Power grid power failure consequence analysis method considering supply chain-gas-electricity fault conduction

Abstract

The invention relates to the technical field of power systems, in particular to a power grid power failure consequence analysis method considering supply chain-gas-electricity fault conduction, which comprises the following steps: S1, modeling an electrical network coupling relationship: identifying a key coupling point; s2, supply chain fragile link analysis: evaluating potential high-risk links in the system; s3, gas pipeline network fault modeling: establishing a pressure and flow calculation model of a natural gas pipeline network; s4, pneumoelectric coupling assembly modeling: establishing mathematical models of a gas turbine and a compressor; s5, urban power grid fault modeling: evaluating the operation state of the power grid under the fault; s6, power failure consequence evaluation index construction: quantifying social influence and recovery priorities in different fault scenes; according to the method, the chain propagation path of the electrical coupling network under the fault condition can be systematically revealed, high-risk coupling components and fragile links are effectively identified, and the understanding depth and the fault evaluation accuracy of a complex coupling energy system are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of power systems, and in particular, to a method for analyzing the consequences of power grid outages considering the conduction of supply chain - gas - power failures. Background Art

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

[0003] Although there have been many studies on integrated energy systems, covering multiple aspects such as electrical coupling modeling, power flow calculation, and optimal dispatching, there are still some obvious deficiencies. Most studies mainly focus on the independent characteristics of energy subsystems, lacking systematic modeling and evaluation of the linkage mechanism between them and the energy supply chain. At the same time, for urban - level, multi - voltage - level, and multi - gas - pressure - level electrical coupling networks, existing studies are still insufficient in terms of network scale, node distribution, and coupling element modeling, making it difficult to comprehensively reveal the fault propagation path and influence range of the electrical system 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 degrees, limiting their application value in actual emergency management and resource allocation. Summary of the Invention

[0004] The present invention provides a method for analyzing the consequences of power grid outages considering the conduction of supply chain - gas - power failures, which can provide a decision - making basis for power system operation units and emergency management departments, improve resource scheduling efficiency and system restoration ability, and enhance the resilience of the integrated energy system in the face of complex disaster scenarios.

[0005] A method for analyzing the consequences of power grid outages considering the conduction of supply chain - gas - power failures includes the following steps:

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

[0007] S2, Analysis of Vulnerable Links in the Supply Chain: Build a power and natural gas supply chain model, use network visualization and graph algorithms to identify key nodes and paths, and evaluate potential high-risk links in the system;

[0008] S3, Fault Modeling of Gas Pipelines: Based on hydraulic calculations and operating constraints of the pipeline network, establish a pressure and flow calculation model for the natural gas pipeline network to simulate the fault state of the gas network;

[0009] S4, Modeling of Gas-Electricity Coupling Components: Establish mathematical models for gas turbines and compressors to describe the relationship between their output and gas volume and electricity, and reflect their operating modes and constraints;

[0010] S5, Fault Modeling of Urban Power Grids: Based on N-k fault analysis, build an optimization model including power generation scheduling, load distribution, and network power flow to evaluate the operating state of the power grid under faults;

[0011] S6, Construction of Power Outage Consequence Evaluation Index: Use the equivalent number of power outage users as an index, set weights in combination with user types, and quantify the social impact and restoration priorities under different fault scenarios.

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

[0013] S11, Identification of the Network Attributes of UPN and GDN: The electrical networks UPN and GDN are energy flow networks with topological structures and physical characteristics. Among them, UPN consists of multiple voltage levels, including high-voltage transmission (HVT), high-voltage distribution (HVD), and medium-voltage distribution (MVD) networks, and GDN includes long-distance gas pipelines, gas power plants, pressure regulating gate stations, and urban gas distribution networks;

[0014] S12, Establishment of a Typical Gas-Electricity Coupling Relationship Structure: At the high-voltage network level, natural gas is transported through pipelines to gas power plants. After the gas power plants generate electricity, the electric energy is transmitted to the distribution network and supplies power to the pressure regulating stations, forming a coupling path. At the same time, the operation of the pressure regulator depends on the power support of the UPN. Faults can be conducted from the power grid to the gas network or from the gas network to the power grid, and the coupling relationship is bidirectional;

[0015] S13, Identification of Key Coupling Components: The key coupling components include pressure regulators and gas power plants. The pressure regulator connects urban gas distribution networks with different pressure levels and depends on electric drive. The gas power plant is the core node of the coupling. Its operating state is affected by the gas source and supplies power to the power grid;

[0016] S14, Proposal of a Modeling Simplification Strategy: Use large-scale communities as the smallest load nodes in UPN and GDN to achieve modeling simplification;

[0017] S15, Definition of Fault Conduction Paths and Stages: Divide the gas-electricity fault conduction process into three stages, specifically including:

[0018] Phase 1: The interruption of the power and natural gas supply chain leads to insufficient gas supply, which in turn causes the gas network to shut down.

[0019] Phase 2: The change in the state of the gas network causes the output of the gas turbine to decrease or the turbine to shut down.

[0020] Phase 3: Insufficient output of the gas turbine, faults in power stations or transmission lines lead to widespread power outages.

[0021] Optionally, the analysis of vulnerable links in the supply chain in S2 includes:

[0022] S21, Supply chain link modeling: Construct a power supply chain structure including fuel production links, fuel transportation links, transfer equipment and transfer machinery links, and power energy equipment links.

[0023] S22, Vulnerable link analysis: Visually analyze the supply chain network, identify key nodes and paths, evaluate key nodes through the loss ratio index E, identify bottleneck paths through graph algorithms, and reveal high-risk areas in the supply chain that cause system interruptions, specifically including:

[0024] S221, Network visualization technology: By introducing Gephi and Neo4j tools, visually model and analyze the power and natural gas supply chain network. Among them, the Gephi tool displays the structure and changes of the power supply chain through force-directed layout, and the Neo4j tool is used for modeling and querying complex relationships between nodes.

[0025] S222, Identification of key nodes and paths: Through the analysis of the visualized network, use the loss ratio index E to identify key nodes, identify key paths through graph algorithms, and at the same time combine bottleneck analysis with the maximum flow minimum cut theorem to locate high-risk paths in resource transmission.

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

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

[0028] S2221, Definition and identification method of key nodes: Key nodes are defined as nodes that undertake connection functions or participate in resource transmission in the network. Key vulnerable link nodes are defined as nodes in the supply chain whose supply volume accounts for a proportion greater than a set threshold in the total supply volume of this item, and this item is irreplaceable in the production process. Key vulnerable link nodes are identified through the loss ratio E, expressed as:

[0029]

[0030] Among them, v t To analyze the target supply, v i The supply quantity of the single supply relationship for the item;

[0031] S2222, Identification and Analysis of Critical Paths in the Supply Chain: Graph algorithms are used to calculate the shortest paths from source nodes to other nodes in the network to identify paths that affect resource or information flow efficiency. Bottlenecks in the paths are identified by monitoring network traffic load and optimized through increased redundancy or load balancing. The maximum flow minimum cut theorem is used to analyze the maximum flow from the source to the sink to identify the critical paths that limit network capacity.

[0032] The graph algorithm adopts Dijkstra algorithm, which is 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 network fault modeling in S3 includes:

[0037] S31, Natural Gas Pipeline Network Hydraulic Calculation: Calculate the flow rates of high-pressure, medium-pressure, and low-pressure gas pipelines, assuming the urban gas pipeline pressure does not exceed 1.6 MPa and Z0 = 1. Specifically, this includes:

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

[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 of the standard state;

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

[0042]

[0043] S32, natural gas pipeline network constraint model: The operation of the high-pressure natural gas pipeline network meets multiple constraints, including node flow balance, pipeline flow upper and lower limits, gas load reduction, and component operation restrictions, which can be 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 are the gas source, gas turbine unit, compressor, and natural gas pipeline set respectively. W s , f c are the gas output of the gas source and the gas flow rate of the branch where the compressor is located respectively.

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

[0052] S41, gas turbine output modeling: The relationship between the output of the gas turbine and the natural gas injection volume 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 respectively, constructing a multi-state output model of the gas generator, and simplifying it into a temperature function. Finally, the function relationship between the output and the natural gas flow rate is obtained, which is used to characterize the power supply capacity of the gas turbine under gas-electricity coupling, expressed as:

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

[0054]

[0055] Among them, W is the total flow rate of natural gas W f and air W a , C pa , C pc are the heat capacities of air and natural gas respectively, and T iis the temperature at different points inside the gas generator, and T1, T2, T3, and T4 are the temperatures at the inlet and outlet of the air compressor, the inlet of the combustion chamber, and the outlet respectively, H u is the lower calorific value of natural gas, P is the power generation of the gas generator, p i is the pressure at different points inside the gas generator, η c 、η t are the efficiencies of the air compressor and the turbine respectively, and 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 gas pipeline transportation. Its power consumption depends on the gas flow rate and the pressure ratio between the inlet and outlet. The operation process satisfies the mass flow rate constraint, compression ratio constraint, and outlet pressure constraint. In addition, multiple working modes are set according to the operation state of the compressor. When the power supply is insufficient, the compressor switches to the offline state and the compression ratio is set to 1;

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

[0061]

[0062] where f is a proportionality factor, RTZ is a constant, the gas parameter R = 500, the temperature T = 273K, the compression parameter Z = 0.9, ρ n is the density of natural gas under standard conditions, M com (t) is the mass flow rate of natural gas passing through the compressor, p out (t) and p in (t) are 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] The compression ratio constraint is expressed as:

[0065] The outlet pressure constraint is expressed as:

[0066] The working modes include:

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

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

[0069] Operating mode 3: The pressure at the outlet of the compressor is a constant;

[0070] Operating mode 4: The compressor is offline.

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

[0072] S51, Establish an urban power grid structure model: The urban 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 power plants, and external power transmission systems. The factors affecting load loss include the economic dispatch of thermal power plants, the operating status of gas power plants, the power grid structure reconstruction ability, and the optimal load shedding strategy;

[0073] S52, Urban power grid dispatching and fault constraint modeling: In urban power grid modeling, an economic dispatch model is adopted and combined with the operating constraints of the N-k fault scenario to uniformly construct a power generation dispatch and fault status analysis model. The power generation dispatch and fault status analysis model aims to minimize the power generation cost and load loss, and comprehensively considers the dispatch decisions of thermal power units, standby power sources, and user load shedding, expressed as:

[0074]

[0075]

[0076] θ ref = 0;

[0077]

[0078] S53, Customer load conversion and substation availability identification: Convert the optimal load shedding into the number of affected customers. If the 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:

[0079]

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

[0081] S61, Construct a cross-domain impact assessment model for electrical-gas faults: Bidirectional fault conduction occurs between the gas network and the power grid through gas turbines and voltage regulators. The restoration process involves the coordinated repair of the electrical and gas systems. The number of affected users is used as an indicator to analyze the impact of the electrical-gas coupled network, expressed as:

[0082]

[0083] S62, User Classification and Weight Coefficient Setting: Users are classified into residential users, commercial users, transportation users, and hospital users according to the urban land use function. Taking residential users as the benchmark, the unit weight is set to 1. Commercial users, transportation users, and hospital users are converted into equivalent residential user numbers based on profit, passenger flow, or the served population to form an evaluation index system.

[0084] Advantages of the present invention:

[0085] In the present invention, by introducing the perspective of the supply chain, comprehensively modeling the power system, natural gas system and their coupling relationship, a cross-domain analysis framework with bidirectional fault conduction ability is constructed. This method can systematically reveal the cascading propagation path of the electrical coupling network under fault conditions, effectively identify high-risk coupling components and vulnerable links, and improve the understanding depth of complex coupling energy systems and the accuracy of fault assessment.

[0086] In the present invention, through power grid modeling, gas network modeling, gas-electricity coupling modeling, supply chain analysis, scheduling optimization and consequence assessment, etc., and establishing a power outage impact index system weighted by user types, the disaster-affected degree and recovery priority of different users can be quantified. This method not only provides decision support for disaster prevention and emergency scheduling of power system operation units, but also helps urban energy management departments to scientifically allocate resources, strengthen the protection of key nodes, improve the risk resistance ability and resilience of urban integrated energy systems, and has significant engineering application value and social benefits. Brief Description of the Drawings

[0087] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following will briefly introduce the drawings required for the implementation examples or the description of the prior art. Obviously, the drawings in the following description are only for the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0088] Figure 1 Schematic diagram of the urban electrical interdependent network according to the embodiment of the present invention;

[0089] Figure 2 Schematic diagram of the power supply chain link according to the embodiment of the present invention;

[0090] Figure 3 Schematic diagram of the supply chain visualization sketch according to the embodiment of the present invention;

[0091] Figure 4 Schematic diagram of the electricity-gas coupling conduction according to the embodiment of the present invention;

[0092] Figure 5 Schematic diagram of the analysis method flow according to the embodiment of the present invention. Detailed Embodiments

[0093] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted here that in order to make the embodiments more detailed, the following embodiments are the best and preferred embodiments. For some well-known technologies, those skilled in the art can also adopt other alternative methods for implementation; moreover, the accompanying drawings are only for more specifically describing the embodiments, and are not intended to specifically limit the present invention.

[0094] It should be noted that in the specification, references to "one embodiment", "an embodiment", "exemplary embodiments", "some embodiments", etc. indicate that the described embodiments may include specific features, structures, or characteristics, but not necessarily every embodiment includes such specific features, structures, or characteristics. Additionally, when combining embodiments to describe specific features, structures, or characteristics, implementing such features, structures, or characteristics in combination with other embodiments (whether explicitly described or not) should be within the knowledge of those skilled in the relevant art.

[0095] Generally, terms can be understood at least in part from their use in context. For example, at least in part depending 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 can be used to describe a combination of features, structures, or characteristics in a plural sense. Additionally, the term "based on" can be understood as not necessarily intended to convey a set of exclusive factors, but rather, at least in part depending on the context, can allow for the existence of other factors that may not be explicitly described.

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

[0097] I. Overview of the interdependence of electrical networks:

[0098] For both the UPN and GDN of the electrical network, they are energy flow networks with topological and physical characteristics. The comparison between their operating principles is the basis for fault propagation modeling. The gas network is extremely similar to the water network in terms of physical structure. However, the coupling relationship between the gas network and the power grid is more complex, mainly reflected in the high - voltage networks. The gas source supplies gas to the gas power plant, and the output of the gas power plant is sent to the distribution network to supply power to the pressure regulating station, and their coupling relationship is closer. At the same time, due to the coupling relationship of gas to the power grid, when a fault occurs in the power grid, the existence of the gas power plant will greatly improve the resilience and reliability of the power grid.

[0099] Figure 1 Illustrates the general coupling relationship between the UPN and GDN. The blue dashed - line arrow indicates that the operation of the pressure regulator component in the pressure regulating station depends on the power supply of the UPN. The two networks are outlined as follows.

[0100] Transmission and distribution network: The UPN is a local power transmission network composed of multiple voltage levels. The high-voltage transmission (HVT) network (e.g., 220 kV in China, 115 / 138 / 230 kV in the United States) forms the backbone of the network and receives external power injection hundreds of kilometers away. The high-voltage distribution (HVD) network (e.g., 110 kV in China, 69 kV in the United States) distributes power within a certain area of the city. The medium-voltage distribution (MVD) network (e.g., 10 kV in China, 13 / 26 kV in the United States) is directly connected to the service transformer of buildings or communities.

[0101] Transmission and distribution gas network: The diameter of the gas transmission pipeline ranges from 150 mm to 1420 mm. The long-distance gas transmission pipeline serves as the gas source of the transmission and distribution gas network. The gas flow is divided into two parts. One part flows to the pressure regulating gate station, and the other part flows to the gas power plant. The gas power plant supplies power to the high-voltage power grid and serves as the most important electrical coupling component in the electrical coupling network. The gas gate station serves as the gas source for urban gas use and is responsible for supplying gas to the urban gas distribution network. In the urban gas distribution network, the gas flow is a pressure reduction process and does not require compression by a compressor, so there is no compressor. Due to the multi-pressure level characteristics of the urban gas distribution network, a pressure regulator is required as the connection point for networks with different pressure levels. The UPN is vulnerable to extreme weather, the GDN is prone to problems such as leakage and insufficient gas pressure, the gas power plant will conduct gas network faults to the power grid, and the pressure regulator will conduct power grid faults to the gas network. To study the process of electrical coupling fault conduction, a two-way electrical coupling fault conduction analysis model needs to be established to evaluate the resilience of the UPN.

[0102] Due to the huge number of nodes in each network, it is not feasible to model each physical node of the network. This article regards large-scale communities as the smallest load nodes in the UPN and GDN.

[0103] The process of gas-electricity fault conduction in the supply chain can be divided into three stages. First, due to the interruption of the power and natural gas supply chain, the gas source supply is insufficient, resulting in the shutdown of the gas network; second, the change in the operating state of the gas network leads to the limitation of the output of gas turbines and may even cause shutdown; finally, the limitation of the output of gas turbines or the damage of power stations and overhead lines lead to large-scale power outages.

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

[0105] In today's society, the stability and security of the power and natural gas supply chain are of utmost importance. Electricity is not only a necessity for households and commercial activities but also the lifeline of critical infrastructures such as hospitals, transportation systems, and communication networks. Therefore, any interruption in the supply chain may lead to serious social and economic impacts. As the power network increasingly relies on advanced technologies and extensive cross-regional logistics systems, the potential vulnerable points in its supply chain also increase, becoming possible targets for attacks.

[0106] In this context, supply chain analysis technology has become crucial. Such a systematic approach can help identify, evaluate, and optimize potential vulnerabilities in the power energy supply chain, thereby taking preventive measures or mitigating potential damage before any actual attack occurs. Especially in the current global political and economic environment full of uncertainties, this technology is particularly important. The power supply chain may face various risks, including malicious attacks, natural disasters, and technical failures. Cyber attackers may disrupt power production or transmission by sabotaging key software and hardware facilities, causing widespread power outages and social unrest.

[0107] Therefore, effective supply chain analysis technology is the key to ensuring the stability and security of the power energy supply chain. Through comprehensive analysis and evaluation, potential vulnerabilities can be detected and addressed in a timely manner, thereby minimizing the likelihood of disruptions and ensuring the normal operation of society and the stable development of the economy.

[0108] 2.1. Supply Chain Link Modeling:

[0109] This study analyzes the contract relationships of natural gas suppliers in recent years (2017 - 2023) and forms the power supply chain structure according to the production links. It focuses on the gas supply chain.

[0110] The fuel production link usually includes: coal, petroleum products, nuclear fuel, and typical suppliers such as: China National Petroleum Corporation (natural gas); the fuel transportation link usually includes: ships, land transportation, and typical suppliers such as: BITMARITIME LIMITED (sea transportation); the transshipment equipment and machinery link usually includes: vehicles, structural metal products; the power energy equipment link usually includes: transmission control equipment, motors, generators, transformers.

[0111] 2.2. Vulnerable Link Analysis:

[0112] Through detailed visual analysis of the modeled supply chain network, the structural vulnerabilities and potential risk areas of the supply chain can be effectively revealed and understood. This analysis process not only involves basic data presentation but also includes in - depth exploration of complex network characteristics, enabling the identification and management of key risk factors in the supply chain from a comprehensive perspective. By visualizing the data, the individual nodes in the supply chain and their connections can be intuitively observed, and these nodes and connections form the basic architecture of the supply chain. Using advanced graphical representation methods, such as changes in node size and color, key nodes and high - risk links in the network can be clearly marked. In addition, by analyzing these visual elements, it is easier to identify the critical paths and vulnerable areas that may lead to the failure of the overall system. This method not only enhances the intuitive understanding of potential problems but also enables more accurate risk positioning.

[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 solution 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 display for various nodes and relationships in the power supply chain. Specifically, the Gephi tool helps to display the structural relationships and their changes in the power supply chain through force-directed layout and dynamic analysis, while the Neo4j graph database is used for precise modeling and querying of complex connections between nodes. This solution can not only monitor the operating status of power facilities in real time, identify potential risks, but also support managers for in-depth analysis through interactive visualization, optimize resource allocation and improve supply chain efficiency. In addition, through the highlighting and dynamic visualization of nodes and edges in the network, users can immediately discover bottlenecks, fault points and risk areas in the power supply chain, thus providing effective decision-making support for power enterprises.

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

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

[0117] Key nodes are usually defined as nodes that play important roles in the network, and their stability, efficiency and connectivity are crucial for the operation of the entire network. Although the specific definition of key nodes may vary depending on the function and purpose of the network, it generally includes the following aspects: controlling information flow, connecting different parts of the network or having a high degree of connectivity.

[0118] Key vulnerable link nodes are defined as: links that can cause significant production capacity losses in the system. Its specific analysis index is quantified by E, that is, according to the proportion of the amount or demand of a single item from a single supplier in the total amount of this item, combined with the necessity of this item and link for production, the proportion of production capacity loss is deduced.

[0119]

[0120] E is the proportion of loss, v t is the analyzed target supply volume, v i is the supply volume of a single supply relationship of this item.

[0121] 2) Identification and analysis of key paths in the supply chain:

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

[0123] The basic principle and formula derivation of Dijkstra's algorithm revolve around how to effectively find the shortest paths from a single source node to all other nodes in a graph. The core of this algorithm is to gradually update the path length estimates and ensure that each update is based on the currently known shortest paths.

[0124]

[0125] The meaning of this formula is that if the path length from the current node u to v through the 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 through u to v.

[0126] These critical paths are usually responsible for the main transmission tasks of resources or information flows. Therefore, their optimization is crucial for improving the overall network performance. Secondly, bottleneck analysis identifies paths with traffic overloads by monitoring network traffic loads. These bottleneck paths may cause 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, traffic analysis is carried out using the maximum flow minimum cut theorem to calculate the maximum flow from the source node to the sink node, thereby further identifying critical paths that affect network capacity and providing theoretical support for optimizing network resource allocation. Through applications in actual supply chain networks, research shows that the comprehensive use of these methods can not only improve network operation efficiency but also enhance the robustness and stability of the system, thus providing a systematic theoretical framework for the optimization of complex networks.

[0127] III. Gas pipeline network failure model:

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

[0129] If customary common units are adopted and considering that the pressure of urban gas pipelines is generally below 1.6 MPa and Z0 = 1, the basic calculation formulas for high- and medium-pressure gas pipelines are as follows:

[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), Q0 is the calculated flow rate of the gas pipeline (Nm 3 / h), d is the inner diameter of the pipeline (mm), ρ0 is the gas density (kg / Nm 3) , λ is the friction resistance coefficient of the gas pipeline, T is the standard temperature of the gas (K), and T0 is the absolute temperature at the standard state (273.15 K).

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

[0133]

[0134] 3.2, Natural gas network constraint model:

[0135] The high-pressure gas network includes node flow balance constraints, pipeline flow upper and lower limit constraints, gas load reduction amount constraints, and component operation constraints, etc. Its model can be expressed 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 are the gas source, gas turbine unit, compressor, and natural gas pipeline sets respectively; W s , f c are the gas output of the gas source and the gas flow in the branch where the compressor is located respectively.

[0143] IV. Electrical network connection:

[0144] 4.1, Gas turbine:

[0145] To clearly show the relationship between the output of a gas generator and the natural gas injection volume, based on the accurate model of the gas generator, it is assumed that the influence of the surrounding environment change on the operation of the gas generator is negligible, and the internal cycle of the gas generator is considered to be completely ideal. Thus, a multi-state output reliability model of the gas generator is established. 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 the total flow rate of natural gas W f and air W a , W = W f +W a ; C pa , C pc are the specific heat capacities of air and natural gas respectively; T i is the temperature at different points inside the gas generator. The subscripts 1, 2, 3, and 4 are the temperatures at the inlet and outlet of the air compressor, the inlet of the combustion chamber, and the outlet respectively. H u is the lower calorific value of natural gas; P is the power generation of the gas generator, where p i is the pressure at different points inside the gas generator; η c , η t are the efficiencies of the air compressor and the turbine respectively; σ is a constant, which is taken as 1.4 in this paper. Since it is assumed that the internal cycle of the gas generator is completely ideal, the pressure of each part of the gas generator remains unchanged. (1.13) and (1.14) can be written as:

[0149]

[0150] T3 - T4 = T3×η t ×K2(0.16)

[0151] 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 the transportation of natural gas, due to the existence of frictional resistance, pressure loss will occur in the gas flow in the natural gas pipeline. To meet the pressure requirements of the town gas gate station and prevent insufficient incoming gas pressure in the long-distance gas transmission main line, the gas gate station is generally equipped with a pressurization device. The electric power consumed at time t is expressed by Equation (1.18):

[0155]

[0156] where f is a proportionality factor, and RTZ is a constant with the gas parameter R = 500, temperature T = 273K, and compression parameter Z = 0.9. ρ n is the density of natural gas under standard conditions, M com (t) is the mass flow rate of natural gas passing through the compressor, p out (t) and p in (t) are 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 passing through the compressor and the ratio of the outlet pressure to the inlet pressure (collectively referred to as the compression ratio) below.

[0157] The mass flow rate during the normal operation of the compressor needs to meet certain upper and lower limit constraints, as shown in Equation (1.19):

[0158]

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

[0160]

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

[0162]

[0163] Under normal circumstances, the electric compressor has multiple working modes. When the operating conditions reach the constraint boundary, the switching of the working mode is triggered. There are approximately four working modes of the electric compressor as follows:

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

[0165] Working mode 2: The pressure ratio at the inlet and outlet of the compressor is constant.

[0166] Working mode 3: The outlet pressure of the compressor is constant.

[0167] Working mode 4: The compressor is offline (at this time, the compression ratio is set to 1).

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

[0169] V. Modeling of Urban Power Grid Fault Conditions:

[0170] System Operating Principle: This section presents a model to characterize the calculation of the impact of N-k faults on load loss and pump operation (function fF2P). Generally, the UPN section is served partly by internal thermal power plants and gas power plants and partly by the external transmission system. The load loss is determined by four factors, including the economic dispatch of thermal power plants, the stable operation of gas power plants, network reconfiguration, and optimal load shedding. The modeling of UPN consists of a meshed HVT network, substations, and an HVD network. Based on the input parameters of line fault conditions and the operation of gas power plants, the 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. The constraint (1.23) enforces the output limits of the generating units. The load shedding limit is given by (1.24 - 1.25). The DC power flow equation is used to model the power flow under N-k fault scenarios, as shown in (1.26)-(1.29). Equation (1.26) specifies the voltage angle of the reference bus. The constraint (1.27) represents the bus power balance. Note: Only a small number of nodes are equipped with generating units; if there is no generator, then it is set to 0. (1.28) represents the branch power flow, which is relaxed if the branch is open. Equation (1.29) limits the upper limit of the branch power flow. If branch (i,j) fails, then P ij,t = 0. (1.30) limits the state of the fault branch. Equation (1.31) indicates that the HVD network maintains a radial structure by opening switches in loop k. The optimal load shedding is converted to the number of affected customers, given by (1.32).

[0176]

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

[0178]

[0179] 6. Evaluation indicators:

[0180] During disasters, faults in gas and power grids are often transmitted across domains via coupled components (such as gas turbines and voltage regulators). During fault recovery, the restoration of the power and gas grids is typically gradual, involving not only the restoration of their own systems but also the restoration of cross-domain energy systems. The impact of power and gas outages on users is complex and diverse. To evaluate the bidirectional cross-domain transmission characteristics of electrical coupling networks, this paper uses the number of affected users as a quantitative indicator and constructs corresponding function curves to analyze the impact of the electrical coupling network.

[0181]

[0182] Failures in electrical coupling networks can directly impact residents' lives, potentially triggering public panic and amplifying public opinion, leading to a series of public events. Existing assessment indicators fail to consider user categorization and are therefore unable to comprehensively assess the consequences of power outages in urban electrical coupling networks. Therefore, this paper proposes a vulnerability indicator system based on importance, as shown in Table 1, based on the nature of urban land use. The weight coefficients in this system are set based on the number of affected residential users, with a power outage per household being considered one unit. For other public users, weight coefficients are defined based on parameters such as total revenue, passenger volume, and the area's population, and converted to an equivalent number of affected residential users.

[0183] Table 1 Vulnerability indicators based on importance

[0184]

[0185]

[0186] The present invention encompasses any alternatives, modifications, equivalents, and solutions that fall within the spirit and scope of the present invention. To provide a thorough understanding of the present invention, specific details are described in detail below in connection with the preferred embodiments of the present invention, but those skilled in the art will be able to fully understand the present invention without these detailed descriptions. Furthermore, to avoid unnecessary confusion regarding the essence of the present invention, well-known methods, processes, procedures, components, and circuits have not been described in detail.

[0187] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A method for analyzing the consequences of power grid outages considering the conduction of supply chain - gas - electricity faults, characterized in that, It includes the following steps: S1, Modeling of the 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 conduction model; S2, Analysis of vulnerable links in the supply chain: Construct models of the power and natural gas supply chains, use network visualization and graph algorithms to identify key nodes and paths, and evaluate potential high-risk links in the system; S3, Modeling of gas pipeline network faults: Based on pipeline hydraulic calculations and operating constraints, establish a pressure and flow calculation model for the natural gas pipeline network to simulate the fault state of the gas network; S4, Modeling of gas-electricity coupling components: Establish mathematical models of gas turbines and compressors to describe the relationship between their output, gas volume, and electricity, and reflect their operating modes and constraints; S5, Modeling of urban power grid faults: Based on N-k fault analysis, construct an optimization model including power generation scheduling, load distribution, and network power flow to evaluate the operating state of the power grid under faults; S6, Construction of power outage consequence assessment indicators: Using the equivalent number of power outage users as an indicator, set weights in combination with user types to quantify the social impact and restoration priorities under different fault scenarios.

2. The power grid blackout consequence analysis method considering supply chain - gas - electricity fault conduction according to claim 1, wherein The modeling of the electrical network coupling relationship in S1 includes: S11, Identifying the network attributes of UPN and GDN: The electrical networks UPN and GDN are energy flow networks with topological structures and physical characteristics. Among them, UPN consists of multiple voltage levels, including high-voltage power transmission, high-voltage power distribution, and medium-voltage power distribution networks, and GDN includes long-distance gas pipelines, gas power plants, pressure regulating gate stations, and urban gas distribution networks; S12, Establishing a typical gas-electricity coupling relationship structure: At the high-voltage network level, natural gas is transported through pipelines to gas power plants. After the gas power plants generate electricity, the electric energy is transmitted to the distribution network and supplies power to the pressure regulating stations, forming a coupling path. At the same time, the operation of the voltage regulator depends on the power support of UPN, and faults are conducted from the power grid to the gas network or from the gas network to the power grid, and the coupling relationship is two-way; S13, Identifying key coupling components: The key coupling components include voltage regulators and gas power plants. The voltage regulator connects urban gas distribution networks with different gas pressure levels and depends on electric drive. The gas power plant is the core node of the coupling. Its 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 smallest load nodes in UPN and GDN to achieve modeling simplification; S15, Defining the fault conduction path and stage: Divide the gas-electricity fault conduction process into three stages, specifically including: Stage 1: The power and natural gas supply chains are interrupted, resulting in insufficient gas sources, and then the gas network is shut down; Stage 2: The state of the gas network changes, resulting in a decrease in the output or shutdown of gas turbines; Stage 3: Insufficient output of gas turbines, faults in power stations or transmission lines cause large-scale power outages.

3. The power grid blackout consequence analysis method considering supply chain - gas - electricity fault conduction according to claim 2, wherein, The analysis of vulnerable links in the supply chain in S2 includes: S21, Modeling of supply chain links: Construct a power supply chain structure including fuel production links, fuel transportation links, transfer equipment and transfer machinery links, and power energy equipment links; S22, Vulnerability Analysis: Conduct a visual analysis of the supply chain network to identify key nodes and paths. Evaluate key nodes through the loss ratio index E, identify bottleneck paths through graph algorithms, and reveal high-risk areas in the supply chain that lead to system interruptions, specifically including: S221, Network Visualization Technology: Through the introduction of Gephi and Neo4j tools, conduct visual modeling and analysis of the power and natural gas supply chain network. Among them, the Gephi tool displays the structure and its changes of the power supply chain through force-directed layout, and the Neo4j tool is used to model and query complex relationships between nodes; S222, Identification of Key Nodes and Paths: Through the analysis of the visual network, use the loss ratio index E to identify key nodes, and identify key paths through graph algorithms. At the same time, combine bottleneck analysis with the maximum flow minimum cut theorem to locate high-risk paths in resource transmission.

4. A power grid blackout consequence analysis method considering supply chain - gas - electricity fault conduction according to claim 3, characterized in that The fuel production link includes coal, petroleum products, and nuclear fuel. The fuel transportation link includes ships and land transportation. The transfer equipment and transfer machinery link includes vehicles and structural metal products. The power energy equipment link includes transmission control equipment, motors, generators, and transformers.

5. A method for analyzing the consequences of power grid outages considering the conduction of supply chain - gas - electricity faults according to claim 4, characterized in that The identification of key nodes and paths in S222 includes: S2221, Definition and Identification Method of Key Nodes: Key nodes are defined as nodes that undertake connection functions or participate in resource transmission in the network. Key vulnerable link nodes are defined as nodes in the supply chain whose supply volume accounts for a proportion greater than the set threshold in the total supply volume of this item, and this item is irreplaceable during the production process. Key vulnerable link nodes are identified through the loss ratio E, expressed as: Among them, v t is the target supply volume for analysis, and v i is the supply volume of a single supply relationship for this item; S2222, Identification and Analysis of Key Paths in the Supply Chain: Calculate the shortest paths from the source node to other nodes in the network through graph algorithms to identify paths that affect the efficiency of resource or information flow. The bottleneck segments in the paths are identified by monitoring network traffic load and optimized by increasing redundancy or load balancing. Use the maximum flow minimum cut theorem to analyze the maximum flow from the source node to the sink node and find the key paths that limit the network capacity; The graph algorithm adopts the Dijkstra algorithm, expressed as: where d[v] is the path length from the source node to v.

6. A method for analyzing the consequences of power grid outages considering the conduction of supply chain - gas - electricity faults according to claim 5, characterized in that The gas pipeline network fault modeling in S3 includes: S31, Hydraulic Calculation of Natural Gas Pipeline Network: On the premise that the pressure of urban gas pipelines does not exceed 1.6 MPa and Z0 = 1, calculate the flow rates of high-pressure, medium-pressure, and low-pressure gas pipelines, specifically including: The flow rates of the high-pressure and medium-pressure gas pipelines are expressed as: 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 in the standard state; The flow rate of the low-pressure gas pipeline is expressed as: S32, Constraint Model of Natural Gas Pipeline Network: The operation of the high-pressure natural gas pipeline network satisfies multiple constraint conditions, including node flow balance, pipeline flow upper and lower limits, gas load reduction amount, and component operation restrictions, expressed as: f mr = V lcak + f rn ; π i,min ≤π i ≤π i,max ； f ij,min ≤ f ij ≤ f ij,max ; W s,min ≤W s ≤W s,max ; 0 ≤ ΔW g ≤ W g ; Among them, Ψ GS , Ψ GT , Ψ GC , Ψ j are the gas source, gas turbine unit, compressor, and natural gas pipeline set respectively, and W s , f c are the gas output of the gas source and the gas flow rate of the branch where the compressor is located respectively.

7. A power grid blackout consequence analysis method considering supply chain - gas - electricity fault conduction according to claim 6, characterized in that, The gas-electric 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 volume 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, and using the temperature, pressure, and efficiency parameters in the thermodynamic process to construct a multi-state output model of the gas generator, which is then simplified into a temperature function. Finally, the functional relationship between the output and the natural gas flow rate is obtained to characterize the power supply capacity of the gas turbine under gas-electric coupling, expressed as: -W×C pa (T2 - T1)+W×C pc (T3 - T4) = P; where W is the total flow rate of natural gas W f and air W a , C pa , C pc are the heat capacities of air and natural gas respectively, T i is the temperature at different points in the gas generator, and T1, T2, T3, and T4 are the temperatures at the inlet and outlet of the air compressor, the inlet of the combustion chamber, and the outlet respectively, H u is the lower calorific value of natural gas, P is the power generation of the gas generator, p i is the pressure at different points in the gas generator, η c , η t are the efficiencies of the air compressor and the turbine respectively, and σ is a constant; T3 - T4 = T3 × η t × K2; S42, Compressor operation model: The compressor is used to compensate for the pressure loss caused by friction during pipeline gas transportation. Its power consumption depends on the gas flow rate and the pressure ratio between the inlet and outlet. The operation process satisfies the mass flow rate constraint, compression ratio constraint, and outlet pressure constraint. In addition, multiple working modes are set according to the operation state of the compressor. When the power supply is insufficient, the compressor switches to the offline state and the compression ratio is set to 1; The electric power consumption of the compressor is expressed as: where f is a proportionality factor, RTZ is a constant, the gas parameter R = 500, the temperature T = 273K, the compression parameter Z = 0.9, ρ n is the density of natural gas under standard conditions, M com (t) is the mass flow rate of natural gas passing through the compressor, p out (t) and p in (t) are the outlet pressure and inlet pressure of the compressor respectively, and k and K1 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 pressure ratio between the inlet and outlet of the compressor is constant; Working mode 3: The outlet pressure of the compressor is constant; Working mode 4: The compressor is offline.

8. A method for analyzing the consequences of power grid outages considering the conduction of supply chain - gas - electricity faults according to claim 7, characterized in that, The urban power grid fault modeling in S5 includes: S51, Establishing the urban power grid structure model: The urban power grid model consists of a high-voltage transmission network, substations, and a high-voltage distribution network. The power supply sources include local thermal power plants, gas power plants, and external power transmission systems. The factors affecting load loss include the economic dispatching of thermal power plants, the operation state of gas power plants, the power grid structure reconstruction ability, and the optimal load shedding strategy; S52, Urban power grid dispatching and fault constraint modeling: In the urban power grid modeling, an economic dispatching model is adopted and combined with the operation constraints of the N-k fault scenario to uniformly construct a power generation dispatching and fault state analysis model. The power generation dispatching and fault state analysis model aims to minimize the power generation cost and load loss, and comprehensively considers the dispatching decisions of thermal power units, standby power sources, and user load shedding, expressed as: θ ref = 0; S53, Customer load conversion and substation availability identification: The optimal load shedding is converted into the number of affected customers. If the 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:

9. The method for analyzing the consequences of power grid blackout considering the conduction of supply chain - gas - electricity faults according to claim 8, wherein The construction of power outage consequence assessment indicators in S6 includes: S61, Constructing a cross-domain impact assessment model for power-gas faults: Bidirectional fault conduction occurs between the gas network and the power grid through gas turbines and voltage regulators. The restoration process involves the coordinated repair of the power and gas systems. The number of affected users is used as an indicator to analyze the impact of the electrical coupling 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 urban land use function. Taking residential users as the benchmark, the unit weight is set to 1, and commercial users, transportation users, and hospital users are converted into equivalent residential user numbers according to profits, passenger flow, or the number of service people to form an assessment index system.

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