconstruction of the electricity-gas-water multi-energy network, a lower-layer mobile emergency resource scheduling optimization model is used to obtain multi-type mobile emergency resource scheduling considering the multi-energy load repair path planning, and the upper-layer load emergency power supply decision model and the lower-layer mobile emergency resource scheduling optimization model interact iteratively to roll over the electricity-gas-water multi-energy network and the repair path strategy; S2. Discretize the dynamic reconstruction model of the power grid, the compressible dynamic energy flow model of the gas grid and the non-steady hydrodynamic energy flow model of the water grid into a system of coupled algebraic equations through time and space grids respectively; S3. Based on the coupled algebraic equations of the power grid, gas grid and water grid, the discrete state data of the spatiotemporal grid of electricity, gas and water energy are extracted to form a snapshot matrix, and its intrinsic mode is decomposed to obtain the optimal orthogonal characteristic basis that characterizes the characteristics of electric energy flow, compressible gas energy flow and hydraulic energy flow. The equivalent linear modal space equations of the dynamic reconstruction model of the power grid, the compressible dynamic energy flow model of the gas grid and the non-constant hydrodynamic energy flow model of the water grid are further derived to obtain the homogenization and dimensionality reduction of the equivalent linear modal space equations, thereby constructing the optimization dimensionality reduction model of the post-disaster load recovery timing decision of electricity, gas and water multi-energy in the modal space; S4. Considering the asynchronous interaction of coupling information caused by the difference in emergency response time scales of different energy systems, the Lagrangian relaxation decomposition method is used to decouple the electricity-gas-water multi-energy post-disaster load recovery timing decision optimization and reduction model into three independent dispatching sub-models with different time scales: power grid dispatching sub-model, water network dispatching sub-model and gas network dispatching sub-model. The dispatching decisions of each dispatching sub-model are optimized in parallel through the coordinated decision variables among the asynchronously interacting dispatching sub-models, and the optimization results and boundary information of each dispatching sub-model are fed back to its associated sub-model respectively. After updating the coordinated variables, each dispatching sub-model is optimized in turn, and the interactive iteration is repeated until the optimal solution of the original electricity-gas-water multi-energy post-disaster load recovery timing decision optimization and reduction model is obtained. The specific contents of the iterative interaction between the upper-layer load emergency power supply decision model and the lower-layer mobile emergency resource scheduling optimization model in S1 to roll over the electricity-gas-water multi-energy network and emergency repair path strategy include: (1) Input the parameters of the power grid, gas grid, and water grid, and set the number of iterations and convergence threshold; (2) Solve the upper-level main problem to obtain the emergency power supply decision of important load nodes, and pass the load restoration decision and network topology update information to the lower-level sub-problems; (3) The lower-level sub-problem determines the water-blocking status of the fault area according to the water level in the fault area, solves the emergency repair resource configuration, and transmits the equipment recovery status of the fault area to the upper-level main problem to update the multi-energy network topology; (4) Calculate the convergence criterion. If the solution of the current iteration meets the preset convergence condition, the iteration ends and the optimal solution is output; otherwise, jump to step (2) and continue iterating until the convergence criterion is met; The specific contents of S3 include: (1) Multi-energy flow spatial intrinsic reconstruction The number of river channel space segments is , the number of scheduling time segments is , before extraction The spatiotemporal discrete state data of river water level and flow in each period constitutes a snapshot matrix of hydraulic energy flow distribution. : ， In the formula, and For the Period Water level and flow at each spatial segment of the river; Extracting the snapshot matrix of hydraulic energy flow distribution through eigenmode decomposition Key hydraulic energy flow characteristics: ， ， ， ， In the formula, for In descending order non-zero hydraulic energy flow spatial eigenvalues; for Arrange the non-zero eigenvalues ​​in descending order orthogonal eigenvectors; for Arrange the non-zero eigenvalues ​​in descending order orthogonal eigenvectors; for OK zero matrix of columns; and They are , Composition , Orthogonal matrix: ， Pick Before Column vectors : ， make , ,express Column vector of exist Projection Records on : ， In the formula, Representation vector and The inner product of For the A unit column vector with 1 components and the rest 0. According to the relationship between the matrix norm and the spectral radius, we can calculate and The truncation error is: ， but The optimal orthogonal characteristic basis for characterizing key hydraulic energy flow characteristics; (2) Dimensionality reduction and extrapolation of spatiotemporal differential projection make , , using the rolling optimization solution method, assuming that the rolling time, then When all variables are known at a certain moment, the coupled algebraic equations of the water network can be written in vector form: ， In the formula, and The time and space steps are respectively, , For the In the period Rainfall intensity at each river section; and For two matrix: ， ， when season The corresponding dimensionality reduction solution ,when season , then the equivalent linear modal space equation of the homogenization and dimensionality reduction of the water network unsteady hydrodynamic energy flow model is obtained as follows: ， In the formula, The modal space state vector representing the projection of the time-domain discrete variables of the hydraulic energy flow onto the optimal orthogonal eigenbasis; Then the dimensionality reduction solution of the non-steady hydrodynamic energy flow model of the water network is obtained after homogenization dimensionality reduction: ， Therefore, the equivalent linear modal space equations of the power grid dynamic reconstruction model and the gas grid compressible dynamic energy flow model are simplified through homogenization and dimensionality reduction processing: ， ， In the formula, The modal space state vector representing the projection of the discrete variables of the electric energy flow in the time domain onto the optimal orthogonal eigenbasis; The optimal orthogonal characteristic basis for characterizing key power flow characteristics; Represents the column vector of the instantaneous matrix of power flow distribution; and For the Period Voltage and current at each transmission line segment; and They represent the vector form of the power grid dynamic reconstruction model and The coefficient matrix of A modal space state vector representing the projection of time-domain discrete variables of electric energy flow and compressible gas energy flow onto an optimal orthogonal eigenbasis; The optimal orthogonal characteristic basis for characterizing the key compressible gas energy flow characteristics; Represents the column vector of the instantaneous matrix of compressible gas energy flow distribution; and For the Period Gas pressure and mass flow at each gas pipeline section; and They represent the isothermal Euler partial differential equation of the gas network compressible fluid in vector form. and The coefficient matrix of The previous results of rolling optimization are transformed into The original solution for the time period Project to the optimal orthogonal eigenvalue basis to obtain the previous Step dimensionality reduction solution , and then by the orthogonal characteristic basis and the The dimension reduction solution of all time periods is recursively obtained by step-by-step dimension reduction solution; (3) High-fidelity dynamic screening feature base The number of orthogonal characteristic basis vectors representing hydraulic energy flow characteristics, electric energy flow characteristics and compressible gas flow characteristics is calculated using the instantaneous image feature high-fidelity dynamic screening method. , thereby constructing a set of optimal orthogonal eigenbases; For the reduced-dimensional solution component obtained by reduced-order extrapolation difference, the truncation error between it and the original solution is: ， In the formula, ,and ; For preset model accuracy , make sure to satisfy Minimum accuracy required ; At the same time, in the process of reduced-order extrapolation, if , then re-extract the spatiotemporal discrete state data to form a new multi-energy energy flow instantaneous image matrix , and construct a new optimal orthogonal eigenbase until the dimensionality reduction solution on all time layers is obtained; 。 2. The homogenization dimensionality reduction decoupling method for collaborative restoration of large-scale heterogeneous non-constant multi-energy systems according to claim 1 is characterized in that: The two-level optimization model for post-disaster load restoration timing decision of electricity, gas and water multi-energy is as follows: The upper load emergency power supply decision model includes: The objective function is to maximize the weighted power failure load recovery: ， In the formula, for At any time, is a set of discrete time points; is the set of power-off nodes in the distribution network; To characterize Time Node A 0-1 variable indicating the load operating state; for Time Node Active power supplied by the system required by other loads except the drainage pump station; For Node The weight coefficient of the load at the location; express Time Node Drainage pump station 0-1 variable of running status; For Node Drainage pump station The load weight factor; for Time Node Drainage pump station Active power of The constraints include: the dynamic reconstruction model of the power grid and its constraints, the compressible dynamic energy flow model of the gas grid and its constraints, and the non-steady hydrodynamic energy flow model of the water grid and its constraints; The lower-level mobile emergency resource scheduling optimization model includes: The scheduling objective function is to minimize the total repair time: ， In the formula, The order of emergency repairs for the faulty area; For the repair team involved in the dispatch A collection of; For the repair team Total repair time; is the set of fault areas, and They are Any fault area in ; For the repair team From the fault area arrive 0-1 variable, if the repair team The path contains the fault area arrive , then the value is 1, otherwise it is 0; For the repair team From the fault area Rushing to the fault area The travel time; For the repair team Repair the faulty area the time required; Constraints include: mobile emergency resource scheduling constraints.

3. The homogenization dimensionality reduction decoupling method for collaborative restoration of large-scale heterogeneous non-constant multi-energy systems according to claim 2 is characterized in that: The power grid dynamic reconstruction model and its constraints include: The electric power dynamic network is modeled using the telegraph partial differential equation that characterizes the characteristics of uniform transmission lines. The dynamic reconstruction model of the power grid is: ， In the formula, and Respectively Transmit online position at all times The voltage and corresponding current at and Respectively represent the time and the coordinates along the transmission line direction; and are the resistance and inductance per unit length of the transmission line, respectively. and They represent the conductance and capacitance per unit length of the transmission line, respectively; The constraints of the power grid dynamic reconstruction model include: ， ， ， ， ， ， ， In the formula, express Timeline Connectivity state variables, Indicates line closure, Indicates that the line is disconnected; is a 0-1 state variable, where Indicates that the line is closed. Indicates that the line is disconnected; is a 0-1 state variable, where Representation Node Is a node The parent node of is a collection of lines; is a set of power grid nodes; For the node A collection of connected nodes; To express Timeline A 0-1 variable for the switch state change, where Indicates that the circuit breaker is closed. Indicates that the line switch is disconnected; and for Mobile power supply vehicle injects nodes at any time Active and reactive power; and for Time Node Active and reactive power generated by the gas turbine; and They are Timeline Active and reactive power flowing through; and They are Timeline Active and reactive power flowing through; for Time Node Reactive power supplied by the system required by other loads except the drainage pump station; for Time Node Drainage pump station Reactive power; The compressible dynamic energy flow model of the gas grid and its constraints include: When the gas flows isothermally in the pipeline, it is characterized by a one-dimensional isothermal Euler partial differential equation. The compressible dynamic energy flow model of the gas network is: ， In the formula, and Respectively Position on pipeline at the moment Gas pressure and mass flow rate at ; is the speed of sound; is the cross-sectional area of ​​the pipe; Indicates the pipe friction coefficient; is the inner diameter of the pipe; The gas grid and the power grid are coupled through a gas turbine, and the coupled device constraints are: ， In the formula, For the operating efficiency of the gas turbine; for The gas mass flow rate input to the gas turbine at all times; is the specific enthalpy of the gas turbine; The gas network operation constraints are: ， ， ， ， In the formula, for Time Node Gas pressure at and They are End time node and the first node Gas pressure at is the node set of the gas network; and Respectively represent the nodes The gas network pipeline set of the first node and the last node; for Time Node Injected gas mass flow rate; and They are Time outflow end node and the inflow node Gas mass flow rate; and Node Upper and lower limits of pressure; and Node Upper and lower limits of mass flow rate; The unsteady hydrodynamic energy flow model of the water network and its constraints include: Assuming the cross section of the river is a rectangle, the relationship between the water level and flow in the river satisfies the non-steady Saint-Venant hydrodynamic partial differential equation: ， ， ， In the formula, and Respectively Current river position Water level and flow at the site; It indicates the amount of water flowing into the river side per unit length; is the acceleration due to gravity; and They represent the riverbed slope and the equivalent friction of the river channel respectively; is the Manning coefficient; is the width of the river; For drainage pumping stations connected to rivers and lakes, the power-flow relationship is: ， ， In the formula, is the density of water; For Node Drainage pump station Static head; for Time Node Drainage pump station Traffic volume; For Node Drainage pump station operational efficiency; For Node Drainage pump station Power factor; Assemble for the drainage pump station; When the water level in the drainage channel is low, the water flow is regarded as a pressureless and unsteady flow, and the one-dimensional Saint-Venant partial differential equation is used to describe the change of hydraulic elements along the channel: ， ， ， ， In the formula, for Time Channel The cross-sectional area of ​​water flow; for Time Channel Confluence flow; for Time Channel water depth; for Time Channel The hydraulic slope of for Time Channel The channel bottom slope; is the width of the channel; is the cross-sectional area of ​​the conduit; is the hydraulic radius; For pipe and channel collection; Simultaneous fault area In the period The water depth, rainfall intensity, drainage capacity of the drainage truck and the amount of water discharged into the pipe network meet the water balance constraints: ， In the formula, Fault area Flooded area; Fault area In the period The depth of waterlogging; It is a collection of flooded sub-areas; For the period area The rainfall intensity within Fault area rainfall area; Assemble emergency drainage vehicles located in flooded areas; and The time periods Emergency drainage vehicle Pumping and drainage volume and inflow into the canal of rainfall; A collection of drainage canals for flooded areas; is the set of fault areas; is the time period length; Mobile emergency resource scheduling constraints include: Path constraints, resource limitation constraints, and time scheduling constraints: ， ， In the formula, Indicates the repair team Upon reaching the fault area moment; The time when all faulty areas are repaired; is a maximum positive real number; and are the starting point and end point sets respectively; It is a 0-1 variable. If the fault area exist If the moment is repaired, the value is 1, otherwise it is 0; Fault area Fix the 0-1 variable of the status, if the fault area The repair team If repaired, the value is 1, otherwise it is 0; At the same time, considering the impact of water accumulation in the fault area on the flooding of power equipment, in order to ensure that the power equipment can resume operation safely and reliably after the emergency repair is completed, the flooding blocking constraint in the fault area is introduced: ， ， In the formula, Indicates the fault area exist The flood blocking state at the moment, if the water level in the fault area is higher than the specified height, the value is 1, otherwise it is 0; Indicates the allowable flooding depth of electrical equipment in the fault area.

4. The homogenization dimensionality reduction decoupling method for collaborative restoration of large-scale heterogeneous non-constant multi-energy systems according to claim 1 is characterized in that: The specific contents of S2 include: The central difference method and Implicit Cell Centered linear difference method are used to discretize the space-time grids of the power grid dynamic reconstruction model and the gas grid compressible dynamic energy flow model into a set of coupled algebraic equations: ， ， In the formula, For the Period The voltage at each transmission line segment; For the Period The current at each transmission line segment; Respectively Period The pressure and mass flow rate at each gas network segment; and are the resistance and inductance per unit length of the transmission line, respectively. and They represent the conductance and capacitance per unit length of the transmission line, respectively; is the speed of sound; is the cross-sectional area of ​​the pipe; Indicates the pipe friction coefficient; is the inner diameter of the pipe; The Preissmann four-point implicit difference method is used to discretize the unsteady hydrodynamic energy flow model of the water network into a set of coupled algebraic equations: ， In the formula, and and space step length, respectively; and For the Period Water level and flow at each river section; and For the In the period and Rainfall intensity at each river section; is the acceleration due to gravity; is the Manning coefficient; is the width of the river.

5. The homogenization dimensionality reduction decoupling method for collaborative restoration of large-scale heterogeneous non-constant multi-energy systems according to claim 1 is characterized in that: The specific contents of S4 include: The Lagrangian relaxation decomposition method is used to decouple the multi-energy post-disaster load restoration timing decision optimization dimensionality reduction model of electricity, gas and water into three independent scheduling sub-models with different time scales. Each scheduling sub-model includes a power grid scheduling sub-model , Water network dispatch sub-model And the gas grid dispatch sub-model ,Will Represents a set of scheduling sub-models, where any scheduling sub-model is denoted as , The associated submodel is denoted as , express The associated submodel A collection of; The original electricity-gas-water multi-energy post-disaster load restoration timing decision optimization dimensionality reduction model is expressed as: ， ， In the formula, express The load recovery function, and Respectively represent the local decision variables and coordination decision variables of each scheduling sub-model; and Respectively Passed to its associated child model And sub-models Pass it to its associated The coordination decision variables of By introducing the dual multiplier Eliminate the coupling variable constraints and further express the original electricity-gas-water multi-energy post-disaster load restoration timing decision optimization dimensionality reduction model as an augmented Lagrangian function : ， In the formula, and They are Passed to its associated child model and its associated sub-models Pass to The dual multiplier of ; The augmented Lagrangian function is decoupled into different scheduling sub-models: 1) Power grid dispatch sub-model The objective function is: ， In the formula, It is the local decision variable of the power grid dispatch sub-model; It is the coordination decision variable between the power grid dispatch submodel and the water grid and gas grid dispatch submodel; and The power grid dispatch sub-model is passed to its associated sub-model and its associated sub-models The dual multiplier passed to the power grid submodel; and The power grid dispatch sub-model is passed to its associated sub-model and its associated sub-models coordination decision variables passed to the grid sub-model; represents the load recovery function of the power grid dispatch submodel; 2) Water network scheduling sub-model The objective function is: ， In the formula, It is the local decision variable of the water network scheduling sub-model; It is the coordination decision variable between the water network dispatch sub-model and the power grid and gas grid sub-models; and The water network scheduling sub-model is passed to its associated sub-model and its associated sub-models The dual multiplier passed to the water grid model; and The water network scheduling sub-model is passed to its associated sub-model and its associated sub-models coordination decision variables passed to the water grid sub-model; represents the load recovery function of the water network dispatch submodel; 3) Gas network dispatch sub-model The objective function is: ， In the formula, It is the local decision variable of the gas grid dispatch sub-model; Includes coordination decision variables between the gas grid dispatch sub-model and the power grid and gas grid sub-models; and The gas grid dispatch sub-model is passed to its associated sub-model and its associated sub-models The dual multiplier passed to the gas grid sub-model; and The gas grid dispatch sub-model is passed to its associated sub-model and its associated sub-models coordination decision variables passed to the gas-grid sub-model; represents the load recovery function of the gas grid dispatch submodel; At the same time, considering the asynchronous interaction of coupled information caused by the differences in emergency response time scales of different energy systems, an asynchronous mutual feedback method is adopted to interact with multi-energy network coordination decision variables, and auxiliary decision variables are introduced and auxiliary multipliers Coordination decision variables used to track asynchronous interactions and the dual multiplier ; The Lagrangian relaxation decomposition method specifically includes the following contents: (1) Initialize the coordination decision variables, dual multipliers, auxiliary decision variables, and auxiliary multipliers of each scheduling sub-model; (2) Parallel optimization of the scheduling decisions of each scheduling sub-model to update the local decision variables and intermediate variables that coordinate decision variables , and its update formula is: ， In the formula, and Respectively represent In iteration Passed to its associated child model The dual multiplier, auxiliary multiplier, auxiliary decision variable and intermediate variable of the coordinated decision variable; (3) Update Coordination decision variables between its associated sub-models ; If in the In the iteration, the associated submodel and To exchange information, use and the previous iteration value Convex combination of updated coordinated interaction variables , which is of the form: ， In the formula, represents the weight coefficient of the convex combination; Otherwise, keep The value of the previous iteration constant; The updated coordinated interaction variable Send to associated child model and accepts the associated child model The coordinated interaction variable ; (4) Update auxiliary decision variables and the dual multiplier ; If in the In the iteration, Receive its associated sub-model The coordinated interaction variable and dual multiplier , then update the auxiliary decision variables respectively and the dual multiplier Otherwise, keep and The value of the previous iteration and ; ， ， The updated dual multiplier Send to associated child model and accepts the associated child model The dual multiplier of ; (5) Update auxiliary multiplier variables ; If in the In the iteration, Receive its associated sub-model Updated dual multiplier , then assign it to ,Right now Otherwise, keep is the auxiliary multiplier variable value of the previous iteration ; (6) For The scheduling sub-model that does not exchange information in the iteration is kept , , and is the value of the previous iteration, that is , , , ; (7) Determine the convergence conditions; interactively and repeatedly iterate and calculate the original residual until the convergence criteria are met, thereby obtaining the optimal solution of the original electricity-gas-water multi-energy post-disaster load restoration timing decision optimization dimensionality reduction model; ， In the formula, Indicates The original residual after iterations; is the convergence accuracy of the original residual.

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