An IEGS distributed low-carbon optimization control method based on gas network division

Abstract

The present application relates to a kind of IEGS distributed low carbon optimization control method based on gas network division.First, according to node distance, i.e.the close degree of contact between gas nodes, construct the modularity function of the natural gas partition structure, and the louvain algorithm is used to optimize modularity function, obtain the maximum of modularity function, and the natural gas network is divided into multiple natural gas network sub-regions.Second, according to the equipment connection relationship between electric, gas network and the boundary coupling relationship of gas network internal sub-region, the decoupling between electric power network and natural gas network and after the sub-region of natural gas network is divided, while protecting the information privacy of electric, gas network, the solving efficiency of model is improved.The present application considers the time delay effect of natural gas transmission, and considers the synergistic effect of ladder type carbon trading mechanism, carbon capture technology and P2G technology on carbon emission reduction, can effectively improve the low carbon of IEGS and system operation flexibility, realizes system safe and stable operation.

Description

Technical Field

[0001] This invention relates to an IEGS distributed low-carbon optimization control method based on gas network partitioning. Background Technology

[0002] Integrated electricity-gas systems (IEGS) tightly couple electricity and natural gas networks through gas turbines (GT) and power-to-gas (P2G) equipment, playing a crucial role in achieving multi-energy complementarity and promoting the consumption of new energy sources. However, electricity and natural gas networks belong to different energy suppliers and are in market competition. Each supplier, concerned about data privacy, is reluctant to share network information, necessitating research into IEGS distributed optimization methods. Furthermore, traditional natural gas system control widely employs steady-state power flow models, neglecting the gas storage capacity of pipelines and the slow transmission speed of natural gas, leading to inaccurate scheduling schemes and failing to guarantee optimal results. Optimization control considering the dynamic characteristics of the gas network suffers from low computational efficiency in gas network models; therefore, the efficiency of IEGS solutions considering the dynamic characteristics of the gas network cannot be ignored.

[0003] Current research on IEGS low-carbon optimization control is mostly based on a centralized optimization framework, which requires uploading global information to a control center for unified optimization decisions. In reality, there is an "information barrier" between power grids and natural gas networks. They do not share private information such as topology, source-load data, and equipment operating parameters. The centralized optimization framework is inconsistent with the decentralized and autonomous operation mode of actual power and gas networks.

[0004] Furthermore, most current distributed control methods are based on steady-state power flow models of natural gas networks. However, compared to the propagation of electricity, the transmission speed of natural gas in pipelines is much slower, exhibiting gas inertia. Ignoring the gas storage capacity of pipelines and the slow transmission speed of natural gas will lead to inaccurate scheduling schemes and fail to guarantee optimal results. Compared to steady-state models, dynamic models of gas networks can more realistically reflect the differences in transmission characteristics between electricity flow and natural gas flow, and are more consistent with actual engineering conditions.

[0005] However, with the expansion of natural gas networks, operators face the challenge of collecting and processing massive amounts of data. Simultaneously, the distributed optimization model of natural gas networks, considering dynamic characteristics, contains numerous non-convex constraints and cross-time coupling constraints, making direct solutions difficult. Dividing the gas network into multiple sub-regions using a gas network partitioning method, with each sub-region independently and in parallel solving its internal sub-problems, is an effective way to address these issues. Network partitioning reduces the scale of solving the distributed optimization model of the natural gas network, significantly improving solution efficiency.

[0006] Therefore, there is an urgent need to study the IEGS distributed low-carbon optimization control method based on gas network division. Summary of the Invention

[0007] The purpose of this invention is to provide a distributed low-carbon optimization control method for IEGS based on gas network partitioning. This method takes into account the delay effect of natural gas transmission and considers the synergistic effect of tiered carbon trading mechanism, carbon capture technology and P2G technology on carbon emission reduction. It can effectively reduce IEGS carbon emissions, improve the low-carbon nature and flexibility of IEGS, and achieve safe and stable operation of the system.

[0008] To achieve the above objectives, the technical solution of the present invention is: a distributed low-carbon optimization control method based on gas network partitioning (IEGS), comprising the following steps:

[0009] (1) Considering the synergistic effect of tiered carbon trading mechanism, carbon capture technology and P2G technology on carbon emission reduction, an IEGGS low-carbon optimization control model is constructed, and the Big-M method and second-order cone relaxation method are used to linearize the gas network model.

[0010] (2) Considering the dynamic characteristics of the gas network, the virtual energy storage characteristics of the pipeline formed by the pipeline storage are used as an additional scheduling resource of the gas network to cope with changes in gas load, improve the operational flexibility of IEGS and the operational reliability of the system.

[0011] (3) In order to reduce the complexity of solving the dynamic model of the gas network, the gas network is divided based on the node distance index, and an IEGS distributed low-carbon optimization control model with decoupled electric and gas networks and gas network partitioning is established. This model can achieve efficient solution of the dynamic model of the gas network while meeting the requirements of decentralized autonomy of electric and gas networks.

[0012] Compared with the prior art, the present invention has the following beneficial effects:

[0013] This invention addresses the issues of "information barriers" in electricity and gas networks and the low computational efficiency of gas network models due to the dynamic characteristics of gas networks. It proposes a distributed low-carbon optimization control method for IEGS (Integrated Energy Storage and Geographic Data System) based on gas network partitioning. First, a modularity function characterizing the natural gas partitioning structure is constructed based on node distance, i.e., the tightness of connections between gas nodes. The Louvain algorithm is then used to optimize this modularity function, obtaining its maximum value, thus dividing the natural gas network into multiple sub-regions. Second, based on the equipment connection relationships between electricity and gas networks and the boundary coupling relationships within the sub-regions of the gas network, decoupling is performed between the electricity and natural gas networks, as well as between the sub-regions after the natural gas network partitioning. This improves the model's solution efficiency while protecting the information privacy of electricity and gas networks. This invention also considers the delay effect of natural gas transmission and the synergistic effect of tiered carbon trading mechanisms, carbon capture technology, and P2G technology on carbon emission reduction. This can effectively reduce IEGS carbon emissions, improve the low-carbon nature and flexibility of IEGS, and achieve safe and stable system operation. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of the IEGS structure.

[0015] Figure 2 This is a flowchart of the distributed low-carbon optimization control method for an integrated electric-gas energy system based on gas grid division, as described in this invention. Detailed Implementation

[0016] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0017] This invention discloses an IEGS distributed low-carbon optimization control method based on gas network partitioning, comprising the following steps:

[0018] (1) Considering the synergistic effect of tiered carbon trading mechanism, carbon capture technology and P2G technology on carbon emission reduction, an IEGGS low-carbon optimization control model is constructed, and the Big-M method and second-order cone relaxation method are used to linearize the gas network model.

[0019] (2) Considering the dynamic characteristics of the gas network, the virtual energy storage characteristics of the pipeline formed by the pipeline storage are used as an additional scheduling resource of the gas network to cope with changes in gas load, improve the operational flexibility of IEGS and the operational reliability of the system.

[0020] (3) In order to reduce the complexity of solving the dynamic model of the gas network, the gas network is divided based on the node distance index, and an IEGS distributed low-carbon optimization control model with decoupled electric and gas networks and gas network partitioning is established. This model can achieve efficient solution of the dynamic model of the gas network while meeting the requirements of decentralized autonomy of electric and gas networks.

[0021] Figure 2The flowchart below shows the distributed low-carbon optimization control method for an integrated electricity-gas energy system based on gas grid partitioning, as described in this invention. The specific implementation of this invention is as follows:

[0022] 1. Structure of the integrated electric-gas energy system

[0023] IEGS uses GT and P2G equipment as the medium for coupling electric and gas energy flows. It integrates carbon capture equipment into thermal power plants, transforming them into carbon capture power plants, thus achieving complementary and tiered energy utilization. The structure is as follows: Figure 1 As shown.

[0024] 2. IEGS Low-Carbon Optimization Control

[0025] 2.1 Objective Function

[0026] The IEGS comprehensive cost expression is as follows:

[0027]

[0028] Equation (5.1) represents, in order, the power generation cost of thermal power units, the cost of purchasing gas, the cost of wind curtailment penalties, the operating cost of P2G equipment, the operating cost of gas storage tanks, the cost of carbon sequestration, and the cost of carbon tax. Where: T is the total dispatch duration; the subscript t represents time (not elaborated further below); Ω e Ω g Ω w Ω p2g Ω s Ω b This refers to a collection of thermal power units, gas sources, fans, P2G equipment, gas storage tanks, and carbon capture power plants; a i b i c i k is the consumption cost coefficient for thermal power units. g k w k p2g k s k f These are the costs of natural gas, wind curtailment penalties, P2G equipment operation costs, gas storage tank costs, and carbon sequestration; P G,i,t F G,i,t P W,i,t , P P2G,i,t , , , These are respectively the power generation of thermal power units, the gas supply of gas sources, the predicted output of wind turbines, the actual absorption of wind turbines, the power consumption of P2G equipment, the input of gas storage tanks, the output of gas storage tanks, and the carbon capture of carbon capture power plants.

[0029] Among them, carbon tax cost C CThe specific expression is as follows:

[0030]

[0031]

[0032] Where: Ω gt For GT, E and D are the actual carbon emissions and carbon emission allowances, respectively. These represent the carbon tax price, the length of the tiered range, and the tiered growth rate, respectively. These are, respectively, the carbon emission allowance per unit of active power output of generators, the carbon emission per unit of active power output of thermal power units, and the carbon emission per unit of active power output of GT; P GT,i,t This refers to the power generation of GT.

[0033] 2.2 Constraints

[0034] The constraints of IEGS include power network constraints, natural gas network constraints, and coupling device constraints.

[0035] (1) Power network constraints

[0036] The power grid adopts a DC power flow model at the transmission network level, which mainly includes unit output constraints (5.4), unit ramping constraints (5.5), wind turbine output constraints (5.6), line power flow safety constraints (5.7), power balance constraints (5.8), and carbon capture power plant operation constraints (5.9).

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043] Where: Ω EL It is a set of power grid nodes; These are the upper and lower limits of output for thermal power units and GT, respectively. These represent the landslide rate and climbing rate of the thermal power unit and GT, respectively; P jk,t , x jk These represent the transmission power, upper limit of transmission power, and reactance of branch jk, respectively; θ j,t Let A be the phase angle at node j; H , , A W , , These are the node-branch, node-thermal power unit, node-GT, node-fan, node-P2G equipment, and node-electrical load correlation matrices, respectively; P H,t P G,t P GT,t , P P2G,t P L,t These are the column vectors representing the transmission power of all branches, the power generation of thermal power units, the power generation of GT equipment, the actual absorption capacity of wind turbines, the electrical energy consumed by P2G equipment, and the electrical load, respectively; η b β and P represent carbon capture efficiency and carbon capture equipment operating energy consumption coefficient, respectively; J,i,t P0, P Y,i,t These are the net output power of carbon capture power plant i, the fixed losses of carbon capture equipment, and the operating energy consumption of carbon capture power plant i, respectively.

[0044] (2) Natural gas network constraints

[0045] The natural gas network adopts a dynamic model with pipeline storage effect, including Weymouth equation constraints (5.10), conventional constraints (5.11), compressor pipeline flow and compressor pipeline head and tail gas pressure constraints (5.12), gas storage device constraints (5.13), dynamic characteristic pipeline storage constraints (5.14), and node flow balance constraints (5.15).

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052] Where: Ω GAA collection of gas pipelines; W represents the average flow rate of pipe pq. pq S pq These are the Weymouth constant and the pipe storage constant for pipe pq, respectively; F represents the air pressure at nodes p and q. C,h,t Let h be the flow rate of the compressor pipe; and These are the input and output flow rates of gas storage tank i, respectively; I S,i,t For binary variables, I S,i,t =0 indicates that the state of gas storage tank i at time t is the output flow rate; F GS,i,t and F GS,i,t-1 , respectively, represent the gas storage capacity of gas storage tank i at times t and t-1; and These represent the flow rates at the beginning and end of pipe p and q, respectively; Q pq,t and Q pq,t-1 Let A be the pipe inventory of pipe pq at times t and t-1, respectively; IN A OUT A C , , A S , These are the node-pipeline start-end, node-pipeline end-end, node-compressor pipeline, node-gas source, node-GT, node-gas storage tank, node-P2G equipment, and node-gas load correlation matrix, respectively. , F C,t F GT,t F P2G,t , , F L,t These are the head flow of all pipelines, the tail flow of all pipelines, the flow of compressor pipeline C, the natural gas consumed by the GT equipment, the natural gas converted by the P2G equipment, the input flow of the gas storage tank, the output flow of the gas storage tank, and the column vector of the gas load. These are the upper and lower limits of the gas pressure at node p, respectively; These are the upper and lower limits of the output power of gas source i, respectively; These are the maximum and minimum compression factors of the compressor, respectively. These are the upper limit of the capacity of the gas storage tank i, the upper limit of the flow rate of the pipeline pq, and the upper limit of the flow rate of the compressor pipeline h, respectively. and These are the upper limits of the input and output flow rates of gas storage tank i, respectively.

[0053] (3) Coupling device constraints

[0054] The power grid and the natural gas grid are tightly coupled through GT and P2G devices. The consumption characteristic equation of GT, the energy conversion equation of P2G device, and the power consumption constraint of P2G device are shown in the following equations:

[0055]

[0056]

[0057] In the formula: η gt and η p2g The conversion efficiencies of GT and P2G are respectively; H HV It is a high-calorific-value natural gas; F GT,i,t and F P2G,i,t These represent the natural gas consumed by GT device i and the natural gas converted by P2G device i, respectively; P P2G,i,t and P GT,i,t These represent the electrical energy consumed by P2G device i and the power generated by GT device i, respectively. This represents the maximum power consumption of the P2G device i.

[0058] 3. Natural gas network partitioning method considering node distance

[0059] This invention first constructs a modularity function representing the natural gas zoning structure based on node distance, i.e., the tightness of the connection between gas nodes; secondly, it uses the Louvain algorithm to optimize the modularity function and obtain its maximum value; finally, based on the regional structure corresponding to the maximum value of the modularity function, the natural gas network is divided into multiple natural gas network sub-regions.

[0060] 3.1 Modularity Function

[0061] The modularity is defined as the proportion of edges within a region to the total number of edges, minus the proportion of the expected number of edges within a region to the total number of edges when edges are randomly placed. The optimal network partitioning is achieved based on the principle of maximizing the modularity function, as shown in the following expression:

[0062]

[0063] In the formula: B pq B represents the weight of the edge connecting nodes p and q. When nodes p and q are directly connected, B... pq =1, B is not connected pq =0; v p and v qLet represent the sum of the weights of all edges connected to nodes p and q respectively; z represents the total weight of all edges in the network; δ(p,q) represents the regional relationship between nodes p and q. If nodes p and q are in the same region, then δ(p,q)=1, otherwise δ(p,q)=0.

[0064] 3.2 Natural Gas Network Partitioning Method Based on Louvain Algorithm

[0065] This invention employs the Louvain algorithm to partition the natural gas network, achieving automatic and rapid partitioning of the natural gas network. The partitioning steps are as follows:

[0066] 1) Obtain the topology parameters of the natural gas network;

[0067] 2) Normalize the pipe distances between gas nodes;

[0068] 3) Initialize the natural gas network partitioning, treating each node in the gas network as a separate region, with the number of regions being the same as the number of nodes, and calculate the function value Q at this time using equation (5.18);

[0069] 4) Randomly select the region containing node p in the network and merge it with other regions to form a new region. Calculate the incremental value ΔQ of the network for each region. If ΔQ max >0, connect the region where node p is located with ΔQ max The corresponding regions are merged into new regions; otherwise, no new regional structure is formed.

[0070] 5) Take the newly formed region as the new node and repeat step 4) until the modularity function value Q of the entire network no longer increases. This is the optimal region partitioning result.

[0071] 4. IEGS Distributed Low-Carbon Optimization Control Model and Solution

[0072] To ensure the privacy of information in power and natural gas networks and improve the solution efficiency of natural gas dynamic models, a distributed IEGS solution framework based on the consensus-based alternating direction method of multipliers (C-ADMM) is proposed, based on the IEGS decomposition and collaboration mechanism.

[0073] 4.1 IEGS Decomposition and Collaboration Mechanism

[0074] The prerequisite for achieving decentralized autonomy and coordinated management of IEGS is to decouple the power and gas networks, including decoupling between the power network and the natural gas network, as well as decoupling the internal sub-regions of the natural gas network after it has been divided.

[0075] (1) Electrical network decoupling mechanism

[0076] This invention decouples the power network and natural gas network at the coupling devices GT and P2G, and introduces virtual nodes and corresponding coupling variables at the decoupling points. To ensure the equivalence of the networks before and after decoupling, the coupling variables of the two networks should satisfy the consistency constraint (5.19):

[0077]

[0078] In the formula: Let i be the coupling variable of the power network with respect to GT device i; F is the coupling variable of the natural gas network with respect to GT device i; GT,i,t for , Coordinating variables; For the power network coupling variables with respect to P2G device i; F is the coupling variable of the natural gas network with respect to P2G device i; P2G,i,t for , Coordinating variables.

[0079] (2) Natural gas network partitioning decoupling mechanism

[0080] Suppose the natural gas network is divided into N regions based on node distances, and these regions are connected by connecting pipelines. The nodes at both ends of the connecting pipelines are called boundary nodes between regions. According to the principle of decomposition and coordination, a node splitting method is used to split any boundary node between regions. The split node is called a coupling node between regions. This coupling node is shared by both regions. The natural gas flowing into the coupling node is called the coupling inflow, and the natural gas flowing out of the coupling node is called the coupling outflow. This completes the decoupling of the natural gas network. To ensure the equivalence of the network before and after decoupling, the above coupling variables should satisfy consistency constraints, as shown in equation (5.20):

[0081]

[0082] In the formula: These are the air pressures at node p+1 in region m and node p+1 in region n, respectively. and These represent the coupled outflow of node p+1 in region m and the coupled inflow of node p+1 in region n, respectively. for Coordinating variables; for , Coordinating variables.

[0083] 4.2 IEGS Distributed Solving Framework Based on C-ADMM

[0084] First, an optimal control model for the power network and an optimal control model for the natural gas sub-region are constructed. Based on the C-ADMM distributed algorithm, the IEGS optimization problem is decomposed into a power network sub-problem and several natural gas network sub-problems. Second, the C-ADMM is used to solve the IEGS distributed low-carbon optimization control model to obtain the optimal control scheme.

[0085] (1) Power network optimization control

[0086] The specific model for power network optimization control is as follows:

[0087]

[0088] In the formula: F e The objective function of the power network; and These are the dual multipliers of the power network for GT and P2G devices, respectively. These are the penalty factors for GT and P2G devices, respectively.

[0089] (2) Optimization control of natural gas network sub-regions

[0090] Based on the natural gas network partitioning results, each natural gas sub-region independently and in parallel solves its internal sub-problems. Compared to directly solving the entire natural gas network optimization control model, solving the sub-problems in each sub-region only requires solving the 0-1 variables within that region, making it a small-scale MISOCP problem, thus improving the solution efficiency of the natural gas network optimization model. The sub-region n optimization control model is as follows:

[0091]

[0092] In the formula: F g,n Let n be the objective function for the natural gas network subregion n; These are the dual multipliers of the natural gas network subregion n with respect to GT and P2G device i, respectively. These are the coupling variables of the natural gas network subregion n with respect to GT and P2G device i, respectively. These are the dual multipliers of gas pressure and coupled flow rate at n coupled nodes in a subregion of the natural gas network, respectively. , These represent the gas pressure and coupled flow rate of the coupled nodes in subregion n of the natural gas network, respectively. These are the penalty factors for the gas pressure and flow rate at the coupling nodes, respectively. and F mn,tThese are the coordination variables for the air pressure and the coupling flow rate of the coupling nodes shared by subregions m and n, respectively.

[0093] (3) C-ADMM solution process

[0094] The specific solution steps for IEGGS distributed low-carbon optimization control based on C-ADMM are as follows:

[0095] 1) Set the iteration number k=0; initialize the dual multipliers. Coordination variables and penalty factor Set the threshold ε for the original residual and the dual residual. pri and ε dual .

[0096] 2) Each sub-region of the power network and natural gas network independently and in parallel solves its own sub-optimization problem to obtain the values ​​of the coupling variables. .

[0097] 3) Update the coordination variables based on the latest values ​​of the coupling variables for each sub-region of the power network and the natural gas network. As shown in the following formula:

[0098]

[0099] In the formula: These represent the gas pressure and coupled flow rate at the coupled nodes of subregion m in the gas network, respectively.

[0100] 4) Determine whether the original residual Lk+1 max and the dual residual Dk+1 max satisfy the algorithm convergence condition (5.26). If they do, stop the iteration and output the result; otherwise, continue to execute 5). The calculation of the original residual and the dual residual is shown in equations (5.24)-(5.25).

[0101]

[0102]

[0103]

[0104] 5) Update the dual multipliers based on the values ​​of the original residual and the dual residual. This updates the penalty factor. For example, as shown in the following formula:

[0105]

[0106] In the formula: This is a constant related to the multiplier update.

[0107] 6) Update the dual multipliers using equation (5.28) based on the latest values ​​of the coupling and coordination variables; set the iteration count k = k + 1 and continue executing step 2).

[0108] .

[0109] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

Claims

1. A distributed low-carbon optimization control method based on gas network partitioning (IEGS), characterized in that, Includes the following steps: (1) Considering the synergistic effect of the stepped carbon emission mechanism, carbon capture technology and P2G technology on carbon emission reduction, an IEGS low-carbon optimization control model is constructed. At the same time, the Big-M method and the second-order cone relaxation method are used to linearize the gas network model. The objective function of the IEGS low-carbon optimization control model is as follows: The IEGS comprehensive cost expression is as follows: In the formula, each term represents, in order, the power generation cost of the thermal power unit, the gas purchase cost, the wind curtailment penalty cost, the P2G equipment operating cost, the gas storage tank operating cost, the carbon sequestration cost, and the carbon tax cost; T represents the total dispatching time; the subscript t represents time; Ω e Ω g Ω w Ω p2g Ω s Ω b This refers to a collection of thermal power units, gas sources, fans, P2G equipment, gas storage tanks, and carbon capture power plants; a i b i c i k is the consumption cost coefficient for thermal power units. g k w k p2g k s k f These are the natural gas cost coefficient, wind curtailment penalty coefficient, P2G equipment operating cost coefficient, gas storage tank cost coefficient, and carbon sequestration cost coefficient, respectively; P G,i,t F G,i,t P W,i,t , P P2G,i,t , , , These are respectively the power generation of thermal power units, the gas supply of gas sources, the predicted output of wind turbines, the actual absorption of wind turbines, the power consumption of P2G equipment, the input of gas storage tanks, the output of gas storage tanks, and the carbon capture of carbon capture power plants. Among them, carbon tax cost C C The specific expression is as follows: Where: Ω gt For GT, E and D are the actual carbon emissions and carbon emission allowances, respectively. These represent the carbon tax price, the length of the tiered range, and the tiered growth rate, respectively. These are, respectively, the carbon emission allowance per unit of active power output of generators, the carbon emission per unit of active power output of thermal power units, and the carbon emission per unit of active power output of GT; P GT,i,t The amount of electricity generated by GT; (2) Considering the dynamic characteristics of the gas network, the virtual energy storage characteristics of the pipeline formed by the pipeline storage are used as an additional scheduling resource of the gas network to cope with changes in gas load, improve the operational flexibility of IEGS and the operational reliability of the system. (3) In order to reduce the complexity of solving the dynamic model of the gas network, the gas network is divided based on the node distance index, and an IEGS distributed low-carbon optimization control model with decoupled electric and gas networks and gas network partitioning is established. This model can achieve efficient solution of the dynamic model of the gas network while meeting the requirements of decentralized autonomy of electric and gas networks.

2. The IEGS distributed low-carbon optimization control method based on gas network partitioning according to claim 1, characterized in that, IEGS uses GT and P2G equipment as the medium for coupling electric and gas energy flows, and adds carbon capture equipment to thermal power plants to transform them into carbon capture power plants, thereby achieving complementary and tiered utilization of energy.

3. The IEGS distributed low-carbon optimization control method based on gas network partitioning according to claim 1, characterized in that, The constraints of the IEGS low-carbon optimization control model are as follows: The constraints of IEGS include power network constraints, natural gas network constraints, and coupling device constraints. 1) Power network constraints: The power network adopts a DC power flow model at the transmission network level. The power network constraints include, in order, the following: unit output constraints, unit ramping constraints, wind turbine output constraints, line power flow safety constraints, power balance constraints, and carbon capture power plant operation constraints. （1） （2） （3） （4） （5） （6） Where: Ω EL It is a set of power grid nodes; These are the upper and lower limits of output for thermal power units and GT, respectively. These represent the landslide rate and climbing rate of the thermal power unit and GT, respectively; P jk,t , x jk These represent the transmission power, upper limit of transmission power, and reactance of branch jk, respectively; θ j,t Let A be the phase angle at node j; H , , A W , , These are the node-branch, node-thermal power unit, node-GT, node-fan, node-P2G equipment, and node-electrical load correlation matrices, respectively; P H,t P G,t P GT,t , P P2G,t P L,t These are the column vectors representing the transmission power of all branches, the power generation of thermal power units, the power generation of GT equipment, the actual absorption capacity of wind turbines, the electrical energy consumed by P2G equipment, and the electrical load, respectively; η b β and P represent carbon capture efficiency and carbon capture equipment operating energy consumption coefficient, respectively; J,i,t P0, P Y,i,t These are the net output power of carbon capture power plant i, the fixed losses of carbon capture equipment, and the operating energy consumption of carbon capture power plant i, respectively. 2) Natural gas network constraints: The natural gas network adopts a dynamic model with pipeline storage effect. The constraints of the natural gas network include the following constraints in sequence: Weymouth equation constraints, conventional constraints, compressor pipeline flow and compressor pipeline head and tail gas pressure constraints, gas storage device constraints, dynamic characteristic pipeline storage constraints, and node flow balance constraints. （7） （8） （9） （10） （11） （12） Where: Ω GA A collection of gas pipelines; pq,t W represents the average flow rate of pipe pq. pq S pq These are the Weymouth constant and the pipe storage constant for pipe pq, respectively; F represents the air pressure at nodes p and q. C,h,t Let h be the flow rate of the compressor pipe; and These are the input and output flow rates of gas storage tank i, respectively; I S,i,t For binary variables, I S,i,t =0 indicates that the state of gas storage tank i at time t is the output flow rate; F GS,i,t and F GS,i,t-1 , respectively, represent the gas storage capacity of gas storage tank i at times t and t-1; and These represent the flow rates at the beginning and end of pipe p and q, respectively; Q pq,t and Q pq,t-1 Let A be the pipe inventory of pipe pq at times t and t-1, respectively; IN A OUT A C , , A S , These are the node-pipeline start-end, node-pipeline end-end, node-compressor pipeline, node-gas source, node-GT, node-gas storage tank, node-P2G equipment, and node-gas load correlation matrix, respectively. , F C,t F GT,t F P2G,t , , F L,t These are the head flow of all pipelines, the tail flow of all pipelines, the flow of compressor pipeline C, the natural gas consumed by the GT equipment, the natural gas converted by the P2G equipment, the input flow of the gas storage tank, the output flow of the gas storage tank, and the column vector of the gas load. These are the upper and lower limits of the gas pressure at node p, respectively; These are the upper and lower limits of the output power of gas source i, respectively; These are the maximum and minimum compression factors of the compressor, respectively. These are the upper limit of the capacity of the gas storage tank i, the upper limit of the flow rate of the pipeline pq, and the upper limit of the flow rate of the compressor pipeline h, respectively. and These are the upper limits of the input and output flow rates of gas storage tank i, respectively; 3) Coupling device constraints: The power grid and the natural gas grid are tightly coupled through GT and P2G devices. The power consumption characteristic equation of GT, the energy conversion equation of P2G device, and the power consumption constraint of P2G device are shown in the following equations: （13） （14） In the formula: η gt and η p2g The conversion efficiencies of GT and P2G are respectively; H HV It is a high-calorific-value natural gas; F GT,i,t and F P2G,i,t These represent the natural gas consumed by GT device i and the natural gas converted by P2G device i, respectively; P P2G,i,t and P GT,i,t These represent the electrical energy consumed by P2G device i and the power generated by GT device i, respectively. This represents the maximum power consumption of the P2G device i.

4. The IEGS distributed low-carbon optimization control method based on gas network partitioning according to claim 1, characterized in that, The specific implementation method of dividing the gas network based on the node distance index is as follows: First, construct a modularity function representing the natural gas partition structure based on the node distance, that is, the tightness of the connection between gas nodes; second, use the Louvain algorithm to optimize the modularity function and obtain the maximum value of the modularity function; finally, based on the regional structure corresponding to the maximum value of the modularity function, divide the natural gas network into multiple natural gas network sub-regions.

5. The IEGS distributed low-carbon optimization control method based on gas network partitioning according to claim 4, characterized in that, The specific expression for the modularity function is as follows: In the formula: B pq B represents the weight of the edge between nodes p and q. When nodes p and q are directly connected, B is the weight of the edge between p and q. pq =1, B is not connected pq =0; v p and v q Let represent the sum of the weights of all edges connected to nodes p and q, respectively; z represents the total number of edge weights in the network. δ(p,q) represents the regional relationship between node p and node q. If node p and node q are in the same region, then δ(p,q)=1, otherwise δ(p,q)=0.

6. The IEGS distributed low-carbon optimization control method based on gas network partitioning according to claim 5, characterized in that, The Louvain algorithm is implemented as follows: 1) Obtain the topology parameters of the natural gas network; 2) Normalize the pipe distances between gas nodes; 3) Initialize the natural gas network partitioning, treating each node in the gas network as a separate region, with the number of regions being the same as the number of nodes, and calculate the function value Q at this time using the modularity function; 4) Randomly select the region containing node p in the network and merge it with other regions to form a new region. Calculate the incremental value ΔQ of the network for each region. If ΔQ max >0, connect the region where node p is located with ΔQ max The corresponding regions are merged into new regions; otherwise, no new regional structure is formed. 5) Take the newly formed region as the new node and repeat step 4) until the modularity function value Q of the entire network no longer increases. This is the optimal region partitioning result.

7. The IEGS distributed low-carbon optimization control method based on gas network partitioning according to claim 3, characterized in that, The specific implementation method of establishing the IEGS distributed low-carbon optimization control model with decoupled electric and gas networks and partitioned gas networks, which satisfies the requirements of decentralized autonomy of electric and gas networks while achieving efficient solution of the gas network dynamic model, is as follows: (S1) IEGS decomposition and coordination mechanism The prerequisite for achieving decentralized autonomy and coordinated management of IEGS is to decouple the power and gas networks, including the decoupling between the power network and the natural gas network, as well as the decoupling of the internal sub-regions after the natural gas network is divided. (S1.1) Electrical-electrical network decoupling mechanism Decoupling is performed at the GT and P2G coupling devices of the power network and the natural gas network, and virtual nodes and corresponding coupling variables are introduced at the decoupling points. To ensure the equivalence of the networks before and after decoupling, the coupling variables of the two networks should satisfy the consistency constraint formula: In the formula: Let i be the coupling variable of the power network with respect to GT device i; F is the coupling variable of the natural gas network with respect to GT device i; GT,i,t for , Coordinating variables; For the power network coupling variables with respect to P2G device i; F is the coupling variable of the natural gas network with respect to P2G device i; P2G,i,t for , Coordinating variables; (S1.2) Natural Gas Network Partition Decoupling Mechanism Suppose the natural gas network is divided into N regions based on node distances, and these regions are connected by connecting pipelines. The nodes at both ends of these pipelines are called boundary nodes between regions. Based on the principle of decomposition and coordination, a node splitting method is used to split any boundary node between regions. The split node is called a coupling node between the two regions. This coupling node is shared by both regions. The natural gas flowing into the coupling node is called the coupling inflow, and the natural gas flowing out of the coupling node is called the coupling outflow. This completes the decoupling of the natural gas network. To ensure the equivalence of the network before and after decoupling, the above coupling variables should satisfy consistency constraints, as shown in the following equation: In the formula: These are the air pressures at node p+1 in region m and node p+1 in region n, respectively. and These represent the coupled outflow of node p+1 in region m and the coupled inflow of node p+1 in region n, respectively. for Coordinating variables; for , Coordinating variables; (S.2) IEGS Distributed Solving Framework Based on C-ADMM First, an optimal control model for the power network and an optimal control model for the natural gas sub-region are constructed. Based on the C-ADMM distributed algorithm, the IEGS optimization problem is decomposed into a power network sub-problem and several natural gas network sub-problems. Second, the C-ADMM is used to solve the IEGS distributed low-carbon optimization control model to obtain the optimal control scheme. The details are as follows: (S2.1) Power Network Optimization Control The specific model for power network optimization control is as follows: In the formula: F e The objective function of the power network; and These are the dual multipliers of the power network for GT and P2G devices, respectively. These are the penalty factors for GT and P2G devices, respectively. (S2.2) Optimization control of natural gas network sub-regions Based on the natural gas network partitioning results, each natural gas sub-region independently and in parallel solves its internal sub-problems. Compared to directly solving the entire natural gas network optimization control model, each sub-region only needs to solve its own 0-1 variables when solving sub-problems, making it a small-scale MISOCP problem, thus improving the solution efficiency of the natural gas network optimization model. The sub-region n optimization control model is as follows: In the formula: F g,n Let n be the objective function for the natural gas network subregion n; These are the dual multipliers of the natural gas network subregion n with respect to GT and P2G device i, respectively. These are the coupling variables of the natural gas network subregion n with respect to GT and P2G device i, respectively. These are the dual multipliers of gas pressure and coupled flow rate at n coupled nodes in a subregion of the natural gas network, respectively. , These represent the gas pressure and coupled flow rate of the coupled nodes in subregion n of the natural gas network, respectively. These are the penalty factors for the gas pressure and flow rate at the coupling nodes, respectively. and F mn,t These are the coordinated variables of air pressure and coordinated variables of coupled flow rate at the coupling nodes shared by subregions m and n, respectively. (S2.3) C-ADMM Solution Flow The specific solution steps for IEGGS distributed low-carbon optimization control based on C-ADMM are as follows: 1) Set the iteration number k=0; initialize the dual multipliers. Coordination variables and penalty factor Set the threshold ε for the original residual and the dual residual. pri and ε dual ; 2) Each sub-region of the power network and natural gas network independently and in parallel solves its own sub-optimization problem to obtain the values ​​of the coupling variables. ; 3) Update the coordination variables based on the latest values ​​of the coupling variables for each sub-region of the power network and the natural gas network. As shown in the following formula: In the formula: These represent the coupled node air pressure and coupled flow rate of subregion m of the gas network, respectively; 4) Determine the original residuals and dual residuals Does the algorithm meet the convergence condition (17)? If it does, the iteration stops and the result is output; otherwise, continue to execute (5). The calculation of the original residual and the dual residual is shown in equations (15)-(16). （15） （16） （17） 5) Update the dual multipliers based on the values ​​of the original residual and the dual residual; update the penalty factor. As shown in the following formula: In the formula: These are constants related to multiplier updates; 6) Update the dual multipliers using equation (18) based on the latest values ​​of the coupling and coordination variables; set the iteration number k = k + 1 and continue executing 2). （18）。

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