A method for evaluating seismic resilience of road traffic-power system considering interdependence

Abstract

A kind of road traffic-power system seismic resilience evaluation method considering interdependence belongs to the technical field of interdependent infrastructure system seismic resilience research.In the whole cycle of earthquake disaster, the dependence between road traffic system and power system is introduced: in the earthquake absorption stage, the dependence of traffic electronic signal lamp facilities on power supply is introduced;In the post-earthquake emergency and recovery stage, the dependence of mobile emergency power supply and power facility maintenance vehicles on road traffic accessibility, and the dependence of damaged elevated bridge maintenance operation on power supply are introduced, to obtain the function coupling and mutual influence in the whole process of earthquake.The power system cascade failure model based on alternating current flow is used to simulate the frequency stability, terminal voltage stability, bus voltage stability and branch overload of power system under earthquake action, and quantitative analysis is carried out.The present application can improve the physical authenticity of the disaster response process of power system, and realize the seismic resilience evaluation of interdependent road traffic-power system.

Description

Technical Field

[0001] This invention belongs to the technical field of seismic toughness research on interdependent infrastructure systems, and relates to a method for evaluating the seismic toughness of road traffic-power systems that takes into account interdependence. Background Technology

[0002] Road traffic systems and power systems are crucial components of a city's critical infrastructure, and their functional integrity directly impacts a city's ability to respond to earthquakes, maintain lifelines, and restore social order. As a vital energy support for modern urban operations, the power system not only provides electricity for residents and industrial production but also ensures the continued operation of critical facilities such as hospital medical equipment, traffic signal control facilities, water pumping stations, and communication base stations. The road traffic system plays a vital role in evacuating people, deploying emergency rescue forces, facilitating repair teams, and transporting disaster relief supplies. Both systems support and constrain each other during post-earthquake emergency response and recovery, jointly influencing the overall seismic resilience of the urban infrastructure system. Historical earthquake damage experience shows that both road traffic systems and power systems are susceptible to varying degrees of functional damage under earthquake stress. Damage to bridges, tunnels, and roads can lead to reduced road network capacity or even partial disruptions; damage to power facilities such as transmission lines, substations, and distribution equipment can cause power outages, reduced power supply capacity, and deterioration of the power grid's operational status. More importantly, there is a significant interdependence between the road traffic system and the power system. For example, the repair of facilities such as traffic electronic signals and tunnel lighting, as well as components of the transportation system, depends on the power supply to maintain normal operation; while the emergency repair of power facilities and the dispatch of mobile emergency power sources depend on the road transportation system to provide accessible routes. Therefore, in the context of an earthquake disaster, the functional degradation of any system may affect the other system through their interdependence, thereby leading to a decrease in the overall resilience of the interdependent road transportation-power system.

[0003] Currently, research on the seismic resilience of urban infrastructure systems largely focuses on disaster damage assessment, functional recovery analysis, or resilience evaluation of single systems, with insufficient characterization of the interdependence between road traffic systems and power systems. Existing research involving road traffic-power systems is mostly geared towards hurricane disaster scenarios, failing to directly reflect the dependencies in processes such as elevated bridge damage, road network disruption, power equipment failure, and post-earthquake repair and scheduling under seismic action. Furthermore, existing research does not adequately consider the dependence of mobile emergency power supplies on traffic accessibility after earthquakes, resulting in an incomplete description of the inter-system interaction mechanisms during the post-earthquake emergency response phase. In addition, in power system disaster response simulation, existing power system cascading failure modeling methods mostly employ complex network betweenness models or DC power flow models. Complex network betweenness models typically focus on network topology characteristics, making it difficult to reflect the power flow distribution in actual power system operation; while DC power flow models have the advantage of high computational efficiency, they usually ignore factors such as reactive power and voltage, making it difficult to comprehensively characterize the real operating characteristics of power systems under seismic disturbances. Therefore, existing methods suffer from insufficient physical mechanism representation and imprecise characterization of operating states when simulating the cascading failure process of power systems under seismic action.

[0004] In summary, the interdependence between road traffic systems and power systems after an earthquake significantly impacts the functional damage, emergency response efficiency, and recovery process of urban road traffic-power systems. How to reasonably characterize the dependence of traffic signal facilities on power supply, the dependence of mobile emergency power supplies and power repair vehicles on traffic accessibility, the power supply requirements for damaged overpass repair operations, and how to more realistically simulate the cascading failure process of power systems under seismic loading have become urgent technical problems to be solved in the seismic resilience evaluation of interdependent road traffic-power systems. Summary of the Invention

[0005] To address the shortcomings of existing technologies, such as incomplete characterization of the interdependence between road traffic systems and power systems, insufficient consideration of the dependence of mobile emergency power supplies on road accessibility after earthquakes, and the inability of existing power system cascade failure models to accurately reflect actual operating characteristics like node voltage and reactive power, leading to incomplete descriptions of the functional evolution of the interdependent road traffic-power system under earthquake disasters and insufficient accuracy in seismic toughness evaluation results, this invention provides a seismic toughness evaluation method for road traffic-power systems that considers interdependence. This invention identifies and models the interdependence between road traffic systems and power systems throughout the entire earthquake disaster cycle: during the earthquake absorption phase, it considers the dependence of traffic electronic signal facilities on power supply; during the post-earthquake emergency and recovery phase, it considers the dependence of mobile emergency power supplies and power facility maintenance vehicles on road accessibility, as well as the dependence of damaged viaduct maintenance operations on power supply, thereby providing a more complete description of the functional coupling and mutual influence between road traffic systems and power systems throughout the entire earthquake process. Meanwhile, this invention employs a cascaded failure model of the power system based on AC power flow to simulate the frequency stability, terminal voltage stability, bus voltage stability, and branch overload of the power system under seismic loading, thereby improving the physical realism of the power system's disaster response process. Based on this, it quantitatively analyzes the functional changes of the interdependent road-traffic-power system during the earthquake damage, emergency response, and recovery phases, enabling an evaluation of the seismic resilience of the interdependent road-traffic-power system.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for evaluating the seismic toughness of a road traffic-power system considering interdependence, the method comprising the following steps: The first step involves collecting data related to the road traffic system, power system, and post-earthquake emergency recovery. Directed graphs of the road traffic system and power system are then constructed to identify the dependencies between them, and a network topology model of the road traffic-power coupled system is established. Details are as follows: Step 1.1: Collect basic data for the road traffic system. This data includes geographic coordinates and attribute data. Geographic coordinates include road intersections, viaducts, and traffic lights. Attribute data includes road grade, number of lanes, free-flow speed, road capacity, and traffic demand. Road intersections and viaducts are abstracted as nodes in the road traffic network, and road segments connecting intersections or viaducts are abstracted as edges, thus constructing a directed graph of the road traffic system. (1) In the formula, For road traffic network; It is the set of nodes in a road traffic network; It is a set of edges in the road traffic network.

[0007] Step 1.2: Collect basic power system data. This data includes the geographical coordinates of power plants, substations, and users; the resistance, reactance, and susceptance of transmission and distribution lines; active and reactive power limits, operating voltage limits, and generation costs of generators; and the active and reactive power of users. Power plants, substations, and users are abstracted as power network nodes, and transmission and distribution lines are abstracted as power network edges, constructing a directed graph of the power system. (2) In the formula, For power grids; A set of nodes in a power network; This is a set of edges in a power network.

[0008] Step 1.3: Collect power supply information for traffic electronic signals, the correspondence between the elevated bridge and nearby user nodes, the geographical coordinates of mobile emergency power supplies and maintenance vehicles, and identify the interdependencies between the road traffic system and the power system, including: during the earthquake absorption phase, the functional status of the electronic signals in the road traffic system requires power supply from the power system; during the post-earthquake emergency phase, mobile emergency power supplies need to utilize the road traffic system to carry out emergency operations; during the post-earthquake recovery phase, maintenance equipment for the damaged elevated bridge requires power supply from the power system, and vehicles responsible for repairing damaged electrical components need to utilize the road traffic system to carry out maintenance operations.

[0009] Step 1.4, based on the directed graph of the road traffic network Directed graph of power network Based on the interdependence between the road traffic system and the power system, a network topology model of the road traffic-power coupled system is established.

[0010] The second step involves using seismic vulnerability analysis and Monte Carlo simulation to determine the seismic damage status of road traffic system and power system components, and then converting the component damage status into functional degradation to obtain the post-earthquake functional degradation results of the damaged road traffic-power system components. Details are as follows: Step 2.1: Based on the seismic intensity and the vulnerability functions of the road traffic system and power system components shown in formula (3), calculate the probability of the elevated bridge, power plant, substation and transmission and distribution line exceeding each damage state.

[0011] (3) In the formula, These are parameters required for the project. This represents the limit state threshold corresponding to different damage and failure levels. i =1, 2, 3, 4, specifically minor injuries. LS1. Moderate injury LS 2. Severe injury LS 3 and complete destruction LS 4. The extreme state thresholds corresponding to the four damage levels; It refers to the intensity of earthquake motion; It is the standard normal distribution function; For the first i The median value of the ground motion intensity corresponding to the damage level; It is the logarithmic standard deviation of the fragility function.

[0012] Step 2.2: Based on the probability of each component exceeding each damage state obtained in Step 2.1, Monte Carlo simulation is used to randomly determine the damage state of each viaduct, power plant, substation and transmission and distribution line to form an earthquake damage scenario; Monte Carlo simulation is repeated to obtain a set of no less than 1000 earthquake damage scenarios that consider the uncertainty of system component damage.

[0013] Step 2.3: Based on the correspondence between the damage status and functional degradation of the viaduct shown in Table 1, the damage status of the viaduct is converted into the percentage decrease in the traffic capacity and free-flow velocity of the viaduct and its underpass. The travel time of the damaged viaduct and underpass is calculated using the BPR road resistance function shown in formula (4). This results in a decline in the functionality of elevated bridges and underpasses.

[0014] (4) In the formula, Road sections with zero traffic flow The travel time is calculated by dividing the road segment length by the free-flow velocity; , Each is a road segment Traffic flow and traffic capacity; The first hindrance coefficient, The second resistance coefficient needs to be calibrated based on the correspondence between traffic volume and travel time under different flow levels of the local road traffic system.

[0015] Table 1: Correspondence between damage status and functional decline of elevated bridges

[0016] Step 2.4: Considering that conventional measures of power system availability have a binary characteristic, this invention assumes that power plants, substations, and transmission and distribution lines cannot function when they are severely damaged or completely destroyed, i.e., their functionality decreases by 100%. Therefore, the functional degradation results of power system components are obtained.

[0017] The functional degradation results of the elevated bridges and underpasses obtained in steps 2.5 and 2.3, together with the functional degradation results of the power system components obtained in step 2.4, constitute the functional degradation results of the post-earthquake damaged road traffic-power system components.

[0018] The third step, based on the road traffic-power coupled system network topology model obtained in the first step and the functional degradation results of the damaged road traffic-power system components obtained in the second step, uses AC power flow to simulate the cascading failure of the power system and a user-balanced current distribution model to simulate the traffic flow distribution under conditions of elevated bridge damage and traffic electronic signal power failure. This yields the operating status of the power system, power system performance, and road traffic system performance during the earthquake absorption phase. Details are as follows: Step 3.1, based on the directed graph of the power system obtained in Step 1.2 Based on the power system component function degradation results obtained in step 2.4, power system islands are identified, and cascading failure analysis based on AC power flow is performed on each island. For each island, it is determined whether both generator nodes and user nodes exist simultaneously. If either generator node or user node is missing, the power system island is deemed to have lost its power supply function. If both generator nodes and user nodes exist simultaneously, the generator node with the largest generating capacity is selected as the relaxation node, and AC power flow calculation is performed.

[0019] Step 3.2: If the AC power flow calculation fails to converge, the loads of user nodes in the power system island are converted into dispatchable loads. The minimum load reduction required to meet the power flow convergence condition is calculated using the optimal AC power flow. To increase the convergence of the optimal power flow, the branch apparent power constraint and the lower limit constraint of the bus voltage are removed. Based on the results of the optimal AC power flow calculation, the user power, generator output, and generator terminal voltage are adjusted, and the AC power flow calculation is performed again. If the optimal AC power flow or the adjusted AC power flow still fails to meet the power flow convergence condition, the power system island is deemed to have lost its power supply function.

[0020] The AC power flow convergence condition refers to the AC power flow calculation obtaining an effective power flow solution within a preset maximum number of iterations, and the active power imbalance of all bus nodes and the reactive power imbalance of all PQ bus nodes not exceeding a preset power flow convergence threshold.

[0021] Step 3.3: When the AC power flow calculation converges, sequentially determine whether the power system islanding meets the frequency stability constraint, generator terminal voltage constraint, bus voltage constraint, and branch apparent power constraint. When the system frequency deviation caused by active power imbalance exceeds the allowable range, perform low-frequency load shedding or over-frequency generator disconnection operations; when the generator reactive power exceeds the over-excitation or under-excitation limit, convert the corresponding generator node from a PV node to a PQ node and fix the reactive power at the corresponding limit; when the bus voltage is lower than the preset lower voltage limit, gradually reduce the active and reactive power of the corresponding user node according to the preset ratio; when the branch apparent power exceeds the long-term allowable power of the branch, disconnect the corresponding branch.

[0022] The allowable range refers to the pre-set allowable variation range of system frequency according to the requirements for safe and stable operation of the power system. The overexcitation limit refers to the maximum reactive power that the generator can continuously output to the power system under the current active power output and terminal voltage conditions, limited by the excitation system capacity, stator current, and rotor excitation current allowable values. The underexcitation limit refers to the lower limit of reactive power corresponding to the maximum reactive power that the generator can continuously absorb from the power system under the current active power output and terminal voltage conditions, limited by the generator's stable operation capability, stator end heating, and excitation system regulation capability. The preset voltage lower limit refers to the minimum allowable operating voltage of the busbar determined in advance according to the busbar voltage level, power system operation mode, user power supply requirements, and low-voltage stability requirements.

[0023] Step 3.4: Update the directed graph of the power system based on the simulation results of Step 3.3, re-identify the power system islands, and repeat Steps 3.1 to 3.3 until the frequency stability constraints, generator terminal voltage constraints, bus voltage constraints, and branch apparent power constraints of each power system island are all satisfied, or the power system island is determined to have lost its power supply function, thus obtaining the operating status of each power system island after cascading failure.

[0024] Step 3.5: Calculate the time based on the active power of each user node after the cascading failure. t Power system performance: (5) In the formula, yes t Power system performance at any given time; It is a set of user nodes in the power system; yes t User nodes at any time The active power; User nodes before the earthquake occurred The active power.

[0025] Step 3.6: Based on the dependence of the functional state of electronic traffic lights in the road traffic system on the power supply of the power system established in Step 1.3, determine the probability that the electronic traffic lights will receive power supply based on the active power ratio of user nodes adjacent to the traffic electronic traffic lights before and after the earthquake. (6) In the formula, It is an electronic traffic light intersection The probability of obtaining a power supply; and It is an electronic traffic light intersection User nodes that provide electricity In the moments before the earthquake t 0 and post-earthquake moments t The active power.

[0026] Subsequently, random numbers that follow a uniform distribution in the interval [0,1] are generated, and the probability of obtaining power supply is combined with the electronic signal lights. The functional state of traffic electronic signals is determined by Bernoulli distribution.

[0027] Step 3.7: Based on the functional status of the traffic electronic signal lights, use the intersection delay model to determine the passage delay of normally signal-controlled intersections and malfunctioning signal-controlled intersections, and add the intersection passage delay to the passage time of the road segment ending at the intersection.

[0028] Step 3.8, based on the directed graph of the road traffic system obtained in Step 1.1 The second step yields the results of the road traffic system function degradation and the intersection delay model from step 3.7. A user balanced flow distribution model is then constructed, and the Frank-Wolfe algorithm is used to solve the traffic flow distribution and road travel time under the earthquake damage scenario.

[0029] Step 3.9: Calculate the time based on the user balanced traffic distribution results. t Road traffic system performance: (7) In the formula, For a moment t The performance of the road traffic system; The number of nodes in the road traffic network; and The moments before the earthquake t 0 and post-earthquake moments t nodes To node The shortest travel time.

[0030] The fourth step, based on the performance of the road traffic system, the operating status and performance of the power system during the earthquake absorption phase obtained in the third step, and the dependency relationship of the mobile emergency power supply needing to utilize the road traffic system for emergency operations as stated in step 1.3, determines the island to which the mobile emergency power supply can be connected and the time required for connection. It then updates the operating status, performance of the power system, and the performance of the road traffic system after the mobile emergency power supply is connected to the island, obtaining the performance results of the road traffic system and power system during the post-earthquake emergency phase. Specifically, as follows: Step 4.1: Based on the operating status of each island in the power system obtained in Step 3.4, identify power system islands that simultaneously contain user nodes and experience user losses, forming a candidate island set for mobile emergency power supply to be connected.

[0031] Step 4.2: Using the post-earthquake travel time of each road segment obtained from the user-balanced traffic distribution model in Step 3.9 as the path weight, the Dijkstra shortest path algorithm is used to calculate the shortest travel time from the mobile emergency power supply to each candidate island access location. When the shortest travel time from the mobile emergency power supply to the candidate island access location is a finite value, the candidate island is determined to be accessible; when the shortest travel time is infinite, the candidate island is determined to be inaccessible.

[0032] Step 4.3: Among the candidate islands with traffic accessibility, the access order of mobile emergency power supplies is determined based on the degree of load loss of users on the island and the shortest travel time from the mobile emergency power supply to the island. Islands with greater user load loss and shorter shortest travel time from the mobile emergency power supply to the island are considered to have higher access priority. Furthermore, the target islands for mobile emergency power supply access are determined under the constraint of the number of mobile emergency power supplies.

[0033] Step 4.4: The shortest travel time from the mobile emergency power supply to the target island is taken as the connection time of the mobile emergency power supply.

[0034] Step 4.5, connect the mobile emergency power supply to the target island according to the following active and reactive power output constraints: (8) (9) In the formula, and These are the active power and reactive power output by the mobile emergency power supply, respectively. and These are the maximum active power and maximum reactive power that the mobile emergency power supply is allowed to output, respectively.

[0035] Step 4.6: After the mobile emergency power supply is connected to the target island, the AC power flow calculation and cascade failure judgment are re-performed, the active power of each user node is updated, and the performance of the road traffic system is recalculated according to steps 3.6-3.9, and the performance of the power system is recalculated according to step 3.5, so as to obtain the performance results of the road traffic system and power system in the post-earthquake emergency stage.

[0036] The fifth step, based on the performance results of the road traffic system and power system during the post-earthquake emergency phase obtained in the fourth step, involves simulating the parallel recovery process of the two systems under the constraints of their interdependence, taking into account the repair priorities, repair durations, and maintenance resource allocation for the damaged viaducts and power system components. This yields the performance curves of the road traffic system and power system over time during the post-earthquake recovery phase. The details are as follows: Step 5.1: Determine the set of damaged viaducts and the set of damaged power system components.

[0037] Step 5.2: Remove each elevated bridge from the road traffic network one by one, calculate the change in the performance of the road traffic system before and after removal, and use the change as an indicator of the importance of the elevated bridge; determine the repair priority of the damaged elevated bridges in descending order of importance.

[0038] Step 5.3: Remove each component in the power system from the grid one by one, calculate the change in power system performance before and after removal, and use the change as an indicator of the importance of the power system components; determine the repair priority of the damaged power system components in descending order of importance.

[0039] Step 5.4: Based on the damage status of each damaged viaduct and damaged power system component, refer to the "Guideline for Seismic Toughness Evaluation of Urban Engineering Systems" (RISN-TG041-2022) to determine the probability distribution parameters of the repair time corresponding to the components with different damage statuses, and use Monte Carlo simulation to generate the repair duration of the damaged viaduct and damaged power system components respectively.

[0040] Step 5.5: The maximum number of maintenance engineering teams is used to consider the limited resource constraints in the recovery process. The maximum number of maintenance engineering teams that can be called up is set for the road traffic system and the power system respectively. Each maintenance engineering team can only execute the maintenance task of the next damaged component according to the repair priority after completing the repair task of the current damaged component.

[0041] Step 5.6: Assign maintenance tasks to the road traffic system maintenance team according to the priority of repairing the damaged viaducts, and determine whether the power supply conditions for the viaduct maintenance work are met based on the active power of the corresponding user nodes. When the active power of the corresponding user node is zero, postpone the maintenance work on the damaged viaduct; when the active power of the corresponding user node is not zero, adjust the maintenance duration of the damaged viaduct according to the ratio of active power of the user node before and after the earthquake, using the following adjustment formula: (10) In the formula, Indicates the damaged viaduct bi The degree of dependence of the repair work on the power system is rated on a scale of 0 to 1. The higher the value, the greater the dependence of the repair work on the power system; It is an elevated bridge bi Repair time assuming sufficient power supply; It is an elevated bridge under the consideration of insufficient power supply. bi Repair time.

[0042] Step 5.7: Assign repair tasks to the power system maintenance engineering team according to the repair priority of damaged power system components, and use Dijkstra's shortest path algorithm to calculate the shortest travel time from the maintenance center to the power system component to be repaired. When there is at least one passable path between the maintenance center and the power system component to be repaired, the power system component is determined to meet the traffic accessibility conditions for maintenance vehicles, and the arrival time of the maintenance vehicles and the start time of maintenance are determined; when there is no passable path, the maintenance work on the corresponding power system component is postponed until traffic accessibility is restored after the road traffic network is updated.

[0043] Step 5.8: Record the start and end times of maintenance for the damaged viaduct and the damaged power system components, respectively.

[0044] Step 5.9: When any damaged viaduct is repaired, restore the traffic capacity and free-flow speed of the viaduct and its underpass, update the directed graph of the road traffic system, re-perform user equalization flow allocation, update the performance of the road traffic system and the accessibility of the repaired vehicles.

[0045] Step 5.10: When any damaged power system component is repaired, reconnect the power system component to the power system, update the directed graph of the power system, and recalculate the AC power flow and cascade failure judgment; based on the updated active power of the user nodes, redetermine the functional status of the traffic electronic signal lights and the repair duration of the damaged overpass, and update the power system performance.

[0046] Step 5.11: Repeat steps 5.6 through 5.10 until all damaged viaducts and damaged power system components are repaired, and the road traffic system performance is obtained. and power system performance The complete recovery process that changes over time.

[0047] Step 6: Based on the system performance changes obtained in steps 3 to 5 during the seismic absorption phase, post-earthquake emergency phase, and post-earthquake recovery phase, construct resilience curves for the road traffic system and the power system, and calculate the interdependent seismic resilience evaluation results of the road traffic-power system. Specifically, this includes: Step 6.1: Construct performance curves for the road traffic system and the power system, respectively, with time as the horizontal axis and the performance of the road traffic system and the power system as the vertical axis.

[0048] Step 6.2: Within the control time, integrate the performance curves of the road traffic system and the power system respectively to calculate the seismic toughness of the road traffic system and the power system. (11) (12) In the formula, To enhance the seismic resilience of road traffic systems that take into account the impact of power system dependence; Seismic toughness of power systems taking into account the dependence of road traffic systems; Control time for resilience evaluation; t 0 represents the time when the earthquake occurred; for t The power system performance at any given time is calculated according to formula (5); for t The performance of the road traffic system at any given time is calculated according to formula (7).

[0049] Step 6.3: For the multiple earthquake damage scenarios generated in the second step, execute steps 3 to 6.2 in sequence to obtain the performance change curves of the road traffic system and power system considering interdependence under multiple earthquake damage scenarios and the seismic toughness evaluation results.

[0050] Step 6.4: Statistical analysis is performed on the evaluation results under multiple earthquake damage scenarios to obtain the probability distribution and cumulative probability curve of the seismic toughness of the road traffic system and power system considering interdependence, and finally the evaluation results of the seismic toughness of the road traffic-power system considering interdependence are formed.

[0051] The beneficial effects of this invention are as follows: (1) This invention can more completely characterize the interdependence between the road traffic system and the power system throughout the entire process of an earthquake disaster. By incorporating the dependence of traffic signal facilities on power supply during the earthquake, as well as the dependence of mobile emergency power supplies and power maintenance vehicles on traffic accessibility and the dependence of damaged viaduct maintenance operations on power supply during the post-earthquake emergency and recovery phases into a unified evaluation framework, it makes up for the problem that existing methods do not adequately consider the post-earthquake emergency response phase.

[0052] (2) This invention can improve the simulation accuracy of power system functional loss and cascading failure processes under seismic action. By adopting a cascading failure model based on AC power flow, it simulates processes such as low-frequency load shedding, over-frequency generator disconnection, generator over-excitation and under-excitation limitation, low-voltage load shedding and branch overload tripping, overcoming the shortcomings of complex network models that only reflect topological characteristics and DC power flow models that ignore reactive power and voltage changes. This makes the islanding formation, user loss and continuous fault propagation process of the power system under seismic disturbance more consistent with the actual operating law, thereby improving the accuracy and engineering applicability of power system performance evaluation results and the interdependent road traffic and power system seismic toughness evaluation results. Attached Figure Description

[0053] Figure 1 These are the implementation steps of a seismic toughness evaluation method for road traffic-power systems that consider interdependence.

[0054] Figure 2 This involves the impact of earthquake damage to the road traffic system on the access time of mobile emergency power supplies and the impact of emergency power supply access on the performance of the power system.

[0055] Figure 3 It is the post-earthquake recovery curve of road transportation systems that rely on the power system.

[0056] Figure 4 It is the post-earthquake recovery curve of the power system that depends on the road traffic system.

[0057] Figure 5 This is the result of the seismic toughness evaluation of road traffic systems that rely on power systems.

[0058] Figure 6 It is the seismic toughness evaluation result of the power system that depends on the road traffic system. Detailed Implementation

[0059] The present invention will be further described below with reference to specific embodiments.

[0060] This embodiment uses the road traffic system of Futian District, Shenzhen and the IEEE 30-node power system to illustrate a method for evaluating the seismic toughness of a road traffic-power system considering interdependence. The main steps are as follows: Figure 1As shown. Specifically, it includes the following steps: The first step involves collecting data related to the road traffic system, power system, and post-earthquake emergency recovery. Directed graphs of the road traffic system and power system are then constructed to identify the dependencies between them, and a network topology model of the road traffic-power coupled system is established. Details are as follows: Step 1.1: Collect basic data of the road traffic system. This data includes geographic coordinates and attribute data. Geographic coordinates include road intersections, viaducts, and traffic lights. Attribute data includes road grade, number of lanes, free-flow speed, road capacity, and traffic demand. To reduce computational complexity, this embodiment selects highways, expressways, and arterial roads within Futian District for road traffic network modeling. Road intersections and viaducts are abstracted as road traffic network nodes, and road segments connecting intersections or viaducts are abstracted as road traffic network edges, constructing a directed graph of the road traffic system. D T .

[0061] Step 1.2: The power system adopts the IEEE 30-node standard test system. Data includes the geographical coordinates of power plants, substations, and users; the resistance, reactance, and susceptance of transmission and distribution lines; generator active and reactive power limits, operating voltage limits, and generation costs; and user active and reactive power, etc. Generators, substations, and users are abstracted as power system nodes, and transmission and distribution lines are abstracted as power system edges, establishing the IEEE 30-node power network. D P .

[0062] Step 1.3: Locate the generator nodes, user nodes, emergency power center, and maintenance center within the Futian District of Shenzhen. In practical applications, the locations of each component use the actual geographical coordinates of the urban road traffic system and power system to be evaluated; the geographical locations in this embodiment are used to illustrate the implementation process of the invention and do not affect the applicability of the method described herein. Further, the interdependence between the road traffic system and the power system is established, including: during the earthquake absorption phase, the functional status of electronic traffic lights in the road traffic system requires power supply from the power system; during the post-earthquake emergency phase, mobile emergency power supplies need to utilize the road traffic system for emergency operations; during the post-earthquake recovery phase, repair equipment for damaged overpasses requires power supply from the power system, and vehicles responsible for repairing damaged power components need to utilize the road traffic system for repair operations. This is based on a directed graph of the road traffic network. Directed graph of power network Based on the interdependence between the road traffic system and the power system, a network topology model of the road traffic-power coupled system is established.

[0063] The second step involves using seismic vulnerability analysis and Monte Carlo simulation to determine the seismic damage status of road traffic system and power system components, and then converting the component damage status into functional degradation to obtain the post-earthquake functional degradation results of the damaged road traffic-power system components. Details are as follows: Step 2.1: The seismic fortification intensity of Futian District, Shenzhen is 7 degrees. This embodiment sets a rare earthquake scenario, with a peak ground acceleration (PGA) of 0.22g. The elevated bridge structure in this embodiment is set as a prestressed reinforced concrete continuous beam bridge. Referring to the "Guideline for Seismic Toughness Evaluation of Urban Engineering Systems" (RISN-TG041-2022), the median and logarithmic standard deviation of the vulnerability functions for elevated bridges, power plants, substations, and transmission and distribution lines are determined. The probability of each component exceeding the states of no damage, slight damage, moderate damage, severe damage, and complete failure when the PGA is 0.22g is calculated.

[0064] Step 2.2: Using the Monte Carlo simulation method, the seismic damage states of the road traffic system and power system components are randomly generated based on the probability of each component exceeding each damage state. In this embodiment, the number of Monte Carlo simulations is set to 1000.

[0065] Step 2.3: For the road traffic system, determine the capacity and free-flow velocity reduction of the viaducts and their underpasses based on the damage status of the viaducts and Table 1. Based on the updated capacity, free-flow velocity, and traffic volume, calculate the post-earthquake travel time for each damaged viaduct and underpass using the BPR road resistance function, where the first and second resistance coefficients are respectively taken as... =0.15 and =4.0.

[0066] Step 2.4: For the power system, power plants, substations and transmission and distribution lines that are in a state of severe damage or complete destruction are identified as functional failures, and the corresponding components are removed from the power system to update the directed graph of the power system.

[0067] The functional degradation results of the elevated bridges and underpasses obtained in steps 2.5 and 2.3, together with the functional degradation results of the power system components obtained in step 2.4, constitute the functional degradation results of the post-earthquake damaged road traffic-power system components.

[0068] The third step, based on the road traffic-power coupled system network topology model obtained in the first step and the functional degradation results of the damaged road traffic-power system components obtained in the second step, uses AC power flow to simulate the cascading failure of the power system and a user-balanced current distribution model to simulate the traffic flow distribution under conditions of elevated bridge damage and traffic electronic signal power failure. This yields the operating status of the power system, power system performance, and road traffic system performance during the earthquake absorption phase. Details are as follows: Step 3.1, based on the directed graph of the power system obtained in Step 1.2 Based on the power system component function degradation results obtained in step 2.4, power system islands are identified, and cascading failure analysis based on AC power flow is performed on each island. For each island, it is determined whether both generator nodes and user nodes exist simultaneously. If either generator node or user node is missing, the power system island is deemed to have lost its power supply function. If both generator nodes and user nodes exist simultaneously, the generator node with the largest generating capacity is selected as the relaxation node, and AC power flow calculation is performed.

[0069] Step 3.2: If the AC power flow calculation fails to converge, the loads of user nodes in the power system island are converted into dispatchable loads. The minimum load reduction required to meet the power flow convergence condition is calculated using the optimal AC power flow. To increase the convergence of the optimal power flow, the branch apparent power constraint and the lower limit constraint of the bus voltage are removed. Based on the results of the optimal AC power flow calculation, the user power, generator output, and generator terminal voltage are adjusted, and the AC power flow calculation is performed again. If the optimal AC power flow or the adjusted AC power flow still fails to meet the power flow convergence condition, the power system island is deemed to have lost its power supply function.

[0070] The AC power flow convergence condition refers to the AC power flow calculation obtaining an effective power flow solution within a preset maximum number of iterations, and the active power imbalance of all bus nodes and the reactive power imbalance of all PQ bus nodes not exceeding a preset power flow convergence threshold.

[0071] Step 3.3: When the AC power flow calculation converges, sequentially determine whether the power system islanding meets the frequency stability constraint, generator terminal voltage constraint, bus voltage constraint, and branch apparent power constraint. When the system frequency deviation caused by active power imbalance exceeds the allowable range, perform low-frequency load shedding or over-frequency generator disconnection operations; when the generator reactive power exceeds the over-excitation or under-excitation limit, convert the corresponding generator node from a PV node to a PQ node and fix the reactive power at the corresponding limit; when the bus voltage is lower than the preset lower voltage limit, gradually reduce the active and reactive power of the corresponding user node according to the preset ratio; when the branch apparent power exceeds the long-term allowable power of the branch, disconnect the corresponding branch.

[0072] The allowable range refers to the pre-set allowable variation range of system frequency according to the requirements for safe and stable operation of the power system. The overexcitation limit refers to the maximum reactive power that the generator can continuously output to the power system under the current active power output and terminal voltage conditions, limited by the excitation system capacity, stator current, and rotor excitation current allowable values. The underexcitation limit refers to the lower limit of reactive power corresponding to the maximum reactive power that the generator can continuously absorb from the power system under the current active power output and terminal voltage conditions, limited by the generator's stable operation capability, stator end heating, and excitation system regulation capability. The preset voltage lower limit refers to the minimum allowable operating voltage of the busbar determined in advance according to the busbar voltage level, power system operation mode, user power supply requirements, and low-voltage stability requirements.

[0073] Step 3.4 updates the directed graph of the power system based on the simulation results of Step 3.3, re-identifies power system islands, and repeats Steps 3.1 to 3.3 until the frequency stability constraints, generator terminal voltage constraints, bus voltage constraints, and branch apparent power constraints of each power system island are all satisfied, or the power system island is determined to have lost its power supply function, thus obtaining the operating status of each power system island after cascading failure. In 1000 earthquake scenarios, the power system was not damaged in 66 scenarios. Table 2 summarizes the characteristics of cascading failure of the power system under 934 earthquake damage scenarios. Cascading failure leads to an average of 16.137 islands in the power system, and the uncertainty of the number of islands is low. The probabilities of islands failing due to power supply shortage exceeding 0.333, 0.706, and 0.800 are 95%, 50%, and 5%, respectively. Furthermore, overloaded branches are common in the process of power system cascading failure. Statistical results of low-frequency load shedding and low-voltage load shedding indicate that low-frequency load shedding is the main load shedding mechanism. Regarding the proportion of over-frequency generators and the proportion of over / under-excited generators, although the median value of the over / under-excited generator proportion is relatively high, the former exhibits greater volatility and significant outliers, resulting in a higher average value for the former compared to the latter. Overall, in IEEE 30-bus power systems, generator frequency stability and branch overload have a greater impact on system function under rare earthquake scenarios.

[0074] Table 2: Statistical Results of Cascade Failure Characteristics in Power Systems

[0075] Step 3.5: Based on the active power of the user nodes after cascading failure, calculate the power system performance according to formula (5). After calculating 1000 earthquake damage scenarios, the median value of the power system performance is 0.209, the first quartile is 0.037, and the third quartile is 0.438.

[0076] Step 3.6: Based on the dependence of the electronic traffic lights in the road traffic system on the power supply of the power system established in Step 1.3, calculate the probability of the traffic electronic traffic lights obtaining power supply according to Formula (6), and determine the functional state of the traffic electronic traffic lights through Bernoulli distribution.

[0077] Step 3.7: Based on the functional status of the traffic electronic signal lights, use the intersection delay model to determine the passage delay of normally signal-controlled intersections and malfunctioning signal-controlled intersections, and add the intersection passage delay to the passage time of the road segment ending at the intersection.

[0078] Step 3.8, based on the directed graph of the road traffic system obtained in Step 1.1 The second step yields the results of the road traffic system function degradation and the intersection delay model from step 3.7. A user balanced flow distribution model is then constructed, and the Frank-Wolfe algorithm is used to solve the traffic flow distribution and road travel time under the earthquake damage scenario.

[0079] Step 3.9: Calculate the performance of the road traffic system according to formula (7). After calculating 1000 earthquake damage scenarios, the median value of the road traffic system performance is 0.590, the first quartile is 0.545, and the third quartile is 0.641.

[0080] The fourth step, based on the performance of the road traffic system, the operating status and performance of the power system during the earthquake absorption phase obtained in the third step, and the dependency relationship of the mobile emergency power supply needing to utilize the road traffic system for emergency operations as stated in step 1.3, determines the island to which the mobile emergency power supply can be connected and the time required for connection. It then updates the operating status, performance of the power system, and the performance of the road traffic system after the mobile emergency power supply is connected to the island, obtaining the performance results of the road traffic system and power system during the post-earthquake emergency phase. Specifically, as follows: Step 4.1: Based on the operating status of each island in the power system obtained in Step 3.4, identify power system islands that simultaneously contain user nodes and experience user losses, forming a candidate island set for mobile emergency power supply to be connected.

[0081] Step 4.2: Using the post-earthquake travel time of each road segment obtained from the user-balanced traffic distribution model in Step 3.9 as the path weight, the Dijkstra shortest path algorithm is used to calculate the shortest travel time from the mobile emergency power supply to each candidate island access location. When the shortest travel time from the mobile emergency power supply to the candidate island access location is a finite value, the candidate island is determined to be accessible; when the shortest travel time is infinite, the candidate island is determined to be inaccessible.

[0082] Step 4.3: Among the candidate islands with traffic accessibility, the access order of mobile emergency power supplies is determined based on the degree of user load loss on the island and the shortest travel time from the mobile emergency power supply to the island. Islands with greater user load loss and shorter shortest travel time from the mobile emergency power supply to the island are considered to have higher access priority. Furthermore, the target islands for mobile emergency power supply access are determined under the constraint of the number of mobile emergency power supplies.

[0083] Step 4.4: The shortest travel time from the mobile emergency power supply to the target island is taken as the connection time of the mobile emergency power supply.

[0084] Step 4.5: In this embodiment, the maximum number of mobile emergency power supplies that can be called up is set to 2. The mobile emergency power supply adopts a vehicle-mounted emergency power generation device capable of simultaneously outputting active and reactive power.

[0085] Step 4.6: After the mobile emergency power supply is connected to the target island, the AC power flow calculation and cascade failure judgment are re-performed, the active power of each user node is updated, and the road traffic system performance is recalculated according to steps 3.6-3.9, and the power system performance is recalculated according to step 3.5, to obtain the power system performance changes during the post-earthquake emergency phase, such as... Figure 2 As shown in the figure, the average time for the mobile emergency power supply to be transported from the emergency center to the target island and connected is 1.781 hours. Before the mobile emergency power supply was connected, the average performance of the power system was 0.248, and after the connection, the average performance improved to 0.591, which means that the power supply capacity equivalent to 34.3% of the total active power users before the earthquake was restored. In the control scenario where the road traffic system was not damaged by the earthquake, the average time for the mobile emergency power supply to connect to the target island was 0.705 hours. Considering the earthquake damage to the road traffic system, the average connection time for the mobile emergency power supply was extended by 1.076 hours. This shows that the present invention can reflect the constraint effect of road traffic accessibility on the scheduling and connection time of mobile emergency power supplies.

[0086] The fifth step, based on the performance results of the road traffic system and power system during the post-earthquake emergency phase obtained in the fourth step, involves simulating the parallel recovery process of the two systems under the constraints of their interdependence, taking into account the repair priorities, repair durations, and maintenance resource allocation for the damaged viaducts and power system components. This yields the performance curves of the road traffic system and power system over time during the post-earthquake recovery phase. The details are as follows: Step 5.1: Determine the set of damaged viaducts and the set of damaged power system components.

[0087] Step 5.2: Remove each elevated bridge from the road traffic network one by one, calculate the change in the performance of the road traffic system before and after removal, and use the change as an indicator of the importance of the elevated bridge; determine the repair priority of the damaged elevated bridges in descending order of importance.

[0088] Step 5.3: Remove each component in the power system from the grid one by one, calculate the change in power system performance before and after removal, and use the change as an indicator of the importance of the power system components; determine the repair priority of the damaged power system components in descending order of importance.

[0089] Step 5.4: Based on the damage status of each damaged viaduct and damaged power system component, refer to the "Guideline for Seismic Toughness Evaluation of Urban Engineering Systems" (RISN-TG041-2022) to determine the probability distribution parameters of the repair time corresponding to the components with different damage statuses, and use Monte Carlo simulation to generate the repair duration of the damaged viaduct and damaged power system components respectively.

[0090] Step 5.5: The maximum number of maintenance engineering teams is used to consider the limited resource constraints in the recovery process. The maximum number of maintenance engineering teams that can be called up is set for the road traffic system and the power system respectively. Each maintenance engineering team can only execute the maintenance task of the next damaged component according to the repair priority after completing the repair task of the current damaged component.

[0091] Step 5.6: Assign maintenance tasks to the road traffic system maintenance engineering team according to the priority of repairing the damaged viaduct, and determine whether the maintenance work of the viaduct meets the power supply conditions based on the active power of the corresponding user node of the damaged viaduct. When the active power of the corresponding user node is zero, postpone the maintenance work of the damaged viaduct; when the active power of the corresponding user node is not zero, adjust the maintenance duration of the damaged viaduct according to formula (10).

[0092] Step 5.7: Assign repair tasks to the power system maintenance engineering team according to the repair priority of damaged power system components, and use Dijkstra's shortest path algorithm to calculate the shortest travel time from the maintenance center to the power system component to be repaired. When there is at least one passable path between the maintenance center and the power system component to be repaired, the power system component is determined to meet the traffic accessibility conditions for maintenance vehicles, and the arrival time of the maintenance vehicles and the start time of maintenance are determined; when there is no passable path, the maintenance work on the corresponding power system component is postponed until traffic accessibility is restored after the road traffic network is updated.

[0093] Step 5.8: Record the start and end times of maintenance for the damaged viaduct and the damaged power system components, respectively.

[0094] Step 5.9: When any damaged viaduct is repaired, restore the traffic capacity and free-flow speed of the viaduct and its underpass, update the directed graph of the road traffic system, re-perform user equalization flow allocation, update the performance of the road traffic system and the accessibility of the repaired vehicles.

[0095] Step 5.10: When any damaged power system component is repaired, reconnect the power system component to the power system, update the directed graph of the power system, and recalculate the AC power flow and cascade failure judgment; based on the updated active power of the user nodes, redetermine the functional status of the traffic electronic signal lights and the repair duration of the damaged overpass, and update the power system performance.

[0096] Step 5.11: Repeat steps 5.6 through 5.10 until all damaged viaducts and damaged power system components are repaired, and the road traffic system performance is obtained. and power system performance The complete recovery process over time. Results are as follows: Figure 3 and Figure 4 As shown, the average time for the road traffic system to fully recover, considering its dependence on the power system, is 856.50 days; the average time for the road traffic system to recover to 82%, 90%, and 95% of its performance is 1.5 days, 4 days, and 9 days, respectively; the average time for the power system to fully recover, considering its dependence on the road traffic system, is 104 days; the average time for the power system to recover to 80%, 90%, and 95% of its performance is 14.5 days, 22 days, and 38 days, respectively.

[0097] Step 6: Calculate the seismic toughness of the road traffic system and the power system. Details are as follows: Step 6.1: Construct performance curves for the road traffic system and the power system, respectively, with time as the horizontal axis and the performance of the road traffic system and the power system as the vertical axis.

[0098] Step 6.2: Within the control time, integrate the performance curves of the road traffic system and the power system respectively to obtain the seismic toughness of the road traffic system and the seismic toughness of the power system under each earthquake damage scenario.

[0099] Step 6.3: For the 1000 earthquake damage scenarios generated in the second step, execute steps 3 to 6.2 in sequence to obtain the performance change curves of the road traffic system and power system considering interdependence under multiple earthquake damage scenarios and the seismic toughness evaluation results.

[0100] Step 6.4 involves statistically analyzing the evaluation results under 1000 earthquake damage scenarios to obtain the probability distribution and cumulative probability curves of the seismic toughness of the road traffic system and power system considering their interdependence. This ultimately forms the seismic toughness evaluation results for the road traffic-power system considering their interdependence. For example... Figure 5 and Figure 6 As shown, under an earthquake scenario with a PGA of 0.22g, considering the uncertainties in system component damage and repair time, the probability of the seismic toughness of a road traffic system dependent on the power system exceeding 0.870 is 86.6%, and the probability of exceeding 0.970 is 28.3%. Conversely, the probability of the seismic toughness of a power system dependent on the road traffic system exceeding 0.325 is 86.6%, and the probability of exceeding 0.875 is 9.8%. It can be seen that the seismic toughness of a road traffic system dependent on the power system is higher, while the seismic toughness of a power system dependent on the road traffic system is significantly lower. This result can provide a basis for improving the seismic toughness of the interdependent road traffic-power system.

[0101] The embodiments described above are merely illustrative of the implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that, for those skilled in the art, adjustments can be made to the research area, road traffic network scale, power system scale, seismic intensity, vulnerability parameters, number of mobile emergency power supplies, number of maintenance engineering teams, and restoration resource allocation methods without departing from the concept of the present invention, and the resulting equivalent technical solutions should all fall within the protection scope of the present invention.

Claims

1. A method for evaluating the seismic toughness of a road traffic-power system considering interdependence, characterized in that, The method for evaluating the seismic toughness of road traffic-power systems includes the following steps: The first step is to collect relevant data on road traffic systems, power systems, and post-earthquake emergency recovery, construct directed graphs of road traffic systems and power systems, identify the interdependencies between road traffic systems and power systems, and establish a network topology model of the road traffic-power coupled system. The second step involves using seismic vulnerability analysis and Monte Carlo simulation to determine the seismic damage status of road traffic system and power system components, and converting the component damage status into functional degradation to obtain the functional degradation results of the damaged road traffic-power system components after the earthquake. The third step, based on the road traffic-power coupled system network topology model obtained in the first step and the functional degradation results of the damaged road traffic-power system components obtained in the second step, uses AC power flow to simulate the cascading failure of the power system and uses the user balanced distribution model to simulate the traffic flow distribution under the conditions of overpass damage and traffic electronic signal power failure, thus obtaining the power system operating status, power system performance and road traffic system performance during the earthquake absorption phase. The fourth step, based on the performance of the road traffic system, the operating status and performance of the power system during the earthquake absorption phase obtained in the third step, and the dependency relationship of the mobile emergency power supply needing to utilize the road traffic system to carry out emergency actions, determines the island to which the mobile emergency power supply can be connected and the time required for connection, and updates the operating status, performance of the power system and the performance of the road traffic system after the mobile emergency power supply is connected to the island, thus obtaining the performance results of the road traffic system and the power system during the post-earthquake emergency phase. The fifth step, based on the performance results of the road traffic system and power system in the post-earthquake emergency phase obtained in the fourth step, is to simulate the parallel recovery process of the two systems under the constraints of the interdependence between the road traffic system and the power system, according to the repair priority, repair duration and maintenance resource allocation of the damaged viaduct and damaged power system components, and to obtain the performance curves of the road traffic system and power system over time in the post-earthquake recovery phase. The sixth step involves constructing resilience curves for the road traffic system and the power system based on the system performance changes obtained in the third to fifth steps during the earthquake absorption phase, the post-earthquake emergency phase, and the post-earthquake recovery phase. It also involves calculating the seismic resilience evaluation results of the interdependent road traffic-power system.

2. The method for evaluating the seismic toughness of a road traffic-power system considering interdependence, as described in claim 1, is characterized in that... The first step is as follows: Step 1.1: Collect basic data of the road traffic system and construct a directed graph of the road traffic system: （1） In the formula, For road traffic network; It is the set of nodes in a road traffic network; It is the edge set in the road traffic network; Step 1.2: Collect basic data of the power system and construct a directed graph of the power system: （2） In the formula, For power grids; A set of nodes in a power network; For the power network edge set; Step 1.3: Collect power supply information for traffic electronic signals, the correspondence between the elevated bridge and adjacent user nodes, the geographical coordinates of mobile emergency power supplies and maintenance vehicles, and identify the interdependencies between the road traffic system and the power system, including: during the earthquake absorption phase, the functional status of the electronic signals in the road traffic system requires power supply from the power system; during the post-earthquake emergency phase, mobile emergency power supplies need to utilize the road traffic system to carry out emergency operations; during the post-earthquake recovery phase, maintenance equipment for the damaged elevated bridge requires power supply from the power system, and vehicles responsible for repairing damaged electrical components need to utilize the road traffic system to carry out maintenance operations. Step 1.4, based on the directed graph of the road traffic network Directed graph of power network Based on the interdependence between the road traffic system and the power system, a network topology model of the road traffic-power coupled system is established.

3. The method for evaluating the seismic toughness of a road traffic-power system considering interdependence, as described in claim 2, is characterized in that... In the first step: In step 1.1, the basic data includes geographic coordinates and attribute data. The geographic coordinates include road intersections, viaducts, and traffic electronic signals. The attribute data includes road grade, number of road lanes, free-flow speed, road capacity, and traffic demand. Road intersections and viaducts are abstracted as road traffic network nodes, and road segments connecting road intersections or viaducts are abstracted as road traffic network edges. In step 1.2, the basic data includes the geographical coordinates of power plants, substations and users, the resistance, reactance and susceptance of transmission and distribution lines, the active and reactive power limits, operating voltage limits and generation costs of generators, and the active and reactive power of users; power plants, substations and users are abstracted as power network nodes, and transmission and distribution lines are abstracted as power network edges.

4. The method for evaluating the seismic toughness of a road traffic-power system considering interdependence, as described in claim 3, is characterized in that... The second step is specific to: Step 2.1: Based on the seismic intensity and the vulnerability functions of the road traffic system and power system components shown in formula (3), calculate the probability of the elevated bridge, power plant, substation and transmission and distribution line exceeding each damage state respectively; （3） In the formula, These are parameters required for the project. This represents the limit state threshold corresponding to different damage and failure levels. i =1, 2, 3, 4, specifically minor injuries. LS 1. Moderate injury LS 2. Severe injury LS 3 and complete destruction LS 4. The extreme state thresholds corresponding to the four damage levels; It refers to the intensity of earthquake motion; It is the standard normal distribution function; For the first i The median value of the ground motion intensity corresponding to the damage level; It is the logarithmic standard deviation of the fragility function; Step 2.2: Based on the probability of each component exceeding each damage state obtained in Step 2.1, Monte Carlo simulation is used to randomly determine the damage state of each viaduct, power plant, substation and transmission and distribution line to form an earthquake damage scenario; Monte Carlo simulation is repeated to obtain a set of no less than 1000 earthquake damage scenarios considering the uncertainty of system component damage. Step 2.3: Based on the correspondence between the damage status of the viaduct and the functional decline, the damage status of the viaduct is converted into the percentage decrease in the traffic capacity and free flow velocity of the viaduct and its underpass. The travel time of the damaged viaduct and underpass is calculated using the BPR road resistance function shown in formula (4). This results in a decline in the functionality of elevated bridges and underpasses. （4） In the formula, Road sections with zero traffic flow The travel time is calculated by dividing the road segment length by the free-flow velocity; , Each is a road segment Traffic flow and traffic capacity; The first hindrance coefficient, The second resistance coefficient needs to be calibrated based on the relationship between traffic volume and travel time under different flow levels of the local road traffic system. Step 2.4: When power plants, substations, and transmission and distribution lines are severely damaged or completely destroyed, they cannot function, i.e., their functionality decreases by 100%; thus, the functional degradation results of the power system components are obtained. The functional degradation results of the elevated bridges and underpasses obtained in steps 2.5 and 2.3, together with the functional degradation results of the power system components obtained in step 2.4, constitute the functional degradation results of the post-earthquake damaged road traffic-power system components.

5. The method for evaluating the seismic toughness of a road traffic-power system considering interdependence, as described in claim 3, is characterized in that... In step 2.3, the correspondence between the damage state of the viaduct and the functional decline is shown in Table 1: Table 1: Correspondence between damage status and functional decline of elevated bridges 。 6. The method for evaluating the seismic toughness of a road traffic-power system considering interdependence, as described in claim 5, is characterized in that... The third step is specifically as follows: Step 3.1, based on the directed graph of the power system obtained in Step 1.2 Based on the power system component functional degradation results obtained in step 2.4, identify power system islands and perform cascade failure analysis based on AC power flow for each island; for each island, determine whether generator nodes and user nodes exist simultaneously. If a generator node or user node is missing, the power system island is deemed to have lost its power supply function; If both generator nodes and user nodes exist, the generator node with the largest generating capacity is selected as the relaxation node, and AC power flow calculation is performed. Step 3.2: If the AC power flow calculation fails to converge, convert the user node load in the power system island into dispatchable load, and use the AC optimal power flow calculation to meet the minimum load reduction required to meet the power flow convergence condition; adjust the user power, generator output and generator terminal voltage according to the AC optimal power flow calculation results, and recalculate the AC power flow; if the AC optimal power flow or the adjusted AC power flow still fails to meet the power flow convergence condition, then the power system island is determined to have lost its power supply function. Step 3.3: When the AC power flow calculation converges, sequentially determine whether the power system islanding meets the frequency stability constraint, generator terminal voltage constraint, bus voltage constraint, and branch apparent power constraint; when the system frequency deviation caused by active power imbalance exceeds the allowable range, perform low-frequency load shedding or over-frequency generator disconnection operation; when the generator reactive power exceeds the over-excitation limit or under-excitation limit, convert the corresponding generator node from a PV node to a PQ node and fix the reactive power at the corresponding limit; when the bus voltage is lower than the preset lower voltage limit, gradually reduce the active power and reactive power of the corresponding user node according to the preset ratio; when the branch apparent power exceeds the long-term allowable power of the branch, disconnect the corresponding branch. Step 3.4: Update the directed graph of the power system based on the simulation results of Step 3.3, re-identify the power system islands and repeat Steps 3.1 to 3.3 until the frequency stability constraints, generator terminal voltage constraints, bus voltage constraints and branch apparent power constraints of each power system island are satisfied, or the power system island is determined to have lost its power supply function, and obtain the operating status of each power system island after cascading failure; Step 3.5: Calculate the time based on the active power of each user node after the cascading failure. t Power system performance: （5） In the formula, yes t Power system performance at any given time; It is a set of user nodes in the power system; yes t User nodes at any time The active power; User nodes before the earthquake occurred The active power; Step 3.6: Based on the dependence of the functional state of electronic traffic lights in the road traffic system on the power supply of the power system established in Step 1.3, determine the probability that the electronic traffic lights will receive power supply based on the active power ratio of user nodes adjacent to the traffic electronic traffic lights before and after the earthquake. （6） In the formula, It is an electronic traffic light intersection The probability of obtaining a power supply; and It is an electronic traffic light intersection User nodes that provide electricity In the moments before the earthquake t 0 and post-earthquake moments t The active power; Generate random numbers that follow a uniform distribution in the interval [0,1], and combine this with the probability of obtaining power supply from electronic signal lights. The functional state of electronic traffic lights is determined by Bernoulli distribution; Step 3.7: Based on the functional status of the traffic electronic signal lights, use the intersection delay model to determine the passage delay of normally signal-controlled intersections and malfunctioning signal-controlled intersections, and add the intersection passage delay to the passage time of the road segment ending at the intersection. Step 3.8, based on the directed graph of the road traffic system obtained in Step 1.1 The second step yields the results of the road traffic system function degradation and the intersection delay model from step 3.

7. A user equilibrium flow distribution model is then constructed to solve the traffic flow distribution and road travel time under earthquake damage scenarios. Step 3.9: Calculate the time based on the user balanced traffic distribution results. t Road traffic system performance: （7） In the formula, For a moment t The performance of the road traffic system; The number of nodes in the road traffic network; and The moments before the earthquake t 0 and post-earthquake moments t nodes To node The shortest travel time.

7. The method for evaluating the seismic toughness of a road traffic-power system considering interdependence, as described in claim 6, is characterized in that... In the third step: In step 3.2: the AC power flow convergence condition means that the AC power flow calculation obtains an effective power flow solution within a preset maximum number of iterations, and the active power imbalance of all bus nodes and the reactive power imbalance of all PQ bus nodes are not greater than the preset power flow convergence threshold. In step 3.3: the allowable range refers to the system frequency variation range pre-set according to the requirements for safe and stable operation of the power system; the overexcitation limit refers to the maximum reactive power that the generator can continuously output to the power system under the current active power output and terminal voltage conditions, limited by the excitation system capacity, stator current and rotor excitation current allowable values; the underexcitation limit refers to the lower limit of reactive power corresponding to the maximum reactive power that the generator can continuously absorb from the power system under the current active power output and terminal voltage conditions, limited by the generator's stable operation capability, stator end heating and excitation system regulation capability; the preset voltage lower limit refers to the minimum allowable operating voltage of the busbar determined in advance according to the busbar voltage level, power system operation mode, user power supply requirements and low voltage stability requirements.

8. The method for evaluating the seismic toughness of a road traffic-power system considering interdependence, as described in claim 7, is characterized in that... The fourth step specifically involves: Step 4.1: Based on the operating status of each island in the power system obtained in Step 3.4, identify power system islands that simultaneously contain user nodes and experience user losses, and form a candidate island set for mobile emergency power supply to be connected. Step 4.2: Using the post-earthquake travel time of each road segment obtained from the user balanced flow distribution model in Step 3.9 as the path weight, the Dijkstra shortest path algorithm is used to calculate the shortest travel time from the mobile emergency power supply to each candidate island access location; when the shortest travel time from the mobile emergency power supply to the candidate island access location is a finite value, the candidate island is determined to have traffic accessibility. When the shortest travel time is infinite, the candidate island is determined to be not accessible by traffic. Step 4.3: Among the candidate islands with traffic accessibility, determine the access order of mobile emergency power supplies based on the degree of load loss of users on the island and the shortest travel time from the mobile emergency power supply to the island. Islands with a higher degree of user load loss and a shorter shortest travel time from the mobile emergency power supply to the island are considered to have a higher access priority. Under the constraint of the number of mobile emergency power supplies, determine the target islands for mobile emergency power supply access. Step 4.4: The shortest travel time from the mobile emergency power supply to the target island is taken as the connection time of the mobile emergency power supply; Step 4.5, connect the mobile emergency power supply to the target island according to the following active and reactive power output constraints: （8） （9） In the formula, and These are the active power and reactive power output by the mobile emergency power supply, respectively. and These are the maximum active power and maximum reactive power that the mobile emergency power supply is allowed to output; Step 4.6: After the mobile emergency power supply is connected to the target island, the AC power flow calculation and cascade failure judgment are re-performed, the active power of each user node is updated, and the performance of the road traffic system is recalculated according to steps 3.6-3.9, and the performance of the power system is recalculated according to step 3.5, so as to obtain the performance results of the road traffic system and power system in the post-earthquake emergency stage.

9. A method for evaluating the seismic toughness of a road traffic-power system considering interdependence, as described in claim 8, is characterized in that... The fifth step is specifically as follows: Step 5.1: Determine the set of damaged viaducts and the set of damaged power system components; Step 5.2: Remove each elevated bridge from the road traffic network one by one, calculate the change in the performance of the road traffic system before and after removal, and use the change as an indicator of the importance of the elevated bridge; determine the repair priority of the damaged elevated bridges in descending order of importance. Step 5.3: Remove each component in the power system from the grid one by one, calculate the change in power system performance before and after removal, and use the change as an indicator of the importance of the power system components; determine the repair priority of the damaged power system components in descending order of importance. Step 5.4: Based on the damage status of each damaged viaduct and damaged power system component, determine the probability distribution parameters of the repair time corresponding to the component with different damage status, and use Monte Carlo simulation to generate the repair duration of the damaged viaduct and damaged power system component respectively. Step 5.5: Consider the limited resource constraints during the recovery process by using the maximum number of maintenance engineering teams. Set the maximum number of maintenance engineering teams that can be called up for the road traffic system and the power system respectively. Each maintenance engineering team can only execute the maintenance task of the next damaged component according to the repair priority after completing the repair task of the current damaged component. Step 5.6: Assign maintenance tasks to the road traffic system maintenance engineering team according to the priority of repairing the damaged viaduct, and determine whether the maintenance work of the viaduct meets the power supply conditions based on the active power of the corresponding user node of the damaged viaduct. When the active power of the corresponding user node is zero, the maintenance work on the damaged viaduct is postponed; when the active power of the corresponding user node is not zero, the maintenance duration of the damaged viaduct is adjusted according to the ratio of the active power of the user node before and after the earthquake, and the adjustment formula is as follows: （10） In the formula, Indicates the damaged viaduct bi The degree of dependence of the repair work on the power system is rated on a scale of 0 to 1. The higher the value, the greater the dependence of the repair work on the power system; It is an elevated bridge bi Repair time assuming sufficient power supply; It is an elevated bridge under the consideration of insufficient power supply. bi Repair time; Step 5.7: Assign repair tasks to the power system maintenance engineering team according to the repair priority of the damaged power system components, and use Dijkstra's shortest path algorithm to calculate the shortest travel time from the maintenance center to the power system component to be repaired. When there is at least one passable path between the maintenance center and the power system component to be repaired, the power system component is determined to meet the traffic accessibility conditions for maintenance vehicles, and the arrival time of the maintenance vehicle and the start time of maintenance are determined; when there is no passable path, the maintenance work on the corresponding power system component is postponed until traffic accessibility is restored after the road traffic network is updated. Step 5.8: Record the start and end times of maintenance for the damaged viaduct and the damaged power system components, respectively. Step 5.9: When any damaged viaduct is repaired, restore the traffic capacity and free flow speed of the viaduct and its underpass, update the directed graph of the road traffic system, re-perform user equalization and traffic allocation, update the performance of the road traffic system and the traffic accessibility of the repair vehicles. Step 5.10: When any damaged power system component is repaired, reconnect the power system component to the power system, update the directed graph of the power system, and recalculate the AC power flow and cascade failure judgment; based on the updated active power of the user nodes, redetermine the functional status of the traffic electronic signal lights and the repair duration of the damaged overpass, and update the power system performance at the same time. Step 5.11: Repeat steps 5.6 through 5.10 until all damaged viaducts and damaged power system components are repaired, and the road traffic system performance is obtained. and power system performance The complete recovery process that changes over time.

10. The method for evaluating the seismic toughness of a road traffic-power system considering interdependence, as described in claim 9, is characterized in that... The sixth step is specifically as follows: Step 6.1: Construct performance curves for the road traffic system and the power system, respectively, with time as the horizontal axis and the performance of the road traffic system and the power system as the vertical axis. Step 6.2: Within the control time, integrate the performance curves of the road traffic system and the power system respectively to calculate the seismic toughness of the road traffic system and the power system. （11） （12） In the formula, To enhance the seismic resilience of road traffic systems that take into account the impact of power system dependence; Seismic toughness of power systems taking into account the dependence of road traffic systems; Control time for resilience evaluation; t 0 represents the time when the earthquake occurred; for t The power system performance at any given time is calculated according to formula (5); for t The performance of the road traffic system at any given time is calculated according to formula (7); Step 6.3: For the multiple earthquake damage scenarios generated in the second step, execute steps 3 to 6.2 in sequence to obtain the performance change curves and seismic toughness evaluation results of the road traffic system and power system considering interdependence under multiple earthquake damage scenarios; Step 6.4: Statistical analysis is performed on the evaluation results under multiple earthquake damage scenarios to obtain the probability distribution and cumulative probability curve of the seismic toughness of the road traffic system and power system considering interdependence, and finally the evaluation results of the seismic toughness of the road traffic-power system considering interdependence are formed.

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