A model for analyzing spatio-temporal evolution of cascading failures in urban power-communication system

Abstract

The application discloses a kind of urban power-communication system cascading failure spatio-temporal evolution analysis model, belong to critical infrastructure security technical field.The model includes interdependent network construction module, initial disturbance scene design module, coupling cascading iteration simulation module and spatio-temporal trajectory analysis and output module.The application explicitly models power to communication power supply dependence and communication to power control dependence, uses outer-inner double-layer iteration structure, simultaneously depicts layer failure propagation and cross-layer cascading / inhibition effect, can complete tracking the multi-stage time evolution process and spatial diffusion path of cascading failure.The application is based on real geographic data to construct network, generates spatio-temporal trajectory dataset containing multidimensional performance index, can effectively solve the problem that prior art only pays attention to final failure state, mechanism is not complete, provides scientific support for vulnerability assessment and resilience of urban power-communication coupled infrastructure.

Description

Technical Field

[0001] This invention belongs to the field of urban critical infrastructure security and complex network cascading failure analysis technology, specifically involving a simulation modeling and spatiotemporal evolution analysis method for cascading failures of interdependent power-communication systems. It can be used for vulnerability assessment, resilience enhancement planning, and disaster emergency response decision-making for urban power and communication coupled infrastructure. Background Technology

[0002] With the rapid advancement of urbanization and digital transformation, urban energy, communication, transportation, emergency response, and public service systems are facing increasing pressure, and the functional interdependence among critical infrastructures is constantly strengthening. In particular, the coupling and interdependence between power infrastructure and communication infrastructure are deepening. Power networks rely on communication networks for monitoring and control, while communication infrastructure relies on electricity to maintain the operation of base stations, aggregation nodes, and core facilities. Due to this two-way dependency, local disturbances in one infrastructure can propagate across the system and trigger cascading failures in another infrastructure. These cascading failures do not occur instantaneously but evolve over time and spread between interconnected components and spatial locations, thus forming complex spatiotemporal failure modes (Zhao et al., 2016; Tong et al., 2026). Understanding the spatiotemporal evolution of cascading failures in interdependent power and communication infrastructures is of great significance for improving the security and resilience of interdependent infrastructure systems.

[0003] Numerous studies have focused on cascading failures in power systems, communication systems, and interdependent networks. Existing research indicates that network interdependence significantly amplifies the impact of disturbances, and the resilience of critical infrastructure cannot be fully understood by examining individual systems in isolation (Tong et al., 2025). However, most existing models still simplify the interaction between power and communication systems in at least two ways. First, many studies primarily focus on failure propagation, while neglecting the reverse mechanisms that may inhibit or mitigate further cascading (Guo et al., 2024). Second, many assessments emphasize the final failure state or overall robustness indicators (Xue and Liang, 2025; Li and Zhang, 2025), but fail to reveal the multi-stage failure process in which disturbances spread, interact, and tend to stabilize in time and geospatial dimensions. Therefore, the spatiotemporal evolution of cascading failures in interdependent power and communication infrastructures requires further investigation. Summary of the Invention

[0004] Purpose of the invention

[0005] To address the aforementioned issues, this invention proposes a simulation model for cascading failures in interdependent power-communication systems. This model explicitly represents the bidirectional coupling between the power grid and the communication network, simultaneously characterizing cross-system cascading effects and bidirectional suppression effects during the failure evolution process. Unlike methods that only focus on the final outcome, the proposed method can track the coupled cascading failure process at multiple stages and record corresponding system performance changes at discrete time steps. This process-oriented design can generate large-scale time-series datasets to reveal how failures arise, propagate, interact, and tend to stabilize. Furthermore, the framework is built based on real infrastructure data from the same geographical region, enabling the modeled interdependencies to better reflect actual spatial co-location relationships and operational performance.

[0006] Technical solution

[0007] The main innovations of this invention are summarized as follows: A bidirectional cascading failure framework for interdependent power-communication infrastructure is proposed. This framework couples a DC power flow overload tripping model with a communication connectivity-capacity rerouting model, and represents cross-layer interactions through power supply dependence from power to communication and control loss feedback from communication to power. A spatiotemporal trajectory analysis model is established to characterize the evolution of the coupled cascading process. By recording the system state at each iteration level, this model can capture cascading stage transitions and performance degradation paths, not just the final failure state. This framework is implemented based on real power and communication infrastructure data from the same geographical region, thereby improving the realism of the modeled interdependencies and the practical reference value of the results. A large-scale time-series simulation dataset is generated from the coupled cascading process, providing detailed time-series observations of failure development and performance degradation for subsequent analysis.

[0008] The specific technical solution adopted is as follows: a spatiotemporal evolution analysis model for cascaded failures in urban power-communication systems, including a mutually dependent network construction module, an initial disturbance scenario design module, a coupled cascaded iterative simulation module, and a spatiotemporal trajectory analysis and output module. The mutually dependent network construction module is used to construct the power network layer and the communication network layer based on real infrastructure data from the same geographical region, and establish a bidirectional cross-layer dependency mapping between the two layers. The initial disturbance scenario design module is used to generate multiple initial failure scenarios on the power side and the communication side, including different failure component types, different failure modes, and different failure scales. The coupled cascaded iterative simulation module adopts an outer-inner two-layer iterative structure, including an inner loop unit in the power layer, an inner loop unit in the communication layer, and a cross-layer outer loop coordination unit. The inner loop unit in the power layer simulates the overload tripping cascade process of the power system based on a DC power flow model, the inner loop unit in the communication layer simulates the congestion failure process of the communication system based on a connectivity-capacity rerouting model, and the cross-layer outer loop coordination unit realizes the state interaction and coupled update between the two layers until the system reaches a stable state. The spatiotemporal trajectory analysis and output module is used to record the system state at each time step during the simulation, generate a cascaded failure spatiotemporal trajectory dataset, and output multi-dimensional performance indicators of the power layer, communication layer, and cross-layer coupling.

[0009] Further, the specific workflow of the interdependent network construction module is as follows: Power network extraction is performed, converting power infrastructure data into a graph model containing bus-type power nodes and power branches. Bus-type power nodes include substation buses, and power branches include lines and transformers. Spatial coordinates, rated voltage levels, and role information are assigned to each bus, and per-unit reactance and thermal capacity limits are assigned to each branch. A balancing bus is automatically selected. Communication network extraction is performed, converting communication infrastructure data into an undirected graph model containing communication nodes and logical fiber optic connections. Communication nodes are divided into sites, aggregation nodes, and core nodes. Route length weights are assigned to each logical fiber optic connection, and demand weights are assigned to each site node. Cross-layer coupling mapping is performed, establishing a power-to-communication dependency mapping relationship from each communication facility to its corresponding power supply bus based on geographical proximity and actual power supply relationships. Simultaneously, based on geographical proximity and control service requirements, one or more candidate communication site groups are specified for each power bus requiring communication support, completing the construction of the communication-to-power dependency mapping.

[0010] Furthermore, the initial disturbance scenario design module supports two types of initial failure scenarios: power-side failure and communication-side failure. Power-side failure uses transmission branches as the initial failure component and is divided into two modes: locally adjacent failure and spatially dispersed failure, with a failure scale of k={1,2,5,10,20,50}. Communication-side failure uses stations and cables as the initial failure components and is also divided into two modes: locally adjacent failure and spatially dispersed failure, with a failure scale of k={1,2,5,10,20,50}.

[0011] Furthermore, the workflow of the power layer internal circulation unit is as follows: solving the core equations of DC power flow on the connected components including the balancing bus: (Yan et al., 2014), among which Here is the nodal susceptance matrix. The phase angle vector of the busbar. Inject a vector for the net active power of the nodes. Calculate the power flow value for each active branch, which is obtained by dividing the phase angle difference between the two buses at the branch ends by the per-unit reactance of the branch and taking the absolute value. Compare the calculated branch power flow value with the per-unit power flow limit of the branch. When the ratio of the branch power flow value to the per-unit power flow limit is greater than the overload trip tolerance factor (this factor is greater than 1), the branch is determined to be overloaded and removed from the network. Repeat the above process until no new overloaded branches are detected.

[0012] Furthermore, the workflow of the communication layer inner loop unit is as follows: Construct the currently running communication subgraph, excluding nodes without power supply and backup power, as well as previously failed communication links and core nodes. Based on baseline anchoring routing rules, reassign communication paths to each active site; if no feasible path exists, the site is considered disconnected. Calculate the total traffic of all active sites on each communication edge and core node to obtain the current load of the communication edge and the current load of the core node, and calculate the overload ratio of the communication edge and the core node, where the overload ratio is the ratio of the current load to the rated capacity. When the overload ratio of the communication edge exceeds the communication link overload threshold (which is greater than 1) or the overload ratio of the core node exceeds the core node overload threshold (which is greater than 1), determine that the corresponding link or core node has failed and remove it from the subgraph (Ren et al., 2018). Repeat the above process until no new failures occur or the preset maximum number of inner loop iterations is reached.

[0013] Furthermore, the workflow of the cross-layer outer loop coordination unit is as follows: During the outer loop iteration process, the power layer continuously provides the communication layer with a set of buses currently in a powered state. Based on the mapping relationship from power to communication, it is determined whether the power supply bus corresponding to each communication facility is powered; if the power supply bus is powered, or the communication facility has a usable backup power supply, then the communication facility is determined to be in an operating state (Parandehgheibi, Modiano, and Hay, 2014). After the communication layer inner loop is solved, the service status of each communication station is obtained, and it is determined whether the station is normally receiving communication services. Based on the mapping relationship from communication to power, it is determined whether at least one station in the candidate communication station group corresponding to each power bus is in a normal service state; if not, the communication control of the bus is determined to be insufficient. For all power branches connected to the bus with insufficient communication control, their power flow limit is multiplied by the communication control derating factor for adjustment, where the value range of the communication control derating factor is greater than 0 and less than or equal to 1. The power layer inner loop is resolved using the adjusted branch limit, and the set of powered buses is updated. The process continues iteratively until the states of the power and communication systems no longer change, or until the preset maximum number of outer loop iterations is reached.

[0014] Furthermore, the system status recorded by the spatiotemporal trajectory analysis and output module covers three dimensions: power layer, communication layer, and cross-layer coupling. Power layer recorded parameters include the number of surviving buses, the number of surviving branches, the cumulative number of failed buses, the cumulative number of failed branches, and the maximum branch overload ratio. Communication layer recorded parameters include the number of operating communication facilities, the number of serviced sites, the communication service ratio, the maximum communication edge overload ratio, and the maximum core node overload ratio. Cross-layer coupling recorded parameters include the number of communication facilities that lost mains power due to power supply bus failure and the number of power buses affected by communication control failure.

[0015] Beneficial effects

[0016] Compared with existing technologies, this invention has the following advantages: First, it establishes an explicit bidirectional coupling mechanism, simultaneously modeling the power supply dependency from power to communication and the control dependency from communication to power. It introduces communication control derating effects and backup power mitigation effects, comprehensively depicting the positive cascading and negative suppression effects of the coupled system, significantly improving the realism of simulation results. Second, it possesses spatiotemporal evolution trajectory tracking capabilities, employing an outer-inner dual-layer iterative structure to record system state changes at each time step. This clearly presents the multi-stage evolution process of cascading failure (initial adjustment, dominant coupling, and final stability) and spatial diffusion paths, overcoming the limitation of existing technologies that only focus on the final state. Third, it adopts a real data-driven modeling mode, constructing a network based on real power and communication infrastructure data from the same geographical region. This ensures that cross-layer dependencies conform to actual spatial co-location and operational logic, providing direct engineering reference value for the analysis results. Fourth, it enables multi-dimensional quantitative assessment, generating a large-scale time-series dataset containing power layer, communication layer, and cross-layer coupling indicators. This supports quantitative analysis of the vulnerability of coupled systems from different dimensions, providing a comprehensive basis for resilience planning and emergency decision-making. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the overall process framework of the spatiotemporal evolution analysis model for cascaded failures of urban power-communication systems described in this invention.

[0018] Figure 2 A visualization of the coupled system state when the outer loop iteration is 0;

[0019] Figure 3 Distribution of key performance indicators under different initial branch failure scales on the power side;

[0020] Figure 4 This is a diagram of cross-layer interactions under the initial failure scenario on the power side.

[0021] Figure 5 Distribution of key performance indicators under different initial failure scales on the communication side;

[0022] Figure 6 This is a diagram of cross-layer interaction relationships under the initial failure scenario of the communication side. Detailed Implementation

[0023] The present invention will be further described below with reference to embodiments.

[0024] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of each core module of the present invention will be clearly and completely described below by way of embodiments. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the described embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0025] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0026] This embodiment provides a specific implementation of a spatiotemporal evolution analysis model for cascaded failures in urban power-communication systems. Taking a certain urban area as the research region, the effectiveness of the model is verified.

[0027] Step 1: Building an Interdependent Power-Communication Network

[0028] Data preprocessing was performed, with power network data sourced from the Open Infrastructure Map and communication network data from the ACCC Mobile Infrastructure Report. In ArcGIS, data was cropped and spatially aligned based on a unified coordinate reference system and the Greater Geelong area boundary to ensure both network layers describe the same geographic region. Power network construction was then undertaken, extracting the region's transmission and distribution networks, including 220kV upstream connections, a 66kV secondary transmission backbone, and 22kV distribution branches. A power network graph model was constructed, with substations and distribution transformers as bus nodes, and power lines and transformers as branches. Per-unit reactance and thermal capacity limits were assigned to each branch, and balancing buses were automatically selected based on power station priority, voltage level, and graph connectivity. Communication network construction was also carried out, integrating mobile site records and switching center location data from Telstra, Optus, and TPG. After merging co-located facilities, wireless sites and a core switching center were obtained. An undirected graph model of the communication network was constructed, including sites, aggregation nodes, and core nodes, as well as logical fiber optic connections connecting each node. Route length weights were assigned to each edge, and site nodes used unit demand weights. Cross-layer coupling mapping is completed. Based on geographical proximity, each communication facility is mapped to the nearest power bus with power supply capability, realizing the dependency binding from power to communication. Three geographically nearest communication sites are designated as candidate control groups for each substation bus. As long as any one of the sites is in normal service, the bus can maintain communication control, realizing the dependency binding from communication to power.

[0029] Step 2: Initial Disturbance Scenario Design

[0030] This embodiment designs two sets of comparative experiments. The power-induced failure experiment uses the transmission branch as the initial failure component and sets two failure modes: local adjacent failure (k=2,5,10,20,50) and spatially dispersed failure (k=1,2,5,10,20,50). The communication-induced failure experiment uses the communication station and cable as the initial failure components and sets two failure modes: local adjacent failure (k=2,5,10,20,50) and spatially dispersed failure (k=1,2,5,10,20,50).

[0031] Table 1. Initial failure categories and group sizes in batch experiments.

[0032] Infrastructure layer Initial failure component Initial Failure Mode Initial failure size electricity branch road Local adjacent failure Spatial Dispersion Failure communication Site Local adjacent failure Spatial Dispersion Failure cable Local adjacent failure Spatial Dispersion Failure

[0033] Step 3: Coupled Cascade Iterative Simulation

[0034] In this embodiment, the core parameters of the model are set as follows: overload trip tolerance coefficient α=1.2, communication link overload threshold θ_E=1.5, core node overload threshold θ_C=1.3, communication control derating coefficient η_ctrl=0.6, maximum number of outer loop iterations is 10, and maximum number of inner loop iterations is 20.

[0035] Taking the initial disturbance of two randomly shutting down transmission branches on the power side as an example, the simulation process is as follows: the outer loop iteration 0 is the initial adjustment stage, in which the two initially failed transmission branches are removed, and the power layer inner loop solves the core equations of DC power flow. The calculation showed that the ratio of the power flow value to the limit for 3 branches exceeded 1.2, indicating overload tripping, and the set of energized buses was updated. Based on the initial energized bus state, the communication layer calculated that 12 communication sites lost mains power supply, but continued to operate due to the availability of backup power, with a communication service ratio of 100%. In the outer loop iteration 1, which is the dominant coupling cascade stage, the updated set of energized buses from the power layer was passed to the communication layer, causing 8 communication sites without backup power to fail. The inner loop of the communication layer performed rerouting, causing the overload ratio of 2 fiber optic links to exceed 1.5, indicating congestion failure, and the communication service ratio dropped to 87%. Insufficient communication control caused 5 power buses to lose control support, and the power flow limit of the corresponding branches was reduced to 60% of the original value. The power layer re-solved the DC power flow and detected overload tripping of 4 more branches, further reducing the number of energized buses. The second iteration of the outer loop is the final stable stage, where the state updates of the power layer and the communication layer no longer trigger new failures, and the system reaches a stable state; the final survival rate of the power system bus is 72%, and the communication service rate is 68%.

[0036] Step 4: Spatiotemporal Trajectory Analysis and Result Output

[0037] The system states of all outer and inner loops during the simulation are recorded, generating a cascaded failure spatiotemporal trajectory dataset, and outputting simulation performance indicators from multiple dimensions. At the power layer level, a total of 11 buses and 12 branches failed, with the maximum branch overload ratio being 1.45. At the communication layer level, 92 communication facilities are in operation, serving 72 sites, with a communication service ratio of 67.9%, and the maximum edge overload ratio being 1.62. At the cross-layer coupling level, 21 communication facilities lost mains power due to power outages, and 7 power buses were affected by communication control failures.

[0038] Batch simulation results show that under medium initial disturbance scale (k=5-10), the uncertainty of cascading failure results is the greatest, which is the key focus range for resilience planning; the impact of power-side disturbances on communication services is significantly greater than the impact of communication-side disturbances on the power system, exhibiting an asymmetric cross-layer effect; the feedback impact of communication cable failure on the power system is stronger than that of site failure, because cable failure will lead to a wider range of communication connectivity loss.

[0039] This embodiment is only a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art can adjust the model parameters, noise scheduling parameters, loss function weighting coefficients, etc., according to actual detection needs. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A spatiotemporal evolution analysis model for cascaded failures in urban power-communication systems, characterized in that, The system comprises an interdependent network construction module, an initial disturbance scenario design module, a coupled cascade iterative simulation module, and a spatiotemporal trajectory analysis and output module. The interdependent network construction module is used to construct the power network layer and the communication network layer based on real infrastructure data from the same geographical region, and establish a bidirectional cross-layer dependency mapping between the two layers. The initial disturbance scenario design module is used to generate various initial failure scenarios for the power and communication sides, including different failure component types, different failure modes, and different failure scales. The coupled cascade iterative simulation module adopts an outer-inner two-layer iterative structure, including an inner loop unit for the power layer, an inner loop unit for the communication layer, and a cross-layer outer loop coordination unit. The inner loop unit for the power layer simulates the overload tripping cascade process of the power system based on a DC power flow model, the inner loop unit for the communication layer simulates the congestion failure process of the communication system based on a connectivity-capacity rerouting model, and the cross-layer outer loop coordination unit realizes the state interaction and coupled update between the two layers until the system reaches a stable state. The spatiotemporal trajectory analysis and output module is used to record the system state at each time step during the simulation, generate a cascaded failure spatiotemporal trajectory dataset, and output multi-dimensional performance indicators of the power layer, communication layer, and cross-layer coupling.

2. The analytical model according to claim 1, characterized in that, The specific workflow of the interdependent network construction module is as follows: Power network extraction is performed, converting power infrastructure data into a graph model containing bus-type power nodes and power branches. Spatial coordinates, rated voltage levels, and role information are assigned to each bus, and per-unit reactance and thermal capacity limits are assigned to each branch. A balancing bus is automatically selected. Communication network extraction is performed, converting communication infrastructure data into an undirected graph model containing communication nodes and logical fiber optic connections. Communication nodes are divided into sites, aggregation nodes, and core nodes. Route length weights are assigned to each logical fiber optic connection, and demand weights are assigned to each site node. Cross-layer coupling mapping is performed, establishing a power-to-communication dependency mapping relationship from each communication facility to its corresponding power supply bus based on geographical proximity and actual power supply relationships. Based on geographical proximity and control service requirements, one or more candidate communication site groups are specified for each power bus requiring communication support, completing the construction of the communication-to-power dependency mapping.

3. The analytical model according to claim 1, characterized in that, The initial disturbance scenario design module supports two types of initial failure scenarios: power-side failure and communication-side failure. Power-side failure uses transmission branches as the initial failure component and is divided into two modes: locally adjacent failure and spatially dispersed failure, with a failure scale of k={1,2,5,10,20,50}. Communication-side failure uses stations and cables as the initial failure components and is also divided into two modes: locally adjacent failure and spatially dispersed failure, with a failure scale of k={1,2,5,10,20,50}.

4. The analytical model according to claim 1, characterized in that, The workflow of the power layer internal circulation unit is as follows: Solve the core equation of DC power flow on the connected component including the balancing bus, calculate the power flow value of each active branch, and compare it with the per-unit power flow limit of that branch. When the ratio of the branch's power flow value to the per-unit power flow limit is greater than the overload trip tolerance factor, the branch trips and is removed from the network, where the overload trip tolerance factor is greater than 1. The iterative calculation continues until no new overloaded branches are detected.

5. The analytical model according to claim 1, characterized in that, The workflow of the communication layer inner loop unit is as follows: Construct the currently running communication subgraph, excluding nodes without power supply and backup power, as well as failed links and core nodes. Reassign routes to each active site based on baseline anchoring routing rules; sites with no feasible paths are considered disconnected. Calculate the load of communication edges and core nodes, and obtain the corresponding overload ratio. When the overload ratio of a communication edge exceeds the communication link overload threshold or the overload ratio of a core node exceeds the core node overload threshold, the corresponding link or core node fails and is removed from the subgraph, where both the communication link overload threshold and the core node overload threshold are greater than 1. Continue iterative calculations until no new failures occur or the maximum number of inner loop iterations is reached.

6. The analytical model according to claim 1, characterized in that, The workflow of the cross-layer outer loop coordination unit is as follows: During the outer loop iteration process, the power layer continuously provides the current set of energized buses to the communication layer. Based on the power-to-communication mapping relationship and considering whether the communication facilities have available backup power, the operating status of each communication facility is determined. After the communication layer inner loop is solved, the service status of each communication station is obtained. Based on the communication-to-power mapping relationship, it is determined whether each power bus receives sufficient communication control support, and a set of buses with insufficient communication control is obtained. For power branches connected to buses with insufficient control, their power flow limits are reduced according to the communication control derating factor, where the value of the communication control derating factor is greater than 0 and less than or equal to 1. The power layer inner loop is solved again using the adjusted branch limits, and the set of energized buses is updated. Continue iterative updates until the power and communication states no longer change or the maximum number of outer loop iterations is reached.

7. The analytical model according to claim 1, characterized in that, The spatiotemporal trajectory analysis and output module records system states covering three dimensions: power layer, communication layer, and cross-layer coupling. The power layer includes the number of surviving buses, the number of surviving branches, the cumulative number of failed buses / branches, and the maximum branch overload ratio; the communication layer includes the number of operating communication facilities, the number of serviced sites, the communication service ratio, and the maximum edge / core overload ratio; and cross-layer coupling includes the number of communication facilities that have lost mains power due to power outages and the number of power buses affected by communication control failures.

8. The analytical model according to claim 2, characterized in that, In the power network extraction step, when branch parameter data is unavailable, it is estimated based on the default parameters corresponding to the voltage level and the branch length; the balancing bus is automatically selected based on the power station priority, voltage level and graph connectivity.

9. The analytical model according to claim 2, characterized in that, In the communication-to-power-dependency mapping step, if at least one station in any candidate site group mapped to a power bus is still being served, then the bus is considered to maintain communication support; otherwise, the bus experiences control degradation.

10. The analytical model according to claim 6, characterized in that, The preferred value range for the communication control derating coefficient is 0.5-0.8.

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