A power grid outage consequence analysis method considering supply chain-gas-electricity fault conduction

Abstract

The present application relates to the technical field of power system, specifically relates to a kind of power grid outage consequence analysis method considering supply chain-gas-electricity fault conduction, comprising the following steps: S1, electrical network coupling relationship modeling: identification key coupling point;S2, supply chain weak link analysis: assess potential high-risk link in system;S3, gas pipeline network fault modeling: establish the pressure and flow calculation model of natural gas pipeline network;S4, gas-electricity coupling component modeling: establish the mathematical model of gas turbine and compressor;S5, urban power grid fault modeling: assess the operating state of power grid under fault;S6, outage consequence evaluation index construction: quantify social influence and recovery priority under different fault scenarios;The present application can systematically reveal the cascading propagation path of electrically coupled network under fault condition, effectively identify high-risk coupling components and weak links, and improve the understanding depth and fault assessment accuracy of complex coupled energy systems.

Description

Technical Field

[0001] This invention relates to the field of power system technology, and in particular to a method for analyzing the consequences of power outages that takes into account the transmission of supply chain-gas-electricity faults. Background Technology

[0002] With the continuous transformation of the energy structure, integrated energy systems have gradually become an important development direction of modern energy systems. This system integrates multiple energy forms such as electricity and natural gas to achieve efficient energy transmission and coordinated optimization, aiming to improve energy utilization efficiency, enhance system flexibility and stability, and promote the development of energy systems towards a green and sustainable direction. In this context of multi-energy interconnection, the coupling relationship between electricity and natural gas systems is becoming increasingly close. Especially with the increasing popularity of gas-fired power generation, gas-electric linkage has become a core link in the operation of integrated energy systems. However, different energy systems have significant differences in operating characteristics, transmission media, and control mechanisms, which can easily lead to the transmission of faults between multiple subsystems, forming cross-domain chain reactions, and thus affecting the safety and stability of the entire urban energy network.

[0003] Although there is already considerable research on integrated energy systems, covering aspects such as electrical coupling modeling, power flow calculation, and optimal scheduling, some significant shortcomings remain. Most studies focus primarily on the independent characteristics of energy subsystems, lacking system modeling and evaluation of their linkage mechanisms with the energy supply chain. Furthermore, for city-level, multi-voltage-level, and multi-pressure-level electrical coupling networks, existing research is still insufficient in terms of network scale, node distribution, and coupling element modeling, making it difficult to fully reveal the fault propagation paths and impact range of electrical systems in complex scenarios. In addition, existing consequence assessment methods generally do not fully consider the differences in user types and the quantification of social impact, limiting their application value in practical emergency management and resource allocation. Summary of the Invention

[0004] This invention provides a method for analyzing the consequences of power outages that considers the transmission of supply chain-gas-electricity faults. This method can provide decision-making support for power system operators and emergency management departments, improve resource scheduling efficiency and system recovery capabilities, and enhance the resilience of integrated energy systems in the face of complex disaster scenarios.

[0005] A method for analyzing the consequences of power outages in a grid system that considers the transmission of supply chain-gas-electricity faults includes the following steps:

[0006] S1, Modeling of electrical network coupling relationship: Analyze the coupling structure between the electrical network UPN and GDN, identify key coupling points, including voltage regulators and gas power plants, and establish a two-way fault propagation model;

[0007] S2, Supply Chain Vulnerability Analysis: Constructing electricity and natural gas supply chain models, using network visualization and graph algorithms to identify key nodes and paths, and assessing potential high-risk links in the system;

[0008] S3, Gas Pipeline Network Fault Modeling: Based on pipeline hydraulic calculation and operational constraints, a pressure and flow calculation model for the natural gas pipeline network is established to simulate the fault state of the gas network;

[0009] S4, Gas-electric coupling component modeling: Establish mathematical models of gas turbines and compressors to describe the relationship between their output and gas and electricity volume, and reflect their operating modes and constraints;

[0010] S5, Urban Power Grid Fault Modeling: Based on Nk fault analysis, an optimization model including generation dispatch, load allocation and network power flow is constructed to evaluate the operating status of the power grid under fault conditions;

[0011] S6, Construction of power outage consequence assessment indicators: Using the equivalent number of power outage users as the indicator, and combining user type to set weights, to quantify the social impact and recovery priority under different fault scenarios.

[0012] Optionally, the electrical network coupling modeling in S1 includes:

[0013] S11, Identify the network attributes of UPN and GDN: Electrical networks UPN and GDN are energy flow networks with topological structure and physical characteristics. UPN consists of multiple voltage levels, including high voltage transmission (HVT), high voltage distribution (HVD) and medium voltage distribution (MVD) networks. GDN includes long-distance gas pipelines, gas-fired power plants, pressure regulating stations and urban gas distribution networks.

[0014] S12, Establish a typical gas-electric coupling relationship structure: At the high-pressure network level, natural gas is transported to the gas-fired power plant through pipelines. After generating electricity, the gas-fired power plant transmits the electricity to the distribution network and supplies power to the pressure regulating station, forming a coupling path. At the same time, the operation of the pressure regulator depends on the power support of the UPN. Faults are transmitted from the power grid to the gas network, or from the gas network to the power grid. The coupling relationship is bidirectional.

[0015] S13, Identify key coupling components: Key coupling components include pressure regulators and gas-fired power plants. Pressure regulators connect urban gas distribution networks with different gas pressure levels and rely on electric power for operation. Gas-fired power plants are the core nodes of the coupling, and their operation is affected by the gas source and they supply power to the grid.

[0016] S14 proposes a modeling simplification strategy: using large-scale communities as the smallest load nodes in UPN and GDN to simplify modeling;

[0017] S15, Define the fault propagation path and stages: Divide the gas-electric fault propagation process into three stages, specifically including:

[0018] Phase 1: Disruptions in the electricity and natural gas supply chains lead to insufficient gas supply, which in turn causes gas grid outages.

[0019] Phase Two: Changes in the gas network status lead to a decrease in gas turbine output or shutdown;

[0020] Phase 3: Insufficient gas turbine output, power plant or transmission line failures causing widespread power outages.

[0021] Optionally, the supply chain vulnerability analysis in S2 includes:

[0022] S21, Supply Chain Modeling: Construct an electric power supply chain structure that includes fuel production, fuel transportation, transfer equipment and machinery, and power energy equipment.

[0023] S22, Vulnerability Analysis: Visual analysis of the supply chain network to identify critical nodes and paths. Critical nodes are assessed using the loss weight index E, and bottleneck paths are identified through graph algorithms. This reveals high-risk areas in the supply chain that could lead to system disruptions. Specifically, this includes:

[0024] S221, Network Visualization Technology: By introducing Gephi and Neo4j tools, the power and natural gas supply chain network is visualized, modeled, and analyzed. Gephi tool displays the structure and changes of the power supply chain through force-directed layout, while Neo4j tool is used to model and query complex relationships between nodes.

[0025] S222, Identification of key nodes and paths: By analyzing the visualized network, key nodes are identified using the loss weight index E, and key paths are identified using graph algorithms. At the same time, by combining bottleneck analysis and the maximum flow minimum cut theorem, high-risk paths in resource transmission are located.

[0026] Optionally, the fuel production stage includes coal, petroleum products, and nuclear fuel; the fuel transportation stage includes ships and land transportation; the transfer equipment and machinery stage includes vehicles and structural metal products; and the power energy equipment stage includes transmission and control equipment, electric motors, generators, and transformers.

[0027] Optionally, the identification of key nodes and paths in S222 includes:

[0028] S2221, Definition and Identification Method of Critical Nodes: A critical node is defined as a node in the network that undertakes connection functions or participates in resource transmission. A critically vulnerable node is defined as a node in the supply chain whose supply volume accounts for a proportion greater than a set threshold in the total supply volume of a particular item, and which is irreplaceable in the production process of that item. Critically vulnerable nodes are identified by the loss proportion E, expressed as:

[0029]

[0030] Among them, v t To analyze the target supply volume, v i This refers to the supply quantity for a single supplier relationship for this item.

[0031] S2222, Identification and analysis of critical paths in the supply chain: Calculate the shortest path from the source to other nodes in the network using graph algorithms to identify paths that affect the efficiency of resource or information flow. Bottlenecks in the path are identified by monitoring network traffic load and optimized by adding redundancy or load balancing. Analyze the maximum flow from the source to the sink using the maximum flow minimum cut theorem to find the critical path that limits network capacity.

[0032] The graph algorithm used is Dijkstra's algorithm, expressed as:

[0033] if:d[u]+w(u,v) <d[v]

[0034] then:d[v]:=d[u]+w(u,v);

[0035] Where d[v] is the path length from the source point to v.

[0036] Optionally, the gas pipeline network fault modeling in S3 includes:

[0037] S31, Hydraulic Calculation of Natural Gas Pipeline Network: Under the premise that the pressure of urban gas pipelines does not exceed 1.6MPa and Z0=1, calculate the flow rate of high-pressure, medium-pressure, and low-pressure gas pipelines, specifically including:

[0038] The flow rates of the high-pressure and medium-pressure gas pipelines are expressed as follows:

[0039]

[0040] Where p1 is the starting pressure of the pipeline, p2 is the ending pressure of the pipeline, L is the calculated length of the pipeline, Q0 is the calculated flow rate of the gas pipeline, d is the inner diameter of the pipeline, ρ0 is the gas density, λ is the friction resistance coefficient of the gas pipeline, T is the standard temperature of the gas, and T0 is the absolute temperature under standard conditions.

[0041] The flow rate of the low-pressure gas pipeline is expressed as follows:

[0042]

[0043] S32, Natural Gas Pipeline Network Constraint Model: The operation of a high-pressure natural gas pipeline network satisfies multiple constraints, including node flow balance, pipeline flow upper and lower limits, gas load reduction, and component operation limitations, expressed as:

[0044]

[0045] f mr =V lcak +f rn ;

[0046] π i,min ≤π i ≤π i,max ;

[0047] f ij,min ≤f ij ≤f ij,max ;

[0048] W s,min ≤W s ≤W s,max ;

[0049] 0≤ΔW g ≤W g ;

[0050] Among them, Ψ GS Ψ GT Ψ GC Ψ j These are respectively a gas source, gas turbine unit, compressor, and natural gas pipeline assembly, W s f c These are the air output from the air source and the air flow rate of the branch where the compressor is located, respectively.

[0051] Optionally, the modeling of the gas-electric coupling component in S4 includes:

[0052] S41, Gas Turbine Output Modeling: The relationship between gas turbine output and natural gas injection rate is modeled based on the energy conversion process under ideal cycle conditions. Ignoring environmental changes, the internal cycle is assumed to be ideal. A multi-state output model of the gas turbine is constructed using temperature, pressure, and efficiency parameters from the thermodynamic process, simplified to a temperature function. The final result is a functional relationship between output and natural gas flow rate, used to characterize the gas turbine's power supply capacity under gas-electric coupling, expressed as:

[0053] -W×C pa (T2-T1)+W×C pc (T3-T4)=P;

[0054]

[0055] Where W is natural gas W f and air W a The total flow, C pa C pc These are the heat capacities of air and natural gas, respectively, in T. iThese are the temperatures at different points inside the gas generator. T1, T2, T3, and T4 are the temperatures at the inlet and outlet of the air compressor, and the inlet and outlet of the combustion chamber, respectively. u P is the lower calorific value of natural gas, and P is the power output of the gas generator. i It is the pressure at different points inside the gas generator, η c η t These are the efficiencies of the air compressor and the turbine, respectively, where σ is a constant;

[0056]

[0057] T3-T4=T3×η t ×K2;

[0058]

[0059] S42, Compressor operation model: The compressor is used to compensate for the pressure loss caused by friction during pipeline gas transmission. Its power consumption depends on the gas flow rate and the ratio of inlet and outlet pressures. The operation process meets the mass flow rate constraint, compression ratio constraint and outlet pressure constraint. In addition, multiple working modes are set according to the compressor operating status. When the power supply is insufficient, the compressor switches to offline state and the compression ratio is set to 1.

[0060] The power consumption of the compressor is expressed as follows:

[0061]

[0062] Where f is a scaling factor, RTZ is a constant, gas parameters R = 500, temperature T = 273 K, compression parameter Z = 0.9, and ρ n M is the density of natural gas under standard conditions. com (t) is the mass flow rate of natural gas through the compressor, p out (t) and p in (t) represents the outlet pressure and inlet pressure of the compressor, respectively, and k and K1 are empirical parameters of the electric compressor;

[0063] The mass flow rate constraint is expressed as:

[0064] Compression ratio constraint is expressed as:

[0065] Export pressure constraints are expressed as:

[0066] The working modes include:

[0067] Operating mode 1: The mass flow rate through the compressor is constant;

[0068] Operating mode 2: The pressure ratio between the compressor inlet and outlet is constant;

[0069] Operating mode 3: The compressor outlet pressure is constant;

[0070] Operating mode 4: Compressor offline.

[0071] Optionally, the urban power grid fault modeling in S5 includes:

[0072] S51, Establish a city power grid structure model: The city power grid model consists of a high-voltage transmission network (HVT), substations, and a high-voltage distribution network (HVD). The power supply sources include local thermal power plants, gas-fired power plants, and external transmission systems. Factors affecting load loss include economic dispatch of thermal power plants, operating status of gas-fired power plants, grid structure reconfiguration capability, and optimal load shedding strategy.

[0073] S52, Urban Power Grid Dispatch and Fault Constraint Modeling: In urban power grid modeling, an economic dispatch model is adopted and combined with the operational constraints of the Nk fault scenario to uniformly construct a generation dispatch and fault state analysis model. The generation dispatch and fault state analysis model aims to minimize generation costs and load losses, comprehensively considering the dispatch decisions of thermal power units, standby power sources, and user load shedding, and is expressed as follows:

[0074]

[0075]

[0076] θ ref =0;

[0077]

[0078] S53, Customer Load Transformation and Substation Availability Identification: The optimal load shedding is converted into the number of affected customers. If a substation does not receive power from the upstream system or gas-fired power plant, or if local power supply is below load requirements, the substation is considered unavailable, as indicated by:

[0079]

[0080] Optionally, the construction of the power outage consequence assessment indicators in S6 includes:

[0081] S61, Construct a cross-domain impact assessment model for electrical-gas faults: A bidirectional fault propagation occurs between the gas grid and the power grid via gas turbines and pressure regulators. The recovery process involves the coordinated repair of both electrical and gas systems. The number of affected users is used as an indicator to analyze the impact of the electrical coupling network, expressed as:

[0082]

[0083] S62, User Classification and Weighting Coefficient Setting: Based on the urban land use function, users are divided into residential users, commercial users, transportation users, and hospital users. The weight of each residential user is set to 1. Commercial users, transportation users, and hospital users are converted into the equivalent number of residential users based on profits, passenger flow, or service population to form an evaluation index system.

[0084] The beneficial effects of this invention are:

[0085] This invention introduces a supply chain perspective and comprehensively models the power system, natural gas system and their coupling relationships to construct a cross-domain analysis framework with bidirectional fault propagation capability. This method can systematically reveal the cascading propagation path of electrical coupling networks under fault conditions, effectively identify high-risk coupling components and vulnerable links, and improve the depth of understanding and accuracy of fault assessment of complex coupled energy systems.

[0086] This invention, through power grid modeling, gas grid modeling, gas-electric coupling modeling, supply chain analysis, scheduling optimization, and consequence assessment, establishes a user-type weighted power outage impact index system, which can quantify the degree of disaster and recovery priority of different users. This method not only provides decision support for disaster prevention and emergency scheduling for power system operators, but also helps urban energy management departments to scientifically allocate resources, strengthen the protection of key nodes, and improve the risk resistance and resilience of urban integrated energy systems, thus having significant engineering application value and social benefits. Attached Figure Description

[0087] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only for this invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0088] Figure 1 This is a schematic diagram of an urban electrical interdependence network according to an embodiment of the present invention;

[0089] Figure 2 This is a schematic diagram of the power supply chain links according to an embodiment of the present invention;

[0090] Figure 3 This is a simplified visualization diagram of the supply chain according to an embodiment of the present invention;

[0091] Figure 4 This is a schematic diagram of the electro-pneumatic coupling conduction in an embodiment of the present invention;

[0092] Figure 5 This is a schematic diagram of the analysis method flow according to an embodiment of the present invention. Detailed Implementation

[0093] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. It should also be noted that, to make the embodiments more comprehensive, the following embodiments are the best and preferred embodiments, and those skilled in the art can use other alternative methods to implement some well-known technologies; moreover, the accompanying drawings are only for more specific description of the embodiments and are not intended to specifically limit the present invention.

[0094] It should be noted that the use of terms such as "an embodiment," "an embodiment," "an exemplary embodiment," and "some embodiments" in the specification indicates that the described embodiment may include a specific feature, structure, or characteristic, but not every embodiment necessarily includes that specific feature, structure, or characteristic. Furthermore, when a specific feature, structure, or characteristic is described in connection with an embodiment, implementing such a feature, structure, or characteristic in conjunction with other embodiments (whether explicitly described or not) should be within the knowledge of those skilled in the art.

[0095] Generally, terms can be understood at least partly from their use in context. For example, depending at least partly on the context, the term "one or more" as used herein can be used to describe any feature, structure, or characteristic in a singular sense, or a combination of features, structures, or characteristics in a plural sense. Additionally, the term "based on" can be understood not necessarily to convey an exclusive set of factors, but rather, alternatively, depending at least partly on the context, to allow for the presence of other factors that are not necessarily explicitly described.

[0096] like Figures 1-5 As shown, a method for analyzing the consequences of power outages in a grid system considering the transmission of supply chain-gas-electricity faults includes the following steps:

[0097] I. Overview of Electrical Network Interdependence:

[0098] Both UPN and GDN are energy flow networks with topological and physical characteristics. Comparing their operating principles forms the basis for fault propagation modeling. Gas networks and water networks are extremely similar in physical structure. However, the coupling relationship between gas networks and the power grid is more complex, mainly in the high-voltage network. Gas sources supply gas to gas-fired power plants, and the output of these power plants is sent to the distribution network to supply power to voltage regulating stations, resulting in a tighter coupling. Furthermore, due to this gas-powered coupling, the presence of gas-fired power plants significantly improves the resilience and reliability of the power grid when a fault occurs.

[0099] Figure 1 This illustrates the general coupling relationship between the UPN and GDN. The blue dashed arrows indicate that the operation of the voltage regulator components in the voltage regulating station depends on the power supply from the UPN. An overview of the two networks is provided below.

[0100] Transmission and Distribution Network: A UPN is a local transmission network composed of multiple voltage levels. High-voltage transmission (HVT) networks (e.g., 220kV in China, 115 / 138 / 230kV in the US) form the backbone of the network, receiving external power injections from hundreds of kilometers away. High-voltage distribution (HVD) networks (e.g., 110kV in China, 69kV in the US) distribute power within a specific area of ​​a city. Medium-voltage distribution (MVD) networks (e.g., 10kV in China, 13 / 26kV in the US) connect directly to service transformers in buildings or communities.

[0101] Gas Transmission and Distribution Network: Gas pipeline diameters range from 150mm to 1420mm. Long-distance gas pipelines serve as the gas source for the transmission and distribution network. The gas flow is divided into two parts: one flows to the pressure regulating station, and the other flows to the gas-fired power plant. The gas-fired power plant supplies power to the high-voltage transmission network and is the most important electrical coupling element in the electrical coupling network. The gas gate station, as the gas source for urban gas consumption, is responsible for supplying gas to the urban gas distribution network. In the urban gas distribution network, gas flow is a depressurization process and does not require compressor pressurization, therefore compressors are not present. Due to the multi-pressure level characteristics of the urban gas distribution network, pressure regulators are needed as connection points for different pressure level networks. UPNs are susceptible to extreme weather, and GDNs themselves are prone to problems such as leakage and insufficient gas pressure. Gas-fired power plants will transmit gas network faults to the power grid, and pressure regulators will transmit power grid faults to the gas network. To study the electrical coupling fault propagation process, a bidirectional electrical coupling fault propagation analysis model needs to be established to assess the resilience of the UPN.

[0102] Due to the massive number of nodes in each network, modeling every physical node in the network is impractical. This paper treats large-scale communities as the smallest load nodes in UPN and GDN.

[0103] The transmission process of gas and electricity faults in the supply chain can be divided into three stages. First, due to the interruption of the power and natural gas supply chain, insufficient gas supply leads to the shutdown of the gas grid; second, changes in the operating status of the gas grid result in limited output of gas turbines, and may even lead to shutdown; finally, limited gas turbine output or damage to power plants and overhead lines leads to widespread power outages.

[0104] II. Techniques for analyzing vulnerable links in the power and natural gas supply chain:

[0105] In today's society, the stability and security of the electricity and natural gas supply chains are of paramount importance. Electricity is not only essential for households and businesses, but also a lifeline for critical infrastructure such as hospitals, transportation systems, and communication networks. Therefore, any disruption to the supply chain can lead to severe social and economic consequences. As electricity networks increasingly rely on advanced technologies and extensive cross-regional logistics systems, the potential vulnerabilities in their supply chains also increase, making them potential targets for attack.

[0106] In this context, supply chain analytics technology becomes crucial. This systematic approach can help identify, assess, and optimize potential vulnerabilities in the power supply chain, enabling preventative measures or mitigation of potential damage before any actual attack occurs. This technology is particularly important in the current uncertain global political and economic environment. The power supply chain can face a variety of risks, including malicious attacks, natural disasters, and technical failures. Cyber ​​attackers could disrupt power production or transmission by compromising critical software and hardware infrastructure, causing widespread blackouts and resulting social unrest.

[0107] Therefore, effective supply chain analysis techniques are crucial for ensuring the stability and security of the power energy supply chain. Through comprehensive analysis and assessment, potential vulnerabilities can be identified and addressed promptly, thereby minimizing the possibility of disruptions and ensuring the normal operation of society and stable economic development.

[0108] 2.1 Supply Chain Link Modeling:

[0109] This study analyzes the contractual relationships of natural gas suppliers in recent years (2017-2023), forming a power supply chain structure based on production stages. The focus is on the gas supply chain.

[0110] The fuel production segment typically includes: coal, petroleum products, and nuclear fuel, with a typical supplier such as PetroChina (natural gas); the fuel transportation segment typically includes: ships and land transportation, with a typical supplier such as BITMARITIME LIMITED (sea transportation); the transfer equipment and machinery segment typically includes: vehicles and structural metal products; and the power energy equipment segment typically includes: transmission and control equipment, electric motors, generators, and transformers.

[0111] 2.2 Vulnerability Analysis:

[0112] Detailed visualization analysis of modeled supply chain networks effectively reveals and helps understand structural vulnerabilities and potential risk areas. This analysis involves not only basic data presentation but also in-depth exploration of complex network characteristics, enabling the identification and management of key risk factors within the supply chain from a comprehensive perspective. Data visualization provides a visual overview of the various nodes in the supply chain and their connections, which constitute the basic architecture of the supply chain. Utilizing advanced graphical representations, such as variations in node size and color, critical nodes and high-risk links in the network can be clearly identified. Furthermore, analyzing these visual elements makes it easier to identify critical paths and vulnerable areas that could lead to overall system failure. This approach not only enhances the intuitive understanding of potential problems but also enables more precise risk localization.

[0113] (1) Network visualization technology:

[0114] In the management of the power energy supply chain, the application of network visualization technology can effectively improve the transparency of the supply chain and optimize the decision-making process. This paper proposes a network visualization scheme based on Gephi and Neo4j. By combining the advantages of large-scale network analysis and graph databases, it aims to provide an intuitive and dynamic visualization of various nodes and relationships in the power supply chain. Specifically, the Gephi tool helps to display the structural relationships and changes in the power supply chain through force-directed layout and dynamic analysis, while the Neo4j graph database is used for accurate modeling and querying of complex connections between nodes. This scheme can not only monitor the operating status of power facilities in real time and identify potential risks, but also support managers to conduct in-depth analysis through interactive visualization, optimize resource allocation, and improve supply chain efficiency. In addition, by highlighting and dynamically visualizing nodes and edges in the network, users can instantly identify bottlenecks, fault points, and risk areas in the power supply chain, thereby providing effective decision support for power companies.

[0115] (2) Identification of key nodes and paths:

[0116] 1) Definition and identification method of key nodes:

[0117] Critical nodes are generally defined as nodes that play a vital role in a network, whose stability, efficiency, and connectivity are crucial to the operation of the entire network. Although the specific definition of a critical node may vary depending on the function and purpose of the network, it generally includes the following aspects: controlling the flow of information, connecting different parts of the network, or having a high degree of connectivity.

[0118] Critical vulnerable links are defined as links that can cause significant losses in system capacity. The specific analytical indicator is quantified using E, which is the proportion of a single item's value or demand from a single supplier to the total demand for that item. This, combined with the necessity of that item and link for production, leads to the inference of the proportion of capacity loss.

[0119]

[0120] E represents the proportion of loss, v t To analyze the target supply volume, v i This refers to the supply quantity for a single supplier relationship for this item.

[0121] 2) Identification and analysis of the critical path in the supply chain:

[0122] In the design and optimization of network systems, identifying and optimizing critical paths is crucial for improving network efficiency and stability. This paper proposes a framework for identifying and optimizing critical paths based on path analysis, bottleneck analysis, and network flow analysis. First, network paths are analyzed using graph algorithms (such as Dijkstra's algorithm and Floyd-Warshall algorithm) to identify critical paths that affect network transmission efficiency.

[0123] The fundamental principle and formula derivation of Dijkstra's algorithm revolve around finding the shortest path from a single source vertex to all other nodes in the graph. The core of the algorithm is to progressively update the path length estimates, ensuring that each update is based on the currently known shortest path.

[0124]

[0125] The meaning of this formula is: if the path length from the current node u to v via edge u,v is less than the known path length d[v] from the source node to v, then update d[v] to the path length from u to v.

[0126] These critical paths typically handle the main transmission tasks of resources or information flows, making their optimization crucial for improving overall network performance. Secondly, bottleneck analysis identifies overloaded paths by monitoring network traffic load; these bottleneck paths can lead to network transmission delays or interruptions. Optimizing bottleneck paths, such as adding redundant channels or adjusting load balancing, helps improve network stability and fault tolerance. Finally, flow analysis using the maximum flow-minimum cut theorem calculates the maximum flow from the source to the sink, further identifying critical paths affecting network capacity and providing theoretical support for optimizing network resource allocation. Through application in real-world supply chain networks, research shows that comprehensively using these methods can not only improve network operating efficiency but also enhance system robustness and stability, thus providing a systematic theoretical framework for optimizing complex networks.

[0127] III. Gas Pipeline Network Fault Model:

[0128] 3.1 Hydraulic calculation of natural gas pipeline network:

[0129] If we use commonly used units and consider that the pressure of urban gas pipelines is generally below 1.6 MPa, and Z0 = 1, then the basic calculation formula for high and medium pressure gas pipelines is:

[0130]

[0131] p1 is the starting pressure of the pipeline (Pa), p2 is the ending pressure of the pipeline (Pa), L is the calculated length of the pipeline (m), and Q0 is the calculated flow rate of the gas pipeline (Nm³). 3 / h), d is the inner diameter of the pipe (mm), ρ0 is the gas density (kg / Nm³). 3) λ is the frictional resistance coefficient of the gas pipeline, T is the standard temperature of the gas (K), and T0 is the absolute temperature under standard conditions (273.15K).

[0132] The basic calculation formula for low-pressure pipelines is:

[0133]

[0134] 3.2 Natural Gas Pipeline Network Constraint Model:

[0135] The high-pressure gas network includes constraints such as node flow balance, pipeline flow upper and lower limits, gas load reduction, and component operation. Its model can be represented as:

[0136]

[0137] f mr =V lcak +f rn (0.6)

[0138] π i,min ≤π i ≤π i,max (0.7)

[0139] f ij,min ≤f ij ≤f ij,max (0.8)

[0140] W s,min ≤W s ≤W s,max (0.9)

[0141] 0≤ΔW g ≤W g (0.10)

[0142] In the formula: Ψ GS Ψ GT Ψ GC Ψ j These are respectively a gas source, gas turbine unit, compressor, and natural gas pipeline assembly; W s f c These are the air output from the air source and the air flow rate of the branch where the compressor is located, respectively.

[0143] IV. Electrical network connections:

[0144] 4.1 Gas turbine:

[0145] To clearly illustrate the relationship between the output of the gas generator and the amount of natural gas injected, a multi-state output reliability model of the gas generator is established based on an accurate model of the gas generator. This model assumes that changes in the surrounding environment have negligible impact on the generator's operation and that the internal circulation of the gas generator is perfectly ideal. The overall energy conversion process of the gas generator can be described by formulas (1.13)-(1.16):

[0146] -W×C pa (T2-T1)+W×C pc (T3-T4)=P(0.11)

[0147]

[0148] Where W is natural gas W f and air W a The total flow, W = W f +W a C pa C pc These are the heat capacities of air and natural gas, respectively; T i These are the temperatures at different points inside the gas generator. Subscripts 1, 2, 3, and 4 represent the temperatures at the inlet and outlet of the air compressor, and the inlet and outlet of the combustion chamber, respectively. (H) u P is the lower calorific value of natural gas; P is the power generation of the gas generator, where p i It refers to the pressure at different points inside the gas generator; η c ,η t These are the efficiencies of the air compressor and turbine, respectively; σ is a constant, taken as 1.4 in this paper. Since it is assumed that the internal circulation of the gas generator is perfectly ideal, the pressure in each part of the gas generator remains constant, and (1.13) and (1.14) can be written as:

[0149]

[0150] T3-T4=T3×η t ×K2(0.16)

[0151] By combining formulas (1.13)-(1.16), the relationship between the output of the gas generator and the injected natural gas flow rate can be obtained:

[0152]

[0153] 4.2 Compressor:

[0154] During natural gas transportation, pressure loss occurs in the gas flow within the pipeline due to frictional resistance. To meet the pressure requirements of urban gas gate stations and prevent insufficient gas pressure in long-distance transmission lines, gas gate stations are generally equipped with pressurization devices. The electrical power consumed at time t is expressed by equation (1.18):

[0155]

[0156] Where f is a scaling factor, and RTZ is a constant given gas parameters R = 500, temperature T = 273 K, and compression parameter Z = 0.9. ρ n M is the density of natural gas under standard conditions. com (t) is the mass flow rate of natural gas through the compressor, p out (t) and p in (t) represents the outlet pressure and inlet pressure of the compressor, respectively, and k and K1 are empirical parameters of the electric compressor. Equation (1.20) shows that the power consumption of the electric compressor is determined by the mass flow rate through the compressor and the ratio of the outlet pressure to the inlet pressure (hereinafter collectively referred to as the compression ratio).

[0157] The mass flow rate of the compressor during normal operation must meet certain upper and lower limits, as shown in equation (1.19):

[0158]

[0159] Its natural gas compression ratio should also meet certain upper and lower limits, as shown in equation (1.20):

[0160]

[0161] Its outlet pressure should also meet certain upper and lower limits, as shown in equation (1.21):

[0162]

[0163] Electric compressors typically have multiple operating modes. When operating conditions reach constraint boundaries, the operating mode is switched. There are roughly four operating modes for electric compressors:

[0164] Operating mode 1: The mass flow rate through the compressor is constant.

[0165] Operating mode 2: The pressure ratio between the compressor inlet and outlet is constant.

[0166] Operating mode 3: The compressor outlet pressure is constant.

[0167] Operating mode 4: Compressor offline (compression ratio set to 1 at this time).

[0168] Operating modes 1-3 automatically switch when the operating limits corresponding to equations (1.21)-(1.23) are triggered. Operating mode 4 indicates that when the compressor's power supply is insufficient to support its normal operation, the compressor will stop working and enter an offline state, which is equivalent to the compressor's compression ratio becoming 1. Consider a two-state model.

[0169] V. Urban Power Grid Fault State Modeling:

[0170] System Operation Principle: This section proposes a model to characterize the impact of Nk faults on load loss and pump operation (function fF2P). Generally, the UPN is partially served by internal thermal power plants and gas-fired power plants, and partially by external transmission systems. Load loss is determined by four factors, including economic dispatch of thermal power plants, stable operation of gas-fired power plants, network reconfiguration, and optimal load shedding. The UPN model consists of a mesh HVT network, substations, and an HVD network. Based on the input parameters of line fault status and gas-fired power plant operation, a simplified economic dispatch model is given by equations (1.22)-(1.31).

[0171]

[0172]

[0173] θ ref =0 (0.26)

[0174]

[0175] The objective function (1.22) minimizes the total cost of generators and load shedding. Constraint (1.23) enforces the output limit of the generator sets. The load shedding limit is given by (1.24-1.25). The power flow under the Nk fault scenario is modeled using DC power flow equations, as shown in (1.26)-(1.29). Equation (1.26) specifies the voltage angle of the reference bus. Constraint (1.27) represents bus power balance. Note: Only a small number of nodes have generator sets installed; if there is no generator, then... Set to 0. (1.28) represents the branch power flow, which is relaxed if the branch is open-circuited. Equation (1.29) limits the upper limit of branch power flow. If branch (i,j) fails, then P ij,t =0. (1.30) Limits the state of the faulty branch. Equation (1.31) shows that the HVD network maintains its radial structure by opening switches in ring k. The optimal load shedding is converted into the number of affected customers, given by (1.32).

[0176]

[0177] If the substation is not powered by an upstream system (including a gas-fired power plant), the substation will be de-energized. In addition, if the substation is de-energized or the local power supply is below the WTP load, the substation is identified as unable to support WTP, as shown in (1.33).

[0178]

[0179] VI. Evaluation Indicators:

[0180] In disaster events, faults in gas and electricity networks typically propagate across domains via coupling elements such as gas turbines and pressure regulators. During fault recovery, the restoration of both the power and gas networks is usually gradual, involving not only the restoration of their respective systems but also the restoration of inter-domain energy systems. The impact of power and gas outages on users is complex and multifaceted. To assess the bidirectional inter-domain propagation characteristics of electrically coupled networks, this paper uses the number of affected users as a quantitative indicator and analyzes the impact of electrically coupled networks by constructing corresponding function curves.

[0181]

[0182] Electrical coupling network failures directly impact residents' lives, potentially triggering public panic and social unrest, and ultimately leading to a series of public incidents. Existing assessment indicators do not consider user classification, making it impossible to comprehensively evaluate the consequences of power outages in urban electrical coupling networks. Therefore, this paper proposes a vulnerability index system based on importance, as shown in Table 1, based on urban land use characteristics. The weighting coefficients of this system are set in units of "the number of affected residential users," with one household's television outage considered as one unit. For other public users, weighting coefficients are defined based on parameters such as total profit, passenger flow, and the population of the jurisdiction, and converted into an equivalent number of affected residential users.

[0183] Table 1 Vulnerability Indicators Based on Importance

[0184]

[0185]

[0186] This invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of this invention. To provide the public with a thorough understanding of this invention, specific details are described in detail in the following preferred embodiments; however, those skilled in the art will fully understand the invention even without these details. Furthermore, to avoid unnecessary misunderstanding of the essence of this invention, well-known methods, processes, procedures, components, and circuits are not described in detail.

[0187] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A power grid outage consequence analysis method considering supply chain-gas-electricity fault propagation, characterized in that, The method comprises the following steps: S1, electrical network coupling relationship modeling: analyzing the coupling structure between the electrical network UPN and the GDN, identifying the key coupling points, including voltage regulators, gas power plants, and establishing a bidirectional fault conduction model; S2, supply chain weak link analysis: constructing a power and natural gas supply chain model, identifying key nodes and paths using network visualization and graph algorithms, and evaluating potential high-risk links in the system; S3, gas pipeline network fault modeling: based on pipeline hydraulic calculation and operation constraints, a pressure and flow calculation model of the natural gas pipeline network is established to simulate the fault state of the gas network; S4, gas-electricity coupling component modeling: a mathematical model of gas turbines and compressors is established to describe the relationship between their output and gas and electricity, and to reflect their operating mode and constraints; S5, urban power grid fault modeling: based on N-k fault analysis, an optimization model including power generation dispatching, load distribution and network power flow is constructed to evaluate the operation state of the power grid under fault; S6, blackout consequence evaluation index construction: taking the equivalent number of outages as the index, combined with user type setting weight, the social impact and recovery priority under different fault scenarios are quantified; The electrical network coupling relationship modeling in S1 comprises: S11, identifying the network attributes of UPN and GDN: the electrical network UPN and the GDN are energy flow networks with topological structure and physical properties, wherein the UPN is composed of multiple voltage levels, including high-voltage transmission, high-voltage distribution and medium-voltage distribution networks, and the GDN includes long-distance gas pipeline, gas power plant, pressure regulating station and urban gas distribution network; S12, establishing a typical gas-electricity coupling relationship structure: at the high-voltage network level, natural gas is transported to the gas power plant through the pipeline, the gas power plant generates electricity and transmits it to the distribution network, and also supplies power to the pressure regulating station, forming a coupling path. At the same time, the operation of the pressure regulator depends on the power support of the UPN, and the fault is transmitted from the power grid to the gas network or from the gas network to the power grid, so the coupling relationship is bidirectional; S13, identifying key coupling components: the key coupling components include pressure regulators and gas power plants. The pressure regulator connects the urban gas distribution network of different pressure levels and relies on electricity for driving. The gas power plant is the core node of the coupling, whose operating state is affected by the gas source and supplies power to the power grid; S14, proposing a modeling simplification strategy: taking large-scale communities as the minimum load nodes in UPN and GDN to realize modeling simplification; S15, defining fault conduction paths and stages: the gas-electricity fault conduction process is divided into three stages, including: Stage one: interruption of the power and natural gas supply chain, leading to insufficient gas supply and causing gas network shutdown; Stage two: changes in the state of the gas network, resulting in a decrease in the output of gas turbines or shutdown; Stage three: insufficient output of gas turbines, failure of power stations or transmission lines, leading to large-scale power outages; The supply chain weak link analysis in S2 comprises: S21, supply chain link modeling: constructing a power supply chain structure including fuel production link, fuel transportation link, transfer equipment and transfer machinery link, and power energy equipment link; S22, weak link analysis: visual analysis of the supply chain network, identification of key nodes and paths, evaluation of key nodes by loss proportion index E, identification of bottleneck paths by graph algorithm, revealing high-risk areas in the supply chain that cause system interruption, including: S221, network visualization technology: through the introduction of Gephi and Neo4j tools, the power and natural gas supply chain network is visualized and analyzed, wherein the Gephi tool displays the structure of the power supply chain and its changes through force-directed layout, and the Neo4j tool is used for modeling and querying the complex relationship between nodes; S222, identification of key nodes and paths: through the analysis of the visualized network, the key nodes are identified by using the loss proportion index E, and the key paths are identified by using the graph algorithm, and the high-risk paths in resource transmission are located by combining bottleneck analysis and the maximum flow minimum cut theorem.

2. The method for power grid outage consequence analysis considering supply chain-gas-electricity fault propagation according to claim 1, characterized in that, The fuel production link includes coal, petroleum products, nuclear fuel, the fuel transportation link includes ships, land transportation, the transfer equipment and transfer machinery link includes vehicles, structural metal products, and the electric power equipment link includes transmission control equipment, electric motors, generators, and transformers.

3. The method for power grid outage consequence analysis considering supply chain-gas-electricity fault propagation according to claim 2, characterized in that, The identification of key nodes and paths in S222 includes: S2221, definition and identification method of key nodes: the key node is defined as a node that undertakes connection function or participates in resource transmission in the network, and the key weak link node is defined as a node in the supply chain whose supply quantity accounts for more than a set threshold in the total supply quantity of the item, and the item is irreplaceable in the production process, the key weak link node is identified by loss proportion E, expressed as: ； wherein, for analyzing the target supply quantity, is the supply quantity of the single supply relationship of the item; S2222, identification and analysis of supply chain critical path: the shortest path from the source point to other nodes in the network is calculated by graph algorithm to identify the path that affects the efficiency of resource or information flow, the bottleneck section in the path is identified by monitoring network traffic load, and is optimized by increasing redundancy or load balancing, the maximum flow from the source point to the sink point is analyzed by using the maximum flow minimum cut theorem, and the key path that limits the network capacity is found out; The graph algorithm uses Dijkstra algorithm, expressed as: ； Where d[v] is the path length from the source point to v.

4. The method for power grid outage consequence analysis considering supply chain-gas-electricity fault propagation according to claim 3, characterized in that, The gas pipe network failure modeling in S3 includes: S31, natural gas pipe network hydraulic calculation: under the premise that the pressure of urban gas pipeline is not more than 1.6 MPa and Z0=1, the flow of high-pressure, medium-pressure and low-pressure gas pipelines is calculated, including: The flow of high-pressure and medium-pressure gas pipelines is expressed as: ； wherein, Pstart is the pipe start pressure, Pend is the pipe end pressure, L is the pipe calculated length, Q is the calculated flow of the gas pipe, D is the pipe internal diameter, Rho is the gas density, F is the friction resistance coefficient of the gas pipe, T is the standard temperature of the gas, T0 is the absolute temperature of the standard state; The flow of low-pressure gas pipeline is expressed as: ； S32, natural gas pipe network constraint model: the operation of high-pressure natural gas pipe network satisfies multiple constraint conditions, including node flow balance, pipeline flow upper and lower limit, gas load reduction amount and element operation limit, expressed as: ； ； ； ； ； ； Wherein, The gas source, the gas unit, the compressor and the natural gas pipeline set respectively, The gas source outflow and the gas flow of the branch where the compressor is located respectively.

5. The method for power grid outage consequence analysis considering supply chain-gas-electricity fault propagation according to claim 4, characterized in that, The gas-electricity coupling component modeling in S4 includes: S41, gas turbine output modeling: the relationship between the output of the gas turbine and the natural gas injection amount is modeled based on the energy conversion process under ideal cycle conditions, ignoring the influence of environmental changes, setting the internal cycle as an ideal state, using the temperature, pressure and efficiency parameters in the thermodynamic process to construct a multi-state output model of the gas generator, and simplifying it into a temperature function, finally obtaining the functional relationship between the output and the natural gas flow, which is used to represent the power supply capacity of the gas turbine under gas-electricity coupling, expressed as: ； ； ； ； wherein, W is the flow rate of natural gas W f and air W a , , are the heat capacities of air and natural gas, respectively, are the temperatures at different points in the gas engine, T1, T2, T3, T4 are the temperatures at the inlet and outlet of the air compressor, at the inlet and outlet of the combustion chamber, respectively, is the lower heating value of natural gas, is the power generated by the gas engine, are the pressures at different points in the gas engine, , are the efficiencies of the air compressor and the turbine, respectively, is a constant; ； ； ； S42, compressor operation model: the compressor is used to compensate for the pressure loss caused by friction during pipeline gas transmission, and its power consumption depends on the gas flow and the inlet-to-outlet pressure ratio. The operation process meets the mass flow rate constraint, compression ratio constraint and outlet pressure constraint. In addition, according to the operating state of the compressor, multiple working modes are set. When the power supply is insufficient, the compressor switches to an offline state, and the compression ratio is set to 1. The electric power consumption of the compressor is expressed as: ； wherein, f is a proportionality factor, is a constant, the gas parameter R = 500, the temperature T = 273 K, the compression parameter Z = 0.9, is the density of natural gas in standard conditions, is the mass flow rate of natural gas through the compressor, and are the outlet pressure and the inlet pressure of the compressor, respectively, and are empirical parameters of the electric compressor; The mass flow rate constraint is expressed as: ; The compression ratio constraint is expressed as: ; The outlet pressure constraint is expressed as: ; The working modes include: Working mode 1: the mass flow rate through the compressor is constant; Working mode 2: the inlet-to-outlet pressure ratio of the compressor is constant; Working mode 3: the outlet pressure of the compressor is constant; Working mode 4: the compressor is offline.

6. The method for power grid outage consequence analysis considering supply chain-gas-electricity fault propagation according to claim 5, characterized in that, The city grid failure modeling in S5 includes: S51, establishing a city grid structure model: the city grid model is composed of high-voltage transmission networks, substations and high-voltage distribution networks. The power supply sources include local thermal power plants, gas power plants and external power transmission systems. The factors affecting load loss include economic dispatching of thermal power plants, operating state of gas power plants, grid structure reconstruction capability and optimal load shedding strategy; S52, city grid dispatching and failure constraint modeling: in the city grid modeling, an economic dispatching model is adopted combined with the operating constraints of N-k failure scenarios to uniformly construct a power generation dispatching and failure state analysis model. The power generation dispatching and failure state analysis model aims to minimize the generation cost and load loss, and comprehensively considers the dispatching decisions of thermal power units, standby power sources and user load reduction, expressed as: ； ； ； ； ； ； ； ； ； ； S53, customer load conversion and substation availability identification: the optimal load shedding is converted into the number of affected customers. If a substation does not receive power from the upstream system or the gas power plant, or the local power supply is lower than the load requirement, the substation is considered unavailable, expressed as: ； 。 7. The method for power grid outage consequence analysis considering supply chain-gas-electricity fault propagation according to claim 6, characterized in that, The post-outage consequence evaluation index construction in S6 includes: S61, constructing an electricity-gas failure cross-domain influence evaluation model: the gas network and the power grid conduct bidirectional failure conduction through the gas turbine and the pressure regulator. The recovery process involves the coordinated repair of the electric and gas systems. The number of affected users is used as an index to analyze the influence of the electrically coupled network, expressed as: ； S62, user classification and weight coefficient setting: users are classified into residential users, commercial users, transportation users and hospital users according to the functions of urban land. The residential users are taken as the benchmark with a unit weight of 1. The commercial users, transportation users and hospital users are converted into equivalent residential user numbers according to their profits, passenger flows or service populations to form an evaluation index system.

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