Method for constructing post-earthquake water-electricity associated network cascade failure model based on functional coupling

Abstract

The invention provides a construction method of a post-earthquake water-electricity associated network cascade failure model based on functional coupling, and belongs to the technical field of research on disaster prevention and reduction toughness of infrastructures. The method comprises the following specific steps: S1, collecting basic information of a water network and a power grid; s2, defining a function coupling relationship, and establishing a water-electricity associated network topological structure model based on a graph theory; s4, based on the vulnerability curve, determining components triggering cascade failure in the water network and the power grid; s5, a failure joint probability method is introduced, and the function failure condition of the component with the function coupling relation is determined; s6, carrying out water network cascade failure analysis; s7, carrying out power grid cascade failure analysis; and S8, carrying out function loss calculation of the water network and the power grid. According to the method, the function coupling relation between the water network and the power grid component is considered, the failure propagation mechanism is simulated based on the physical characteristics, and the internal mechanism and the external behavior of the cascade failure of the water-electricity associated network can be reflected more effectively and accurately.

Description

Technical Field

[0001] The present invention belongs to the technical field of research on resilience of infrastructure disaster prevention and mitigation, and relates to a method for constructing a post-earthquake water-electricity correlation network cascade failure model based on functional coupling. Background Art

[0002] Water supply network (abbreviated as: water network) and power supply network (abbreviated as: power grid) are typical representatives of urban lifeline networks, playing a pivotal role in daily production and life and post-disaster recovery and reconstruction. Earthquake damage data over the years show that damage to water and power grids will inevitably lead to extremely serious consequences. For example, on September 6, 2018, a magnitude 6.9 earthquake occurred in Hokkaido, Japan, resulting in damage to power facilities and power outages lasting two days; many water treatment plants also stopped working, affecting 2.95 million households. Traditional earthquake damage research on water and power grids usually only conducts reliability or resilience analysis on a single system, etc., ignoring the mutual influence between networks. However, water networks and power grids are highly correlated and complexly coupled. For example, water plants need electricity supply to maintain normal operation, and electric pumps that lift water to higher ground or floors also need electricity supply; cooling water systems also play an important role in the operation of power plants or nuclear power plants. When an earthquake occurs, the damage of a network component will cause the failure of some network functions, and will also affect its associated network components, causing the loss of associated network functions, and then multiple networks will fail one after another. Therefore, the correlation between the water network and the power grid cannot be ignored. In-depth research on the cascading failure process of the hydropower related network functions under earthquake damage is of great significance to improving the disaster prevention resilience of the urban lifeline network.

[0003] At present, there are many studies on the correlation modeling methods of hydropower networks at home and abroad, which can be summarized into the following categories: modeling based on system dynamics, modeling based on economic theory, modeling based on subject, and modeling based on network. These models characterize the dependency relationship of hydropower networks from different angles and deepen the understanding of the mechanism of dependency. Among them, the network modeling method emphasizes the topological structure and flow of the lifeline network, and uses network connections to intuitively represent various dependencies. It is widely used in the correlation modeling of hydropower networks. Most of the existing studies on cascading failure of hydropower networks considering interdependencies analyze network topological attribute indicators. For example, Zhang et al. proposed an interdependent hydropower network cascading failure model to analyze the vulnerability of the network. The study established the dependency relationship of the hydropower network through the dependency matrix and used the average shortest path length to measure the vulnerability of the network. (Zhang Y, Yang N, Lall U. Modeling and simulation of the vulnerability of interdependent power-water infrastructure networks to cascading failures [J]. Journal of Systems Science and Systems Engineering, 2016, 25: 102-118.) The study ignored the failure mechanism of network components under specific disasters and the physical operating characteristics of the system, which greatly overestimated the disaster resistance of the hydropower coupling network. Some scholars have emphasized the physical characteristics of water networks and power grids, but only studied the one-way cascading fault propagation of hydropower coupling networks. For example: Pournaras et al. conducted a cascading failure study on interconnected hydropower networks, and based on the dynamic network flow simulation of power grids and water networks, revealed the impact of power grid failures on water supply shortages in water networks. (Pournaras E, Taormina R, Thapa M, et al. Cascading failures in interconnected power-to-water networks[J]. ACM SIGMETRICS PerformanceEvaluation Review, 2020, 47(4): 16-20.) In addition, for earthquake disaster scenarios, the study of cascading failures of only a single water network or power grid is considered, which has certain reference value for the study of cascading failures of hydropower coupled networks. Summary of the invention

[0004] In order to overcome the shortcomings of the prior art, the present invention proposes a post-earthquake water-electricity associated network cascading failure model that considers the functional coupling relationship between network components. The model considers the functional coupling relationship between water network and power grid components, introduces the joint failure probability and functional coupling strength to determine the failure probability of the coupling components, introduces the node carrying function and the line capacity function to determine the failure judgment conditions, and simulates the failure propagation process based on the physical operation characteristics of the system, which can more effectively and accurately reflect the internal mechanism and external behavior of the cascading failure of the water-electricity associated network.

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

[0006] A method for constructing a post-earthquake water-electricity correlation network cascading failure model based on functional coupling, the construction method first collects basic information on the water network and the power grid. Secondly, the functional coupling relationship is defined, and a water-electricity correlation network topological structure model is established based on graph theory. Third, based on the vulnerability curve, the components that trigger cascading failures in the water network and the power grid are determined. Fourth, the joint probability of failure method is introduced to determine the functional failure of components with coupling relationships in the water network and the power grid. Fifth, the functional failure components in the water network are used as input to carry out water network cascading failure analysis, and the node load function is introduced as a judgment condition for water network cascading failure. Sixth, the functional failure components in the power grid are used as input to carry out power grid cascading failure analysis, and the line capacity function is introduced as a judgment condition for power grid cascading failure. Finally, when the cascading failure of the water network and the power grid is terminated, the functional loss of the water network and the power grid is evaluated. The specific steps include:

[0007] Step S1: Collect basic information of water network and power network. Details are as follows:

[0008] The basic information of the water network includes the number of reservoirs, total water head, the number of pools, elevation, initial water level, minimum water level, maximum water level, diameter, the number of pumps, head curve, the number of users, water demand, elevation, the number of pipelines, start and end nodes, diameter, length, roughness coefficient. The basic information of the power grid includes the number of nodes, injected active power, the number of branches, start and end nodes, and reactance.

[0009] Step S2: Define the functional coupling relationship and establish the water-electricity network topology model based on graph theory. The details are as follows:

[0010] Based on graph theory, reservoirs, pools, and users are regarded as nodes and recorded as The pipeline and pump station are set as the connection between nodes, denoted as This is abstracted into a water network topology, and W(V W ,E W ) represents; where V W represents the node set of the water network, Indicates the first water network node, Indicates the second water network node, represents the mth water network node, E W represents the edge set of the water network, Indicates the first water network edge. Indicates the second water network edge. represents the nth water network edge. Based on graph theory, power plants, substations, and users are regarded as nodes and recorded as The line is regarded as the connection between nodes, denoted by This is abstracted into a power grid topology structure, using H(V H ,E H ) represents; where V H represents the set of nodes in the power grid, represents the first grid node, represents the second grid node, represents the oth grid node, E H represents the edge set of the power grid, Indicates the first grid connection edge, Indicates the second grid connection edge, Represents the qth grid connection. From the perspective of functional supply and demand, the present invention defines the functional coupling relationship between the water network and the power grid, and then adopts a multi-layer infrastructure network topology modeling method (Zhang P, Peeta S. A generalized modeling framework to analyze interdependencies among infrastructure systems [J]. Transportation Research Part B: Methodological, 2011, 45 (3): 553-579.) to establish a water-electricity associated network topology model. On this basis, a hydraulic model is used to calculate the initial water pressure of the water network node, and a DC power flow model is used to calculate the initial power of the power grid line.

[0011] Step S21: Table 1 shows the functional coupling relationship between the water network and the power grid. Among them, the functional coupling component of the power grid is the power plant, that is, the normal operation of the power plant requires the water plant or water pool in the water network to provide cooling water, and the functional transfer direction is water plant / water pool → power plant, that is, when the water plant or water pool in the water network is damaged, the power plant function will be weakened or fail. The functional coupling components in the water network are water plants and pumping stations, that is, the normal operation of water plants and pumping stations requires the substation in the power grid to provide power supply, and the functional transfer direction is substation → water plant / pumping station, that is, when the substation in the power grid is damaged, the water plant or pumping station in the water network will not be able to operate normally.

[0012] Table 1 Functional coupling relationship between water network and power grid

[0013]

[0014] Step S3: Based on the vulnerability curve, determine the components in the water network and the power grid that trigger cascading failures, as follows:

[0015] With reference to the earthquake intensity table of the China Earthquake Parameter Zoning Map (GB18306-2015), the vulnerability curve proposed by the Federal Emergency Management Agency (FEMA) of the United States is used to determine the probability of different damage states of various components of the water network and the power grid under different intensity earthquake impacts, as shown in Table 2. To simplify the calculation, the present invention first divides the damage state of each component in the water network and the power grid into two states, namely, a normal functional state and a functional failure state. Then, the component reaching a moderate damage state after the earthquake is defined as a functional failure state, and the probabilities of the moderate damage state and above are summed to obtain the probability of the component being in a functional failure state after the earthquake, as shown in Table 2. Finally, the random method is used to estimate the component functional failure, which is used as the component that triggers cascading failure in the water network and the power grid.

[0016] Table 2 Component damage status and probability

[0017]

[0018] Among them, the value range of p1, p2, p3, and p4 is 0 to 1, and p1+p2+p3+p4=1; P N ,P F The value range of P is 0 to 1, and N +P F =1.

[0019] Step S4: Introduce the joint probability of failure method to determine the functional failure of components with functional coupling relationships, as follows:

[0020] The joint failure probability is introduced to determine the failure probability of components with functional coupling relationship, and the functional coupling strength is defined to analyze the possibility of functional failure transmission of components with functional coupling relationship between water network and power grid. Then, the random method is used to estimate the functional failure of components with functional coupling relationship.

[0021] Step S41: The failure probability calculation method of components with functional coupling relationship is as follows: Assuming that the coupling component (denoted as u) of the water network (denoted as W) is taken as an example, its functional failure includes two situations: one is that the earthquake directly causes damage to the coupling component u, which is denoted as event The probability of its occurrence is recorded as The other is that the grid component (denoted as H) on which the water network coupling component u depends fails, and its failure is transmitted to the component u, which is denoted as event The probability of its occurrence is recorded as For the failure of the water network coupling component u, it is recorded as event W u , introduce the failure joint probability model to express the probability of occurrence of the event P(W u ), which can be considered as an event and events The calculation formula is as follows:

[0022]

[0023] Furthermore, formula (1) can be equivalent to:

[0024]

[0025] Under the action of earthquake, the destruction events of water network component u and power grid component v are independent of each other, that is, event and events are mutually independent events, so formula (2) can be converted to:

[0026]

[0027] Where, the functional failure probability of component u is Determined according to the calculation method of step S3, that is, based on the fragility curve, the probability of component u having different damage states under earthquake action is obtained, and then the probabilities of medium damage state and above are summed up to obtain the functional failure probability The probability of cascading failure for component u is The calculation method is:

[0028]

[0029] Formula (4) represents the functional coupling between water grid component u and power grid component v. The cascading failure event of water grid component u is Caused by the failure of grid component v, the probability of cascading failure of component u is is the failure probability P(H v ) and the conditional probability of failure of component u under the condition of component v failure P(H v ) is the failure probability of component v in the power grid H. If this component has a functional coupling relationship with other components, then P(H v ) is solved according to the probability calculation method of formula (1); otherwise, P(H v ) is the functional failure probability of component v under earthquake action, and is solved in the same way as the calculation method in step S3.

[0030] The conditional probability Defined as the functional coupling strength Φ between component u and component v uv, that is, the possibility of functional failure transmission, and the direction of functional failure transmission is from component u to component v, the formula is as follows:

[0031]

[0032] In the formula, when Φ uv =0, it means that there is no functional coupling relationship between component u and component v, that is, when the function of component u fails, it will not be transmitted to another component v; when 0<Φ uv <1, it indicates that there is a weak coupling relationship between the two components. Specifically, when Φ uv →0, indicating that the looser the functional coupling relationship between the two components, the less likely the failure effect of the water network component u will be transmitted to the power grid component v; when Φ uv →1, indicating that the stronger the functional coupling relationship between the two components, the easier it is for the failure effect of the water network component u to be transmitted to the power grid component v, thus causing the component v to fail. uv =1, indicating that the two components are strongly coupled, that is, the failure of component u will inevitably lead to the failure of coupled component v.

[0033] Step S5: Conduct water network cascading failure analysis, as follows:

[0034] For the analysis of cascading failure of water network, the hydraulic model of pipeline failure points after earthquake in water network is adopted (Han Chao, Ma Donghui, Hou Benwei, et al. Hydraulic analysis of water supply network after earthquake based on pressure-driven node water distribution model. Science China: Technological Sciences, 2019, 49: 351-362), the initial functional failure components are removed, the water network topology is updated, and hydraulic adjustment is performed. During the hydraulic adjustment process, the node water distribution is gradually adjusted by an iterative method based on the pressure-driven node water distribution model (see formula (6)). The node load function (see formula (9)) is used to determine whether there is a new failed node: if there is a new failed node, the failed node is removed, the water network topology is updated again, and the hydraulic adjustment is calculated until no new failed nodes appear in the network, that is, the cascading failure of the water network ends, and then the functional loss of the water network is evaluated. The calculation method is shown in step S7; if there is no new failed node, step S7 is directly performed to calculate the functional loss of the water network.

[0035] The pressure driven node water distribution model is shown in formula (6).

[0036]

[0037] In the formula, and are the actual water supply and demand of node k respectively; P k is the node water pressure, is the minimum node water pressure required when the water distribution of node k is greater than 0, is the service water pressure at node k to meet the demand.

[0038] The present invention assumes that pipeline damage under earthquake action is a random independent event and follows Poisson distribution along the length of the pipeline. Therefore, the probability of pipeline damage due to earthquake is:

[0039]

[0040] Where P l is the probability of pipeline l being damaged under earthquake damage; l is the pipe length; RR l is the average pipeline damage rate, which is calculated by fitting the existing earthquake motion data and the water supply pipeline damage data, see formula (8).

[0041]

[0042] Where PGV is the peak ground velocity and D is the pipe diameter.

[0043] Furthermore, after the earthquake, water tanks, water towers, and pumping stations in the water network were initially damaged, and pipelines were disconnected or leaking. The water pressure of some nodes did not meet the requirements and could not meet the water supply needs of the nodes. Therefore, the nodes lost their service functions, which led to cascading failure of the water network functions. Therefore, the present invention defines a node load function to determine whether the node has failed, that is, the minimum load capacity of the node is proportional to the initial load of the node, and the formula is as follows:

[0044]

[0045] In the formula, α k Indicates the tolerance parameter of node k, ranging from 0 to 1.

[0046] Step S6: Conducting power grid cascading failure analysis, as follows:

[0047] For the grid cascading failure analysis, the initial failed component is removed and the grid topology is updated. The connectivity of the remaining grid topology is determined: if the connected cluster (composed of the connected nodes and edges in the remaining grid topology) contains a power plant node, the DC power flow model is used to calculate the line power in the connected cluster; if the connected cluster does not contain a power plant node, the grid cascading failure ends, and step S7 is directly performed to calculate the grid function loss. Further, the line capacity function (see formula (10)) is used in the connected cluster to determine whether there is a new failed line: if the line power exceeds the line capacity, there is a new failed line, the failed line is removed, the grid topology is updated again, and the line power is calculated until no new failed lines appear in the network, that is, the grid cascading failure ends, and finally the grid function loss is evaluated, and the calculation method is shown in step S7; if the line power does not exceed the line capacity, there is no new failed line, and step S7 is directly performed to calculate the grid function loss.

[0048] In the power grid, the propagation process of cascading failure is complex and has many influencing factors. The successive failures of the lines are the main driving factors for the propagation of cascading failures. Each line is equipped with a relay. When the line current exceeds the capacity limit and lasts for a long time, the overcurrent relay will protect the line and trip it. Therefore, the present invention assumes that the line capacity C i With the initial power f i (0), the formula is as follows:

[0049] C i =(1+β i )f i (0)(10)

[0050] In the formula, β i Indicates the tolerance parameter of line i, and its value range is 0 to 1.

[0051] Step S7: Calculate the function loss of the water network and the power grid, as follows:

[0052] The functional loss of the hydropower coupling network is defined as the demand loss rate and the edge loss rate. Refers to the ratio between the amount of unmet demand of the node and the demand; edge loss rate is the ratio of the number of links in the network that are in a state of functional failure after the cascading failure to the number of initial links, see formulas (11)-(14). Due to the randomness of earthquake damage, the Monte Carlo method is used to perform multiple simulations, and the average value of the demand loss rate and the average value of the link loss rate of the hydropower network are used as the final functional loss calculation results.

[0053]

[0054] In the formula, Q i are the actual supply and demand of the ith node in any network in the kth simulation; L k is the number of edges in any network that are in a normal functional state in the kth simulation; DS and LS are the demand satisfaction rate and connectivity rate of any network respectively. s and z are the number of user nodes and edges of any network respectively; N is the number of Monte Carlo simulations.

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] (1) Different from the existing modeling methods of the association relationship between water and electricity networks, the present invention defines the functional coupling relationship between water network and power grid components from the perspective of functional supply and demand relationship, and establishes a water-electricity association network topology structure model based on the multi-layer infrastructure network topology modeling method.

[0057] (2) Most studies have not considered the physical damage and functional failure of post-earthquake coupling components. The present invention introduces the joint probability of failure to determine the failure probability of components with functional coupling relationships and defines the functional coupling strength to analyze the possibility of functional failure transmission of components with functional coupling relationships between the water network and the power grid.

[0058] (3) The present invention introduces node load function and line capacity function as the judgment conditions for cascading failure of water network and power grid, and simulates the cascading failure process of water-electricity correlation network under the action of earthquake based on hydraulic model and DC flow model.

[0059] (4) The present invention defines demand loss rate and connection loss rate as indicators of post-earthquake water network and power grid function loss, which can be used to quantify the severity of the damage to network functions caused by earthquakes and coupling failures.

[0060] In summary, the present invention can effectively and accurately reflect the inherent mechanism and operation mechanism of cascading failure of water-electricity related networks, which is of great significance for improving the disaster resilience of urban lifeline networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 It is a flow chart of the method for constructing the post-earthquake water-electricity correlation network cascade failure model based on functional coupling of the present invention.

[0062] Figure 2 It is a water-electricity associated network topology model of an embodiment of the present invention.

[0063] Figure 3 is a diagram showing the cascading failure propagation results of a water-electricity correlation network under an earthquake scenario according to an embodiment of the present invention; Figure 3 (a) shows the cascading failure propagation results of the water grid and the power grid when PGA = 0.06g; Figure 3 (b) shows the cascade failure propagation results of the water network and the power grid when PGA = 0.15g; Figure 3 (c) shows the cascading failure propagation results of the water network and the power grid when PGA = 0.30g; Figure 3 (d) in the figure is the cascade failure propagation result of the water network and the power grid when PGA=0.60g.

[0064] Figure 4 is a simulation diagram of the effect of functional coupling strength on network function loss in an embodiment of the present invention; Figure 4 (a) shows the influence trend of functional coupling strength on water network edge loss rate when PGA = 0.06, 0.15, 0.3, and 0.6g; Figure 4 (b) shows the influence trend of functional coupling intensity on water network demand loss rate when PGA = 0.06, 0.15, 0.3, and 0.6g; Figure 4(c) shows the influence trend of functional coupling intensity on power grid connection loss rate when PGA = 0.06, 0.15, 0.3, and 0.6g; Figure 4 (d) in the figure shows the influence trend of functional coupling intensity on grid demand loss rate when PGA=0.06, 0.15, 0.3, and 0.6g.

[0065] Figure 5 is a simulation diagram of the impact of the tolerance coefficient on network function loss in an embodiment of the present invention; Figure 5 (a) shows the influence trend of the tolerance coefficient on the water network edge loss rate when PGA = 0.06, 0.15, 0.3, and 0.6g; Figure 5 (b) shows the influence trend of tolerance coefficient on water network demand loss rate when PGA = 0.06, 0.15, 0.3, and 0.6g; Figure 5 (c) shows the influence trend of the tolerance coefficient on the power grid connection loss rate when PGA = 0.06, 0.15, 0.3, and 0.6g; Figure 5 (d) in FIG. 5 is the influence trend of the tolerance coefficient on the grid demand loss rate when PGA = 0.06, 0.15, 0.3, and 0.6g. Specific implementation methods

[0067] The technical solution of the present invention will be further described below in conjunction with specific embodiments and drawings.

[0068] The construction method of the post-earthquake water-power network cascade failure model based on functional coupling is as follows:

[0069] Step S1: Collect basic information of water network and power network. Details are as follows:

[0070] The basic information of the water network includes the number of reservoirs, total water head, the number of pools, elevation, initial water level, minimum water level, maximum water level, diameter, the number of pumps, head curve, the number of users, water demand, elevation, the number of pipes, start and end nodes, diameter, length, and roughness coefficient. The basic information of the power grid includes the number of nodes, injected active power, the number of branches, start and end nodes, and reactance. In order to more intuitively display the actual effect of the present invention, this model is applied to a certain city water network and IEEE 118 node network. A certain city water network contains 4 reservoir nodes, with total water heads of 76.95, 74.31, 83.58, and 81.98 m, 49 user nodes, and 78 pipe sections. The Hezen-Williams roughness coefficient of pipe section 1 is 80, the roughness coefficients of pipe sections 44, 45, 46, and 49 are 90, and the roughness coefficients of the remaining pipe sections are 120. It is assumed that the pipe section with a diameter greater than 600 mm is made of steel pipe (riveted joint); the pipe section with a diameter less than 600 mm is made of ductile iron (rubber sealed joint). The IEEE118 node network contains 118 buses, 19 generators, 35 synchronous capacitors, 64 users, and 186 lines (including 9 transformers). The basic information can refer to the case information in the MATPOWER software. In addition, the present invention assumes that the 9 transformers are substations, and the information is shown in Table 3.

[0071] Table 3 Substation information

[0072]

[0073] Step S2: Define the functional coupling relationship and establish the water-electricity network topology model based on graph theory. The details are as follows:

[0074] Based on graph theory, the reservoirs, water towers, and users of the water network are regarded as nodes, and the pipelines and pumping stations are set as the connections between the nodes, which is abstracted as the water network topology. The generators, substations, and users of the power grid are regarded as nodes, and the lines are regarded as the connections between the nodes, which is abstracted as the power grid topology. From the perspective of functional supply and demand, the functional coupling relationship between the water network and the power grid is defined, and a multi-layer infrastructure network topology modeling method is used to establish a water-electricity associated network topology model. On this basis, the hydraulic model is used to calculate the initial water pressure of the water network nodes, and the DC power flow model is used to calculate the initial power of the power grid lines.

[0075] Further, the step S2 is specifically as follows:

[0076] Step S21: From the perspective of functional supply and demand, determine the functional coupling relationship between the water network and the power grid, and establish a water-power association network topology model, such as Figure 2As shown. Among them, the water-electricity association network includes 12 pairs of functional coupling elements. In the water network, there is a functional coupling relationship between the reservoir, the pump station and the substation node in the power grid, that is, the substation provides power supply for the reservoir and the pump station. In the embodiment, the functional coupling node pairs formed by the substation node and the reservoir node are (S1, R50), (S2, R51), (S7, R52), (S5, R53). The functional coupling node pairs formed by the substation node and the pump station are (S4, P1), (S3, P2), (S8, P3), (S6, P4). In the power grid, there is a functional coupling relationship between the power plant node and the user node in the water network, that is, the water network needs to provide cooling water for the power plant. In the embodiment, the functional coupling node pairs formed by the user node and the power plant node are (J39, G10), (J40, G49), (J42, G66), (J23, G80). On this basis, the hydraulic model is used to calculate the initial water pressure of the water network node, and the DC power flow model is used to calculate the initial power of the power grid line.

[0077] Step S3: Based on the vulnerability curve, determine the components in the water network and the power grid that trigger cascading failures, as follows:

[0078] This embodiment sets four earthquake scenarios, and the peak accelerations (PGA) of the earthquake are 0.06, 0.15, 0.3, and 0.6g, respectively. The vulnerability curve proposed by FEMA is used to calculate the probability of different damage states of various components in the water network and the power grid under different PGAs. Further, the damage state of each component in the water network and the power grid is divided into two states, namely, a normal functional state and a functional failure state. Then, it is defined that the component reaching a moderate damage state after the earthquake is a functional failure state. The probability of the component being in a functional failure state after the earthquake is summed up, and the probability of the component being in a functional failure state after the earthquake can be obtained. The component functional failure is estimated using a random method: when the probability of component functional failure is greater than the random number, the component is judged to be functionally failed, and this is used as the initial trigger component for the cascading failure of the water network and the power grid; when the probability of component functional failure is less than or equal to the random number, the component is judged to be functionally normal.

[0079] Step S4: Introduce the joint probability of failure method to determine the functional failure of components with functional coupling relationships, as follows:

[0080] Define the functional coupling strength of the functional coupling components, calculate the failure probability of the components with functional coupling relationship according to formulas (1)-(5), and then use the random method to estimate the functional failure of the components with functional coupling relationship: when the functional failure probability of the components with functional coupling relationship is greater than the random number, the component is judged to be functionally failed; when the functional failure probability of the components with functional coupling relationship is less than or equal to the random number, the component is judged to be functionally normal.

[0081] Further, the step S4 is specifically as follows:

[0082] Step S41: Define that there is a weak coupling relationship between the substation node and the reservoir node, and set the functional coupling strength Φ sr =0.5, the function transfer direction is substation node → reservoir node, that is, when the substation node function fails, there is a 50% probability that it will be transferred to the reservoir node, causing the reservoir node function to fail. Define that there is a strong coupling relationship between the substation node and the pump station, and set the functional coupling strength Φ sp =1, the function transfer direction is substation node → pump station, that is, when the substation node function fails, the pump station function will inevitably fail. Define that there is a weak coupling relationship between the power plant node and the user node in the water network, set Φ jg =0.75, the function transfer direction is user node→power plant node, that is, when the user node function in the water network fails, there is a 75% probability that it will be transferred to the power plant node. Then, the failure probability of the components with functional coupling relationship is calculated according to formulas (1)-(5), and then the random method is used to estimate the functional failure of the components with functional coupling relationship.

[0083] Step S5: Conduct water network cascading failure analysis, as follows:

[0084] Under the scenarios of PGA of 0.06, 0.15, 0.3, and 0.6g, the Monte Carlo method was used to simulate and the results of cascading failure of the water network were obtained as follows: Figure 3 The cascading failure propagation stages of the water network are 6, 6, 6, and 3, respectively. The first three scenarios have more cascading failure propagation stages. When PGA = 0.6g, the initial damage to network components caused by the earthquake is larger and wider, which may lead to large-scale failure or collapse of the network, and the range of cascading failure propagation drops sharply.

[0085] Step S6: When PGA is 0.06, 0.15, 0.3, and 0.6g respectively, the Monte Carlo method is used to simulate and the results of the power grid cascading failure are as follows: Figure 3 As shown in the figure, the cascading failure propagation stages of the power grid are 12, 13, 7, and 3. As the PGA increases, the cascading failure propagation stages of the power grid gradually decrease, indicating that the initial damage of the earthquake to the power grid increases, and the impact of the cascading failure propagation gradually decreases.

[0086] Step S7: Based on step S5 and step S6, the Monte Carlo method is used to calculate the functional loss results of the water network and the power grid with or without functional coupling relationship based on formulas (11)-(14), as shown in Table 4. From a vertical perspective, with the increase of PGA, the functional loss of the water network and the power grid with or without functional coupling relationship gradually increases. From a horizontal perspective, the functional loss of the water network and the power grid with functional coupling relationship is higher than that without functional coupling relationship, and the degree of functional loss of the power grid is more obvious than that of the water network.

[0087] Table 4 Results of water network and power grid function loss with and without functional coupling

[0088]

[0089] Note: FC means that there is a functional coupling relationship between the power grid and the water grid, and NFC means that there is no functional coupling relationship between the power grid and the water grid.

[0090] In addition, to supplement the above embodiment, based on the established water-electricity associated network cascading failure model, the control variable method is used to analyze the impact of functional coupling strength and tolerance on the functional loss of the water network and the power grid.

[0091] Figure 4 This is a simulation diagram of the effect of functional coupling strength on network function loss. In the scenarios where PGA is 0.06, 0.15, 0.3, and 0.6g, the effect of functional coupling strength on network function loss is analyzed. The tolerance value of each user node in the water network is set to 0.5, and the tolerance value of each transmission line in the power grid is set to 0.2. Monte Carlo simulation is performed 1000 times to obtain the changing trend of network function loss with functional coupling strength under different earthquake scenarios. Figure 4 (a) and (b) show that with the increase of PGA, the water network function loss gradually increases, while the functional coupling intensity has almost no effect on the edge loss rate and has a slight effect on the demand loss rate. Figure 4 (c) and (d) show that when PGA = 0.06, as the functional coupling strength increases, the power grid function loss gradually increases; when PGA>0.06, the functional loss remains almost unchanged. The reason is that the initial damage to the power grid caused by the earthquake is serious, the propagation range of cascading failure is sharply reduced, and the influence of functional coupling strength on cascading failure is reduced.

[0092] Figure 5The following is a simulation diagram of the impact of tolerance on network function loss. In the scenarios where PGA is 0.06, 0.15, 0.3, and 0.6g, the impact of tolerance on network function loss is analyzed. The functional coupling strength between reservoir nodes and substation nodes is set to 0.5, the functional coupling strength between pump stations and substation nodes is set to 1, and the functional coupling strength between power plant nodes and user nodes in the water network is set to 0.5. Monte Carlo simulation is performed 1000 times to obtain the changing trend of network function loss with tolerance under different earthquake scenarios. Figure 5 (a) and (b) show that with the increase of PGA, the loss of water network function gradually increases; while the change of water network tolerance value has almost no effect on the edge loss rate, and has a slight impact on the demand loss rate. Figure 5 (c) and (d) show that under the first three earthquake scenarios, the loss of power grid function gradually decreases with the increase of tolerance value, while when PGA = 0.6g, the influence of tolerance on the loss of power grid function remains almost unchanged. The reason is that the earthquake causes serious initial damage to the power grid and cascading failures rarely occur.

[0093] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for constructing a post-earthquake water-electricity correlation network cascade failure model based on functional coupling, characterized in that: The construction method first collects basic information of the water network and the power network; Secondly, define the functional coupling relationship and establish the water-power network topology model based on graph theory; thirdly, determine the components that trigger cascading failures in the water and power grids based on vulnerability curves; fourth , introduce the joint probability of failure method to determine the functional failure of components with coupling relationship in water network and power grid; fifth, take the functional failure components in water network as input, carry out cascading failure analysis of water network, and introduce node load function as the judgment condition of cascading failure of water network; Sixth, the functional failure components in the power grid are used as input to carry out power grid cascading failure analysis, and the line capacity function is introduced as the judgment condition for power grid cascading failure; finally, when the cascading failure of the water network and the power grid is terminated, the functional loss of the water network and the power grid is evaluated.

2. The method for constructing a post-earthquake water-electricity correlation network cascading failure model based on functional coupling according to claim 1 is characterized in that: The construction method specifically comprises the following steps: Step S1: Collect basic information of water network and power network; Step S2: Define the functional coupling relationship and establish a water-electricity network topology model based on graph theory; the details are as follows: Based on graph theory, reservoirs, pools, and users are regarded as nodes and recorded as The pipeline and pump station are set as the connection between nodes, denoted as This is abstracted into a water network topology structure, and W(V W ,E W ) represents; where V W represents the node set of the water network, Indicates the first water network node, Indicates the second water network node, represents the mth water network node, E W represents the edge set of the water network, Indicates the first water network edge. Indicates the second water network edge. Indicates the nth water network edge; Based on graph theory, power plants, substations, and users are regarded as nodes and recorded as The line is regarded as the connection between nodes, denoted by This is abstracted into a power grid topology structure, using H(V H ,E H ) represents; where V H represents the set of nodes in the power grid, represents the first grid node, represents the second grid node, represents the oth grid node, E H represents the edge set of the power grid, Indicates the first grid connection edge, Indicates the second grid connection edge, represents the qth grid connection; Define the functional coupling relationship between the water network and the power grid, and then use the multi-layer infrastructure network topology modeling method to establish the water-power association network topology structure model; use the hydraulic model to calculate the initial water pressure of the water network node, and use the DC power flow model to calculate the initial power of the power grid line; Step S3: Based on the vulnerability curve, determine the components in the water network and the power grid that trigger cascading failures, as follows: The vulnerability curve is used to determine the probability of different damage states of various components in the water network and power grid under different intensity earthquake impacts; first, the damage state of each component in the water network and power grid is divided into two states, namely, normal function state and functional failure state; then, the component reaching a moderate damage state after the earthquake is defined as a functional failure state, and the probability of the component in the functional failure state after the earthquake is summed up by the probabilities of the moderate damage state and above; finally, the component functional failure state is estimated by the random method, which is used as the component that triggers cascading failure in the water network and power grid; Step S4: Introduce the joint probability of failure method to determine the functional failure of components with functional coupling relationships, as follows: The joint probability of failure is introduced to determine the failure probability of components with functional coupling relationship, and the functional coupling strength is defined to analyze the possibility of functional failure transmission of components with functional coupling relationship between water network and power grid; then the random method is used to estimate the functional failure of components with functional coupling relationship; Step S5: Conduct water network cascading failure analysis, as follows: For the cascading failure analysis of the water network, the hydraulic model of the pipeline damage point after the earthquake of the water network is used, the initial functional failure components are removed, the water network topology is updated, and hydraulic adjustment is performed; during the hydraulic adjustment process, the node water distribution is gradually adjusted by an iterative method based on the pressure-driven node water distribution model; the node load function is used to determine whether there are new failed nodes: if there are new failed nodes, the failed nodes are removed, the water network topology is updated again, and the hydraulic adjustment is calculated until no new failed nodes appear in the network, that is, the cascading failure of the water network ends, and then the water network function loss is evaluated, and the calculation method is shown in step S7; if there are no new failed nodes, step S7 is directly performed to calculate the function loss of the water network; Assuming that pipeline damage under earthquake action is a random independent event and follows Poisson distribution along the length of the pipeline, the probability of pipeline damage is: Where P l is the probability of pipeline l being damaged under earthquake damage; l is the pipe length; RR l is the average pipeline damage rate; Step S6: Conducting power grid cascading failure analysis, as follows: For the grid cascading failure analysis, the initial failed components are removed and the grid topology is updated; the connectivity of the remaining grid topology is determined: if the connected cluster formed by the connected nodes and edges in the remaining grid topology contains a power plant node, the DC power flow model is used to calculate the line power in the connected cluster; if the connected cluster does not contain a power plant node, the grid cascading failure ends, and step S7 is directly performed to calculate the grid function loss; Step S7: Calculate the function loss of the water network and the power grid, as follows: The functional loss of the hydropower coupling network is defined as the demand loss rate and the connection loss rate. Due to the randomness of earthquake damage, the Monte Carlo method is used to perform multiple simulations, and the average demand loss rate and the average connection loss rate of the hydropower network are used as the final functional loss calculation results.

3. The method for constructing a post-earthquake water-electricity correlation network cascading failure model based on functional coupling according to claim 2 is characterized in that: In step S1, the basic information of the water network includes the number of reservoirs, total water head, the number of pools, elevation, initial water level, minimum water level, maximum water level, diameter, the number of pumps, head curve, the number of users, water demand, elevation, the number of pipelines, start and end nodes, diameter, length, and roughness coefficient; the basic information of the power grid includes the number of nodes, injected active power, the number of branches, start and end nodes, and reactance.

4. The method for constructing a post-earthquake water-electricity correlation network cascading failure model based on functional coupling according to claim 2 is characterized in that: The step S2 is specifically as follows: Table 1 shows the functional coupling relationship between the water network and the power grid; among them, the functional coupling component of the power grid is the power plant, that is, the normal operation of the power plant requires the water plant or water pool in the water network to provide cooling water, and the functional transfer direction is water plant / water pool → power plant, that is, when the water plant or water pool in the water network is damaged, the power plant function will be weakened or fail; the functional coupling components in the water network are water plants and pumping stations, that is, the normal operation of water plants and pumping stations requires the substation in the power grid to provide power supply, and the functional transfer direction is substation → water plant / pumping station, that is, when the substation in the power grid is damaged, the water plant or pumping station in the water network will not be able to operate normally; Table 1 Functional coupling relationship between water network and power grid 5. The method for constructing a post-earthquake water-electricity correlation network cascading failure model based on functional coupling according to claim 2 is characterized in that: In step S3, the probabilities of different damage states are shown in Table 2: Table 2 Component damage status and probability Among them, the value range of p1, p2, p3, and p4 is 0 to 1, and p1+p2+p3+p4=1; P N ,P F The value range of P is 0 to 1, and N +P F =1.

6. The method for constructing a post-earthquake water-electricity correlation network cascading failure model based on functional coupling according to claim 2 is characterized in that: The step S4 is specifically as follows: The calculation method of the failure probability of components with functional coupling relationship is as follows: Assume that the coupling component u of the water network W is used as an example, and its functional failure includes two situations: one is that the earthquake directly causes damage to the coupling component u, which is recorded as event The probability of its occurrence is recorded as The other is that the grid H component v that the water grid coupling component u depends on fails, and its failure is transmitted to the component u, which is recorded as event The probability of its occurrence is recorded as For the failure of the water network coupling component u, it is recorded as event W u , introduce the failure joint probability model to express the probability of occurrence of the event P(W u ), which can be considered as an event and events The calculation formula is as follows: Formula (1) can be equivalent to: Under the action of earthquake, the destruction events of water network component u and power grid component v are independent of each other, that is, event and events are mutually independent events, so formula (2) is converted to: Where, the functional failure probability of component u is Determined according to the calculation method of step S3, that is, based on the fragility curve, the probability of component u having different damage states under earthquake action is obtained, and then the probabilities of medium damage state and above are summed up to obtain the functional failure probability The probability of cascading failure for component u is The calculation method is: Formula (4) represents the functional coupling between water grid component u and power grid component v. The cascading failure event of water grid component u is Caused by the failure of grid component v, the probability of cascading failure of component u is is the failure probability P(H v ) and the conditional probability of failure of component u under the condition of component v failure The product of P(H v ) is the failure probability of component v in the power grid H. If this component has a functional coupling relationship with other components, then P(H v ) is solved according to the probability calculation method of formula (1); otherwise, P(H v ) is the functional failure probability of component v under earthquake action, which is solved in the same way as the calculation method in step S3; The conditional probability Defined as the functional coupling strength Φ between component u and component v uv , that is, the possibility of functional failure transmission, and the direction of functional failure transmission is from component u to component v, the formula is as follows: In the formula, when Φ uv =0, it means that there is no functional coupling relationship between component u and component v, that is, when the function of component u fails, it will not be transmitted to another component v; when 0<Φ uv <1, it indicates that there is a weak coupling relationship between the two components. Specifically, when Φ uv →0, indicating that the looser the functional coupling relationship between the two components, the less likely the failure effect of the water network component u will be transmitted to the power grid component v; when Φ uv →1, indicating that the stronger the functional coupling relationship between the two components, the easier it is for the failure effect of the water network component u to be transmitted to the power grid component v, thus causing the component v to fail. uv =1, indicating that the two components are strongly coupled, that is, the failure of component u will inevitably lead to the failure of coupled component v.

7. The method for constructing a post-earthquake water-electricity correlation network cascade failure model based on functional coupling according to claim 2, characterized in that: In the step S5: The pressure-driven node water distribution model is shown in formula (6); In the formula, and are the actual water supply and demand of node k respectively; P k is the node water pressure, is the minimum node water pressure required when the water distribution of node k is greater than 0, The service water pressure of node k to meet the demand; The average pipeline damage rate RR l The calculation method using the existing earthquake motion data and water supply pipeline earthquake damage data fitting is shown in formula (8); Where PGV is the peak ground velocity and D is the pipe diameter; The node load function is used to determine whether the node has failed, that is, the minimum load capacity of the node is proportional to the initial load of the node, and the formula is as follows: In the formula, α k Indicates the tolerance parameter of node k, ranging from 0 to 1.

8. The method for constructing a post-earthquake water-electricity correlation network cascading failure model based on functional coupling according to claim 2 is characterized in that: In the step S6, the line capacity function shown in formula (10) is used in the connected group to determine whether there is a new failed line: if the line power exceeds the line capacity, there is a new failed line, the failed line is removed, the grid topology is updated again, and the line power is calculated until no new failed lines appear in the network, that is, the grid cascade failure ends, and finally the grid function loss is evaluated. The calculation method is shown in step S7; if the line power does not exceed the line capacity, there is no new failed line, and step S7 is directly performed to calculate the grid function loss; The line capacity function is: Assuming the line capacity C i With the initial power f i (0), the formula is as follows: C i =(1+β i )f i (0)(10) In the formula, β i Indicates the tolerance parameter of line i, and its value range is 0 to 1.

9. The method for constructing a post-earthquake water-electricity correlation network cascading failure model based on functional coupling according to claim 2 is characterized in that: In step S7, the demand loss rate Refers to the ratio between the amount of unmet demand of the node and the demand; edge loss rate is the ratio of the number of edges in a functional failure state in the network after the cascade failure to the number of initial edges, see formulas (11)-(14): In the formula, Q i are the actual supply and demand of the ith node in any network in the kth simulation; L k is the number of edges in any network that are in a normal functional state in the kth simulation; DS and LS are the demand satisfaction rate and connectivity rate of any network respectively; s and z are the number of user nodes and edges of any network respectively; N is the number of Monte Carlo simulations.

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