A method and system for improving robustness of a cyber-physical system of power based on motif optimization and flow interaction

Abstract

The application discloses a kind of based on body optimization and flow interaction's electric power information physical system robustness promotion method and system, and it is related to electric power system safety and regulation and control technical field.The method comprises: constructing three-layer CPPS topology model consisting of electric power layer, information layer and cross-layer coupling, and using correlation matrix to describe intra-layer connection and inter-layer dependency relationship;Establish an information flow transmission, control decision and energy flow regulation closed-loop interaction system, quantize response delay and interaction accuracy;Identify key network motifs including three-node closed-loop subgraph and four-node star subgraph, establish optimization model and constraint conditions with the goal of minimizing fault propagation risk, and solve the optimal motif configuration scheme;Optimization effect is verified by typical fault scenario simulation.The application strengthens local topological structure through progressive design, effectively reduces the scope of fault influence, and improves the stable operation ability of the system under complex disturbance.

Description

Technical Field

[0001] This invention relates to the field of power system security and control technology, and in particular to a method and system for improving the robustness of power cyber-physical systems based on modal optimization and flow dynamic interaction. Background Technology

[0002] Cyber-Physical Power Systems (CPPS), as the core carrier of smart grids, achieve coordinated scheduling and control of energy and information flows through deep integration of primary power systems and information communication systems, significantly improving the observability, controllability, and operational efficiency of power systems. With the widespread application of numerous synchronous phasor measurement units (PMUs), wide-area measurement systems (WAMS), and intelligent terminal devices, the information sensing depth and control coverage of CPPS are continuously expanding, making it a key infrastructure for the safe and stable operation of modern power systems.

[0003] However, while CPPS brings flexibility in regulation, its deep coupling between the power layer and the information layer also introduces new security risks. Due to the increasingly dense interaction channels between the physical and information spaces, disturbances or faults can easily propagate across inter-layer boundaries, potentially triggering cross-domain cascading reactions from local anomalies that were originally confined to a single space, seriously threatening the safe and stable operation of the power system. Numerous studies have shown that dynamic factors such as coupling strength and interaction delay have a significant impact on the cross-layer propagation range and evolution speed of faults; however, current technologies are insufficient in characterizing these dynamic interaction characteristics. Therefore, how to construct a CPPS model that accurately reflects the dynamic coupling relationship between the power and information layers, and on this basis, effectively suppress fault propagation and improve system robustness, has become a key technical problem urgently needing breakthroughs in the field of power system security.

[0004] Currently, scholars both domestically and internationally have conducted extensive research on CPPS modeling. Existing methods are mostly based on complex network theory or graph theory, using correlation matrices or adjacency matrices to represent the topology of power networks and information networks respectively, and describing the dependencies between the two networks through coupling matrices. These methods are relatively mature in static topology representation and can reflect the network's connectivity and basic statistical characteristics. However, most existing models treat the power layer and information layer as two relatively independent structures, simplifying cross-layer coupling to a static binary mapping relationship of "power supply-power consumption" or "monitoring-monitored" between nodes, failing to fully reflect the dynamic interaction characteristics of energy flow and information flow over time. Especially in actual operation, dynamic factors such as information acquisition delays, communication link errors and packet loss, and control command response deviations can all have a substantial impact on the fault evolution process of CPPS. Existing models generally lack quantitative description methods for these dynamic interaction characteristics, making it difficult to accurately reconstruct the true time-series process of fault propagation across layers.

[0005] In the area of ​​robustness optimization for CPPS, existing research has mainly followed two technical paths. The first is a key component reinforcement strategy based on node or line importance identification, which enhances system resilience by increasing redundancy or optimizing protection configurations. However, this type of method typically focuses on a single physical or information layer, neglecting the suppression of cross-layer coupled fault propagation. The second is a global optimization strategy based on topology reconstruction or weight adjustment, which enhances resilience by holistically modifying the network structure. However, limited by the search efficiency of centralized algorithms, it is difficult to apply to dynamic optimization scenarios in large-scale CPPS. It is worth noting that the above methods generally overlook the important role played by high-frequency subgraph structures—i.e., "phantoms"—that are ubiquitous in complex networks during fault propagation. As the basic units constituting the local topology of complex systems, the density and distribution characteristics of network phantoms directly affect the availability of redundant paths, the integrity of sensing coverage, and the reliable delivery rate of control commands. They are key microstructures for suppressing the evolution of local faults into global cascading failures, but have not yet been systematically applied in CPPS robustness optimization research.

[0006] In summary, existing technologies still have the following shortcomings in CPPS modeling and robustness improvement: (1) the characterization of cross-layer coupling is mostly limited to static mapping, lacking real-time quantitative description of the dynamic interaction characteristics of energy flow and information flow; (2) system-level optimization methods ignore the blocking effect of local topological motif structures on fault propagation, making it difficult to accurately suppress cross-layer cascading faults. To this end, this invention proposes a CPPS modeling and robustness improvement method based on motif optimization and flow dynamic interaction, aiming to synergistically enhance the system's anti-disturbance capability from two levels: topology modeling and local structure optimization. Summary of the Invention

[0007] To address this, embodiments of the present invention provide a method and system for improving the robustness of power cyber-physical systems based on phantom optimization and dynamic flow interaction. This method solves the problems in the prior art where cross-layer coupling representation remains statically mapped and lacks real-time quantitative description of the dynamic interaction characteristics of energy flow and information flow. Furthermore, system-level optimization ignores the blocking effect of local topological phantom structures on fault propagation, making it difficult to accurately suppress cross-layer cascading faults.

[0008] To address the aforementioned technical problems, this invention provides a method for improving the robustness of a power cyber-physical system based on phantom optimization and flow dynamics interaction, comprising the following steps:

[0009] Step S1: Construct a three-layer CPPS topology model consisting of a power layer, an information layer, and cross-layer coupling. Use the power layer correlation matrix to describe the node connection relationship within the power layer, use the information layer correlation matrix to describe the node connection relationship within the information layer, and use the cross-layer coupling matrix to quantify the cross-layer dependency relationship between power nodes and information nodes, thus obtaining three-layer topology data containing intra-layer topology connections and inter-layer coupling associations.

[0010] Step S2: Based on the three-layer topology data, establish a closed-loop interactive system that includes information flow transmission, control decision-making, and energy flow regulation. The real-time operating data of the power layer is converted into information flow through the measurement equipment and transmitted to the control center. The control center generates regulation commands and transmits them to the power layer through the information layer to perform energy flow adjustment. The mutual conversion and real-time response characteristics between energy flow and information flow are plotted in real time to obtain the dynamic interactive characteristic data of CPPS.

[0011] Step S3: Based on the three-layer topology data and the dynamic interaction characteristic data, identify the key network modules that support the core functions of the system in the CPPS topology, select the module types that appear frequently and have statistical significance as optimization objects, and obtain the set of key modules and their parameterized description data.

[0012] Step S4: Based on the set of key phantoms and their parameterized description data, with the goal of minimizing the risk of fault propagation, establish the objective function and constraints for phantom optimization, optimize the density, distribution and topological embedding position of the key phantoms, and obtain the optimal phantom configuration scheme.

[0013] Step S5: Update the three-layer CPPS topology model based on the optimal phantom configuration scheme, and simulate fault propagation by setting typical fault scenarios. Compare the system operating status before and after optimization to verify the effect of phantom optimization on the robustness of CPPS.

[0014] Preferably, in step S1, the power layer is an undirected graph. Characterization, in which For a set of power nodes, The set of power links; the power layer association matrix The element is defined as:

[0015] ;

[0016] in, For link Real-time transmission power, This represents the maximum transmission capacity of the link.

[0017] The information layer uses directed graphs Characterization, in which For a set of information nodes, The information link set; the information layer association matrix The element is defined as:

[0018] ;

[0019] in, For link Real-time transmission latency, The maximum allowable latency of the link. For bit error rate, For bandwidth utilization;

[0020] The cross-layer coupling matrix The elements are in tuples Describe the power supply support strength, monitoring coverage, and control response rate between power nodes and information nodes.

[0021] Preferably, in step S2, the closed-loop interaction process of the energy flow and information flow includes:

[0022] The observation status of the information node on the power node is represented by the following formula:

[0023] ;

[0024] in, The variable is 0-1, with 1 representing an information node. For power nodes Observable, with 0 representing unobservable; , These are binary parameters, with values ​​of 1 indicating information nodes. , Configure the measurement equipment; a value of 0 indicates that it is not configured. For power link set The elements in the table represent power nodes. and The connection relationship, A set of information nodes;

[0025] The adjustment of power layer energy flow corresponding to the control command is characterized by the adjustment of generator output as follows:

[0026] ;

[0027] in, For power generation nodes In the stage The output value; For the stage Power generation node Corresponding information nodes The working status indicates whether the control commands are effectively transmitted; , Respectively, power generation nodes Minimum and maximum output limits; For power generation nodes The output value in the previous stage.

[0028] Preferably, in step S2, the dynamic interaction characteristic data is quantitatively described by response latency and interaction accuracy:

[0029] Define total response delay Total time spent from information flow generation to energy flow adjustment:

[0030] ;

[0031] in, The transmission delay from energy flow to information flow, To delay decision-making in the control center, The transmission delay from information flow to energy flow;

[0032] Define comprehensive interaction precision for:

[0033] ;

[0034] in, To improve the efficiency of information flow generation, The energy flow adjustment accuracy is the deviation rate between the target value of the control command and the actual change in energy flow.

[0035] Preferably, in step S3, the key network module includes a three-node closed-loop subgraph and a four-node star subgraph;

[0036] Frequency of occurrence of phantoms Calculate using the following formula:

[0037] ;

[0038] in, This represents the actual number of occurrences of the target subgraph. This represents the total number of nodes in the CPPS topology. The number of nodes in the module. From Select from nodes The number of combinations of nodes;

[0039] The statistical significance score of the subplots was quantified using the Z-score method. :

[0040] ;

[0041] in, This represents the average frequency of occurrence of this subgraph in the random topology. The standard deviation is denoted as ; when When this occurs, the subgraph is identified as a key motif with statistical significance.

[0042] Preferably, in step S3, the parameterized description data of the key motif includes:

[0043] phantom density coefficient Characterizing the motif within a unit topological region The number of configurations is defined as:

[0044] ;

[0045] in, For the model The actual number of configurations, For the motif within this topological region The maximum number that can be configured;

[0046] Distribution rationality coefficient The coverage of the quantification model in high-fault areas is defined as:

[0047] ;

[0048] in, For the phantom in the high-incidence area of ​​failure The number of configurations, For the model Total number of configurations;

[0049] Local connectivity enhancement coefficient Differentiated definitions based on phantom type:

[0050] ;

[0051] in, This represents the number of actually available communication paths in a three-node closed-loop subgraph. The number of nodes in a four-node star subplot to configure measurement devices;

[0052] Interaction Adaptability Coefficient The ability of a quantization module to support the interaction of energy flow and information flow is defined as:

[0053] ;

[0054] in, For the model The surrounding interaction latency deviation, This represents the maximum allowable interaction latency of the system.

[0055] Preferably, in step S4, the objective function is to minimize the comprehensive value of fault propagation risk:

[0056] ;

[0057] in, This is the comprehensive risk value for fault propagation, with a value range of [0,1]. The smaller the value, the lower the probability of fault propagation. This represents the total number of nodes in the CPPS topology. For the set of key motifs; , , , respectively phantom The density coefficient, distribution rationality coefficient, local connectivity enhancement coefficient, and interaction adaptation coefficient;

[0058] The constraints include:

[0059] Cost constraints in phantom configuration:

[0060] ;

[0061] in, For a single phantom Configuration cost, Choose a variable for the motif type. This represents the maximum allowable configuration cost threshold for the system.

[0062] Topology compatibility constraints:

[0063] ;

[0064] in, The determinant of the topological correlation matrix of the motif embedding region is given. The minimum topological connectivity threshold;

[0065] Interactive data adaptation constraints:

[0066] ;

[0067] in, The minimum interaction adaptation threshold.

[0068] Preferably, in step S4, a distributed two-layer cooperative competitive optimization algorithm is used to solve the objective function and constraints. The algorithm includes:

[0069] The local competition layer is used to perform multi-directional independent search through a hybrid selection operator, motif crossover operator, and motif mutation operator, and to optimize the population by combining an artificial immune framework to generate an approximately optimal motif configuration scheme.

[0070] The global competition layer is used to receive the best individuals uploaded by each local process through asynchronous queue communication, update the global population using a fusion operator, perform additional iterative optimization, and output the globally optimal motif configuration scheme.

[0071] Preferably, in step S5, the typical fault scenarios include transmission line faults, information node failures, and cross-layer coupling link interruptions.

[0072] By comparing the load failure rate, node survival rate, and fault propagation range of the system before and after motif optimization under the same fault scenario, the effect of motif optimization on the robustness of CPPS is evaluated.

[0073] This invention also provides a robustness enhancement system for power cyber-physical systems based on phantom optimization and flow dynamics interaction. This system is used to implement the aforementioned robustness enhancement method for power cyber-physical systems based on phantom optimization and flow dynamics interaction, specifically including:

[0074] The topology modeling module is used to construct a three-layer CPPS topology model consisting of a power layer, an information layer, and cross-layer coupling. It uses a power layer correlation matrix to describe the node connection relationship within the power layer, a information layer correlation matrix to describe the node connection relationship within the information layer, and a cross-layer coupling matrix to quantify the cross-layer dependency relationship between power nodes and information nodes, thus obtaining three-layer topology data that includes intra-layer topology connections and inter-layer coupling associations.

[0075] The dynamic interactive simulation module is used to establish a closed-loop interactive system based on the three-layer topology data, including information flow transmission, control decision and energy flow regulation. The real-time operation data of the power layer is converted into information flow through the measurement equipment and transmitted to the control center. The control center generates regulation commands and transmits them to the power layer through the information layer to perform energy flow adjustment. The module also displays the mutual conversion and real-time response characteristics between energy flow and information flow in real time, thus obtaining the dynamic interactive characteristic data of CPPS.

[0076] The motif optimization module is used to identify key network motifs supporting the core functions of the CPPS topology based on the three-layer topology data and the dynamic interaction characteristic data, and to select motif types that appear frequently and have statistical significance as optimization objects, thereby obtaining a set of key motifs and their parameterized description data.

[0077] The fault inference module is used to establish the objective function and constraints for the optimization of the key phantoms based on the set of key phantoms and their parameterized description data, with the goal of minimizing the risk of fault propagation. It optimizes the density, distribution and topological embedding position of the key phantoms to obtain the optimal phantom configuration scheme.

[0078] The robustness evaluation module is used to update the three-layer CPPS topology model based on the optimal phantom configuration scheme, and to simulate fault propagation by setting typical fault scenarios. The module compares the system operating status before and after optimization to verify the effect of phantom optimization on the robustness of CPPS.

[0079] As can be seen from the above technical solutions, this invention application has the following beneficial effects:

[0080] First, this invention constructs a three-layer CPPS topology model consisting of a power layer, an information layer, and cross-layer coupling. It uses the power layer correlation matrix, information layer correlation matrix, and cross-layer coupling matrix to characterize the intra-layer node connection relationships and inter-layer dependencies such as power supply support, status monitoring, and control command transmission. Furthermore, it establishes a closed-loop interactive system encompassing information flow transmission, control decision-making, and energy flow regulation. By quantifying the dynamic interaction characteristics of the two flows through response delay and interaction accuracy, it solves the problem in existing technologies where cross-layer coupling representation remains static and lacks real-time quantitative description of the dynamic interaction characteristics of energy flow and information flow. This provides a precise model foundation for the dynamic analysis and fault evolution reconstruction of CPPS.

[0081] Second, this invention identifies high-frequency and statistically significant three-node closed-loop subgraphs and four-node star-shaped subgraphs in the CPPS topology as key network modules. It then uses topological structural features and dynamic interaction data to parametrically describe their density coefficients, distribution rationality coefficients, local connectivity enhancement coefficients, and interaction adaptation coefficients. An optimization model is established with the goal of minimizing fault propagation risk, incorporating configuration cost constraints, topology compatibility constraints, and interaction data adaptation constraints. A distributed two-layer cooperative competitive optimization algorithm is employed to solve for the optimal density, distribution, and topological embedding position of the key modules. This addresses the problem in existing technologies where system-level optimization neglects the role of local topological module structure in blocking fault propagation, achieving precise enhancement of local topological structures and effective blocking of fault propagation paths.

[0082] Third, this invention simulates fault propagation by setting up three typical fault scenarios: transmission line fault, information node failure, and cross-layer coupling link interruption. Using load loss rate, node survival rate, and fault propagation range as core verification indicators, it compares the changes in the system's operating status before and after optimization under the same fault scenarios. It proves that in the single fault scenario, the system load loss rate decreases significantly and the node survival rate increases significantly with the increase of phantom density. In the multi-fault scenario, the optimal phantom configuration has a lower load loss rate and a smaller fault propagation range compared to the random configuration. Under different fault types, the CPPS with phantom optimization has shorter interaction latency and lower fault propagation risk, effectively improving the system's stable operation capability under complex disturbances. Attached Figure Description

[0083] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly described below. Referring to the drawings will make the features and advantages of the present invention clearer. The drawings are illustrative and should not be construed as limiting the present invention in any way. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0084] Figure 1 This is a flowchart of a method for improving the robustness of a power cyber-physical system based on phantom optimization and flow dynamic interaction, provided by an embodiment of the present invention.

[0085] Figure 2 This is a schematic diagram of the CPPS three-layer model according to an embodiment of the present invention;

[0086] Figure 3 This is a schematic diagram of the closed-loop conversion process of energy flow to information flow according to an embodiment of the present invention;

[0087] Figure 4 This is a schematic diagram illustrating the implementation process of improving CPPS robustness based on key network motifs in an embodiment of the present invention;

[0088] Figure 5 This is a block diagram of a robustness enhancement system for a power cyber-physical system based on phantom optimization and flow dynamic interaction, provided by an embodiment of the present invention. Detailed Implementation

[0089] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0090] Example 1:

[0091] To address the problem that existing technologies rely on static mapping for cross-layer coupling representations, lacking real-time quantitative descriptions of the dynamic interaction characteristics of energy and information flows, and that system-level optimization neglects the role of local topological structures in blocking fault propagation, thus making it difficult to accurately suppress cross-layer cascading faults. For example... Figure 1 As shown in the figure, this invention proposes a method for improving the robustness of a power cyber-physical system based on phantom optimization and flow dynamic interaction. The method includes the following steps:

[0092] Step S1: Construct a three-layer CPPS topology model consisting of a power layer, an information layer, and cross-layer coupling. Use the power layer correlation matrix to describe the node connection relationship within the power layer, use the information layer correlation matrix to describe the node connection relationship within the information layer, and use the cross-layer coupling matrix to quantify the cross-layer dependency relationship between power nodes and information nodes, thus obtaining three-layer topology data containing intra-layer topology connections and inter-layer coupling associations.

[0093] Step S2: Based on the three-layer topology data, establish a closed-loop interactive system that includes information flow transmission, control decision-making, and energy flow regulation. The real-time operating data of the power layer is converted into information flow through the measurement equipment and transmitted to the control center. The control center generates regulation commands and transmits them to the power layer through the information layer to perform energy flow adjustment. The mutual conversion and real-time response characteristics between energy flow and information flow are plotted in real time to obtain the dynamic interactive characteristic data of CPPS.

[0094] Step S3: Based on the three-layer topology data and the dynamic interaction characteristic data, identify the key network modules that support the core functions of the system in the CPPS topology, select the module types that appear frequently and have statistical significance as optimization objects, and obtain the set of key modules and their parameterized description data.

[0095] Step S4: Based on the set of key phantoms and their parameterized description data, with the goal of minimizing the risk of fault propagation, establish the objective function and constraints for phantom optimization, optimize the density, distribution and topological embedding position of the key phantoms, and obtain the optimal phantom configuration scheme.

[0096] Step S5: Update the three-layer CPPS topology model based on the optimal phantom configuration scheme, and simulate fault propagation by setting typical fault scenarios. Compare the system operating status before and after optimization to verify the effect of phantom optimization on the robustness of CPPS.

[0097] As can be seen from the above technical solution, this invention proposes a method for improving the robustness of a power cyber-physical system based on modal optimization and dynamic interaction. This method involves: Step S1, constructing a three-layer CPPS topology model consisting of a power layer, an information layer, and cross-layer coupling, and using a multi-dimensional correlation matrix to achieve a refined characterization of intra-layer connections and inter-layer dependencies, providing a precise topology data foundation for subsequent dynamic interaction analysis and modal optimization; Step S2, establishing a closed-loop interaction system for information flow transmission, control decision-making, and energy flow regulation based on the three-layer topology data, converting real-time operating data of the power layer into information flow, and generating regulation commands via the control center to react on the power layer. The dynamic characterization of the mutual conversion between the two flows and the real-time response characteristics is achieved through the quantification of response delay and interaction accuracy, providing interactive characteristic data support for the selection and adaptation of key modalities; Step S3, identifying key network modalities in the CPPS topology that support core functions such as power supply guarantee, monitoring redundancy, and control response based on the three-layer topology data and dynamic interaction characteristic data, and obtaining a three-node closed loop through frequency calculation and Z-score statistical significance screening. The subgraph and four-node star subgraph are parametrically described with density coefficient, distribution rationality coefficient, local connectivity enhancement coefficient, and interaction adaptation coefficient, providing a quantitative basis for phantom optimization. Step S4 establishes an optimization model based on the key phantom set and its parametric description data, with the goal of minimizing fault propagation risk. The model includes objective function, configuration cost constraints, topology compatibility constraints, and interaction data adaptation constraints. A distributed two-layer cooperative competitive optimization algorithm is used to solve for the optimal density, distribution, and topology embedding position of the key phantoms, thereby achieving precise enhancement of the local topology and effective blocking of fault propagation paths. Step S5 updates the three-layer CPPS topology model based on the optimal phantom configuration scheme and sets three typical fault scenarios: transmission line fault, information node failure, and cross-layer coupling link interruption, to simulate fault propagation. By comparing the load loss rate, node survival rate, and fault propagation range before and after optimization, the significant improvement effect of phantom optimization on CPPS robustness is verified. Finally, a complete progressive robustness improvement is achieved from topology modeling to dynamic interaction characterization to phantom optimization deployment and fault verification.

[0098] The steps described above are explained in detail below.

[0099] like Figure 2 As shown, this embodiment constructs a three-layer CPPS topology model consisting of a power layer, an information layer, and cross-layer coupling. Figure 2The three-layer model architecture of CPPS is demonstrated, including physical-information fusion nodes, primary / secondary equipment nodes, and information application nodes. It clearly shows the power layer (including primary and secondary equipment nodes), the information layer (including information application nodes, communication gateway nodes, control center, etc.), and the cross-layer coupling relationship (power-information interaction is realized through physical-information fusion nodes), providing an architectural foundation for subsequent refined modeling of intra-layer and inter-layer relationships.

[0100] (1) Power layer modeling: using undirected graphs Characterizing the power network, in which It is a collection of power nodes, encompassing power nodes such as generators, loads, and busbars. This represents a set of power links (transmission lines). A power layer correlation matrix is ​​used. Describes the connection relationships between nodes within a layer; the matrix elements are defined as follows:

[0101] ;

[0102] in, For link Real-time transmission power, This represents the maximum transmission capacity of the link. This matrix element not only identifies whether nodes are connected, but also embeds physical attributes such as line transmission capacity, intuitively reflecting the line's operational load status. Simultaneously, the matrix embeds node power supply priority coefficients. For example, generator nodes Ordinary load nodes This provides data support for subsequent power flow analysis and fault prediction.

[0103] (2) Information layer modeling: using directed graphs Characterizing information networks, in which It is a collection of information nodes, including the control center, synchronization phasor measurement unit (PMU), communication relays, and other information nodes. This is a set of information links (communication links). An information layer correlation matrix is ​​used. Describe the topology within the layer; matrix elements are defined as follows:

[0104] ;

[0105] in, For link Real-time transmission latency, The maximum allowable latency of the link. For bit error rate, This represents bandwidth utilization. The matrix elements integrate information attributes such as communication bandwidth, transmission delay, and bit error rate, providing data support for the quantification of dynamic interactive characteristics.

[0106] (3) Cross-layer coupling modeling: constructing the cross-layer coupling matrix Matrix elements are in tuples Describe the dependencies between power nodes and information nodes:

[0107] Energy supply support strength ,in For power nodes For information nodes The actual power supply capacity, Rated power for information nodes;

[0108] Monitoring coverage ;

[0109] Control response rate ,in This is the actual response time. To meet response time requirements.

[0110] This matrix fully depicts the dependencies between the power layer and the information layer, including power supply support, status monitoring, and control command transmission, forming a three-layer topology data that includes intra-layer topological connections and inter-layer coupling relationships. This provides a precise topological foundation for subsequent dynamic interactive analysis and robustness optimization.

[0111] like Figure 3 As shown, this embodiment establishes a closed-loop interactive system based on the three-layer topology data, which includes information flow transmission, control decision-making, and energy flow regulation. Figure 3 The closed-loop conversion process of energy flow to information flow is demonstrated. S21 represents the conversion from energy flow to information flow (real-time data from the power layer is collected by sensors and digitized into information flow). S22 represents the generation of control decisions (the control center generates control commands based on the information flow execution state estimation and optimal power flow calculation). S23 represents the conversion from information flow to energy flow (control commands are transmitted from the information layer to the power layer actuators to complete the energy flow adjustment). S24 represents the quantification and optimization of interaction characteristics (comprehensive evaluation of response delay and interaction accuracy to achieve closed-loop optimization). The dynamic closed-loop process of mutual conversion between the two flows and real-time response characteristics is fully demonstrated.

[0112] (1) Energy Flow to Information Flow Conversion: Real-time operating data from primary equipment nodes in the power layer is collected by sensors (PMU / RTU) and digitized into an information flow via an A / D converter. This information flow is then transmitted to the control center via information layer routers, optical fibers, and other links. Define the information flow generation efficiency. ,in To effectively collect data, This represents the total amount of data collected. When... At this time, it triggers information layer bandwidth expansion or sensor redundancy configuration to ensure the effectiveness of data acquisition.

[0113] The observation status of the information node on the power node is represented by the following formula:

[0114] ;

[0115] in, The variable is 0-1, with 1 representing an information node. For power nodes Observable (i.e., power data is successfully converted into an information stream), 0 indicates unobservable; , These are binary parameters, with values ​​of 1 indicating information nodes. , Configure the measurement equipment; a value of 0 indicates that it is not configured. For power link set The elements in the table represent power nodes. and The connection relationship.

[0116] (2) Control Decision Generation: After receiving the information stream, the control center performs state estimation and optimal power flow calculation based on real-time data from the power layer to generate control commands. Decision delay is defined. ,in For information reception time, The time required to complete the decision. In such cases, the complexity of the control center algorithm can be optimized or computing nodes can be added to improve decision-making efficiency.

[0117] (3) Information flow to energy flow conversion: The control command is transmitted to the power layer actuator via the information layer communication link, and the actuator completes the energy flow adjustment. The power layer energy flow adjustment corresponding to the control command is represented by the generator output adjustment as follows:

[0118] ;

[0119] in, For power generation nodes In the stage The output value; For the stage Power generation node Corresponding information nodes The working status indicates whether the control commands are effectively transmitted; , Respectively, power generation nodes Minimum and maximum output limits; For power generation nodes Output value of the previous stage. Define energy flow adjustment precision. ,in To exert force for the commanded objective. When In this process, feedback is used to optimize the reliability of information layer transmission or the response speed of the actuator, ensuring the accuracy of instruction execution.

[0120] (4) Quantification of interaction characteristics: Based on the above process, the total response delay is defined. ,in The transmission delay from energy flow to information flow, The transmission delay from information flow to energy flow. Define the overall interaction precision. .when or In this process, the bandwidth configuration of the information layer or the control parameters of the power layer are dynamically adjusted to achieve closed-loop optimization of the interaction process. The dynamic interaction characteristic data of CPPS (including response latency, interaction accuracy, information flow generation efficiency, etc.) obtained through the above methods provide a basis for subsequent module optimization.

[0121] like Figure 4 As shown, this embodiment identifies key network modules that support the core functions of the CPPS topology based on the three-layer topology data and the dynamic interaction characteristic data. Figure 4 This paper demonstrates the implementation process for improving the robustness of CPPS based on key network motifs. Specifically, it includes: first, extracting topological features and dynamic interaction data from the three-layer topology model of CPPS to construct a basic dataset for motif recognition; then, using a distributed two-layer cooperative competitive optimization algorithm (divided into a local competition layer and a global competition layer, combined with selection, crossover, mutation operators and queue communication mechanism) to achieve efficient solution of motif optimization; finally, setting up Monte Carlo simulations for multiple failure scenarios, and measuring the feasibility of the solution through indicators such as system load failure rate and node survival rate. Figure 4 The entire logical chain from phantom identification to optimization solution to verification and evaluation is shown.

[0122] (1) Subgraph Enumeration: Subgraph enumeration is performed on the CPPS topology using the adjacency matrix traversal method. All 3-node and 4-node subgraphs are traversed, and the connection relationships of each subgraph are recorded. The frequency of occurrence of each subgraph is calculated. , defined as the ratio of the number of times a subgraph appears in the topology to the total number of all possible subgraphs at that size:

[0123] ;

[0124] in, This represents the actual number of occurrences of the target subgraph. This represents the total number of nodes in the CPPS topology. The number of nodes in the module. From Select from nodes The number of combinations of nodes.

[0125] (2) Significance screening: The Z-score method was used to quantify the statistical significance score of the subplots. :

[0126] ;

[0127] in, This represents the average frequency of occurrence of this subgraph in the random topology. is the standard deviation. When this occurs, the subgraph is identified as a key motif with statistical significance. In this embodiment, three-node closed-loop subgraphs and four-node star-shaped subgraphs are selected as optimization targets.

[0128] (3) Parametric Description: The selected key motifs are parametrically described to obtain the set of key motifs and their parametric description data, specifically including:

[0129] phantom density coefficient Characterizing the motif within a unit topological region The number of configurations is defined as ,in For the model The actual number of configurations, For the motif within this topological region The maximum number that can be configured;

[0130] Distribution rationality coefficient The coverage of the quantification phantom in high-fault areas is defined as follows: ,in For the phantom in the high-incidence area of ​​failure The number of configurations, For the model Total number of configurations;

[0131] Local connectivity enhancement coefficient Based on the motif type, differentiated definition: for a three-node closed-loop subgraph For a four-node star subgraph ,in This represents the number of actually available communication paths in a three-node closed-loop subgraph. The number of nodes in a four-node star subplot to configure measurement devices;

[0132] Interaction Adaptability Coefficient The ability of a quantization module to support the interaction of energy flow and information flow is defined as... ,in For the model The surrounding interaction latency deviation, This represents the maximum allowable interaction latency of the system.

[0133] In this embodiment, step S4, based on the set of key phantoms and their parameterized description data, establishes an objective function and constraints for phantom optimization with the goal of minimizing the risk of fault propagation, and solves it using a distributed two-layer cooperative competitive optimization algorithm. It also employs methods such as... Figure 4 The distributed two-layer cooperative competition optimization algorithm shown is used to solve this problem.

[0134] (1) Objective function: Minimize the comprehensive value of fault propagation risk:

[0135] ;

[0136] in, This is the comprehensive risk value for fault propagation, with a value range of [0,1]. The smaller the value, the lower the probability of fault propagation. This represents the total number of nodes in the CPPS topology. For the set of key motifs; respectively phantom The density coefficient, distribution rationality coefficient, local connectivity enhancement coefficient, and interaction adaptation coefficient.

[0137] (2) The constraints include:

[0138] Cost constraints in phantom configuration: ,in For a single phantom Configuration costs (such as the cost of adding communication links and measurement equipment). Choose a variable for the motif type. This represents the maximum allowable configuration cost threshold for the system.

[0139] Topology compatibility constraints: ,in The determinant of the topological correlation matrix of the motif embedding region is given. The minimum topological connectivity threshold;

[0140] Interactive data adaptation constraints: ,in To minimize the interaction adaptation threshold, ensure that modifier optimization does not affect the normal interactive functions of the system.

[0141] (3) Optimization algorithm: A distributed two-layer cooperative competition optimization algorithm is adopted, which is divided into a local competition layer and a global competition layer.

[0142] Local competition layer: This layer generates near-optimal phantom configuration schemes through independent searches in multiple optimization directions. The specific process includes:

[0143] Initial population generation: Based on the CPPS topology model, an initial population is generated. Each topological individual It includes different motif densities and distribution schemes to ensure that the node degree distribution conforms to the scale-free property;

[0144] Hybrid selection operator: Employs a hybrid selection strategy combining roulette wheel, tournament, and KNN to select high-quality topological individuals;

[0145] Module crossover operator: for two parent topologies and Perform a phantom base crossing operation. Randomly select a crossing position and extract the phantom bases surrounding that position. and Identify the exchanged phantom basis that satisfies the invariant node degree distribution constraint. For a four-node phantom basis with a node degree distribution of (2,2,2,2), disconnect the link pair. and Rebuild link and Generate offspring topology , ,in , The recombined motif base;

[0146] Motif mutation operator: based on mutation probability Modify the phantom basis connectivity of the topological individuals. Randomly select phantom basis. For a three-node closed-loop subgraph, adjust the connection node of one link; for a four-node star subgraph, replace the central node.

[0147] Artificial Immune Framework Optimization: An artificial immune mechanism is introduced to assess antibody affinity (affinity) in crossover and mutated topological individuals. Individuals with affinity below the threshold are removed, and newly generated topological individuals are added to maintain population diversity.

[0148] Global Competition Layer: Through asynchronous communication and fusion operators, local optima are evolved into global optima. The specific process includes:

[0149] Uploading of locally optimal individuals: After each local iteration is completed a fixed number of times (20 times in this example), the optimal individual in the current population is extracted and uploaded to the queue communication mode. ;

[0150] Global Model Fusion: Global Optimization Process From queue Extract the locally optimal individuals and replace the individuals with the lowest affinity in the global population using the fusion operator;

[0151] Global self-optimization: The global population performs 10 additional iterations of selection, crossover, and mutation operations to enhance the robustness of the global optimal solution;

[0152] Optimal solution output: When the change in affinity of the global population over 10 consecutive iterations is less than... When the time is right, stop optimization and output the globally optimal module configuration scheme.

[0153] The complete optimization execution process is as follows:

[0154] Step 1: Input and Initialization of Topological Data: Input the correlation matrix and dynamic interaction data of the CPPS three-layer topological model, initialize 6 local populations, and set the algorithm parameters;

[0155] Step 2, Local Population Evolution: Each local area independently executes mixed selection, motif crossover, and motif mutation operators, and optimizes the population in conjunction with an artificial immune framework to generate topological individuals with high-quality motif configurations;

[0156] Step 3: Upload Local Optimal Individual: After each local iteration is completed (20 iterations), the current best individual is uploaded to the communication queue. ;

[0157] Step 4: Global Model Update: Global Optimization Process From queue Extract all locally optimal individuals, update the global population using the fusion operator, and remove inferior individuals;

[0158] Step 5, Global Self-Optimization: The global population performs 10 iterations of evolutionary operations to optimize motif density and distribution, and improve the affinity of the global optimal solution;

[0159] Step Six: Convergence Judgment: Determine if the global population meets the convergence condition (the change in affinity is less than 1 / 2000 for 10 consecutive iterations). If the conditions are met, the optimal phantom configuration scheme is output; otherwise, return to step two and continue local population evolution.

[0160] Step 7: Phantom Configuration and Deployment: Deploy the optimal phantom configuration scheme to the CPPS topology model, update the topology association matrix, and complete the phantom optimization.

[0161] In this embodiment, step S5 updates the three-layer CPPS topology model based on the optimal phantom configuration scheme, sets typical fault scenarios to simulate fault propagation, compares the system operating status before and after optimization, and verifies the effect of phantom optimization on the robustness of CPPS.

[0162] (1) Fault scenario design: Set up three typical fault scenarios - transmission line fault (simulating line overload tripping), information node failure (simulating measurement equipment failure or communication relay interruption), and cross-layer coupling link interruption (simulating power node power supply interruption to information node).

[0163] (2) Verification indicators and procedures: The core verification indicators are load failure rate, node survival rate, and fault propagation range (or comprehensive value of fault propagation risk). By comparing the changes in indicators of the system before and after optimization under the same fault scenario, the effect of the module optimization on the robustness improvement is evaluated.

[0164] This embodiment verifies the optimization effect through three sets of comparative experiments:

[0165] Experiment 1 (Single Fault Scenario): The system was divided into three groups (low, medium, and high) based on phantom density. Robustness indices were observed after simulating a single fault. The experimental results show that as the phantom density increases from low to high, the system load failure rate under single fault conditions decreases significantly, the risk of fault propagation continues to decrease, and the node survival rate increases significantly. This indicates that increasing the density of critical phantoms can strengthen local topological connectivity and reduce the impact of single faults on the system.

[0166] Experiment 2 (Multi-fault Scenario): Two control groups were set up: one with a randomly configured phantom and the other with an optimal phantom configuration. As the number of faults in vulnerable nodes gradually increased, the system failure rate and fault propagation range were observed. The results show that the system failure rate with the optimal phantom configuration was consistently lower than that with the random configuration, and the fault propagation range was also smaller. This indicates that the optimal phantom configuration can effectively suppress the cascading propagation of multiple faults by accurately covering high-fault areas and collaboratively optimizing density and distribution.

[0167] Experiment 3 (Comparison with Traditional Model): Two control groups were set up: the traditional CPPS model and the CPPS model with motif optimization. Interaction latency, node survival rate, and fault propagation risk were observed under different fault types. The results show that, regardless of the fault type, the CPPS with motif optimization performs better, with shorter interaction latency, higher node survival rate, and lower fault propagation risk.

[0168] The above verification demonstrates the significant effect of the method of the present invention in improving the robustness of CPPS.

[0169] Example 2:

[0170] This invention provides a robustness enhancement system for power cyber-physical systems based on phantom optimization and flow dynamics interaction. This system is used to implement the robustness enhancement method for power cyber-physical systems based on phantom optimization and flow dynamics interaction described in Embodiment 1 above. Figure 5 As shown, it specifically includes:

[0171] The topology modeling module is used to construct a three-layer CPPS topology model consisting of a power layer, an information layer, and cross-layer coupling. It uses an association matrix to describe the node connections within the power layer, an association matrix to describe the node connections within the information layer, and a cross-layer coupling matrix to quantify the cross-layer dependencies between power nodes and information nodes, resulting in a three-layer topology structure that includes intra-layer topological connections and inter-layer coupling relationships. This module is implemented using an association matrix algorithm, supports importing preset standard topologies or custom topology parameters, and automatically generates models of intra-layer node connections and inter-layer dependencies.

[0172] The dynamic interactive simulation module is used to establish a closed-loop interactive system based on the three-layer topology data, including information flow transmission, control decision-making, and energy flow regulation. Real-time operating data from the power layer is converted into an information flow by measurement equipment and transmitted to the control center. The control center generates regulation commands and transmits them to the power layer via the information layer to execute energy flow adjustments. The module visualizes the mutual conversion and real-time response characteristics between energy flow and information flow in real time, obtaining dynamic interactive characteristic data of the CPPS. This module uses a power flow calculation algorithm to simulate changes in power layer energy flow, combined with delay and flow transmission algorithms to simulate information flow transmission in the information layer, outputting characteristic data such as interaction delay and adaptability.

[0173] The motif optimization module, based on the three-layer topology data and the dynamic interaction characteristic data, identifies key network motifs supporting the core functions of the CPPS topology, filters out motif types that appear frequently and have statistical significance as optimization objects, and obtains a set of key motifs and their parameterized description data. This module is based on a distributed two-layer optimization algorithm. In the local competition layer, it explores near-optimal motif configurations through hybrid selection and crossover mutation operators; in the global competition layer, it evolves the globally optimal solution through asynchronous communication and fusion operators.

[0174] The fault simulation module, based on the set of key phantoms and their parameterized description data, aims to minimize the risk of fault propagation. It establishes an objective function and constraints for phantom optimization, optimizing the density, distribution, and topological embedding position of the key phantoms to obtain the optimal phantom configuration. This module simulates cascading propagation logic according to preset fault types (transmission line faults, information node failures, and cross-layer coupling link interruptions), determines the fault impact range based on the topology model and interactive data, and updates the system operating status in real time.

[0175] The robustness assessment module is used to update the three-layer CPPS topology model based on the optimal phantom configuration scheme, and to simulate fault propagation in typical fault scenarios. It compares the system operating states before and after optimization to verify the improvement effect of phantom optimization on CPPS robustness. Based on the fault simulation results, this module generates an assessment report using algorithms to calculate indicators such as load failure rate and node survival rate, quantifying the software optimization effect.

[0176] This embodiment presents a robustness enhancement system for a power cyber-physical system based on phantom optimization and flow dynamic interaction, used to implement the aforementioned robustness enhancement method for a power cyber-physical system based on phantom optimization and flow dynamic interaction. Therefore, the specific implementation methods of each module of this system can be found in the corresponding step descriptions in Embodiment 1. To avoid redundancy, they will not be repeated here.

[0177] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0178] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0179] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0180] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for improving the robustness of a power cyber-physical system based on phantom optimization and flow dynamic interaction, characterized in that, Includes the following steps: Step S1: Construct a three-layer CPPS topology model consisting of a power layer, an information layer, and cross-layer coupling. Use the power layer correlation matrix to describe the node connection relationship within the power layer, use the information layer correlation matrix to describe the node connection relationship within the information layer, and use the cross-layer coupling matrix to quantify the cross-layer dependency relationship between power nodes and information nodes, thus obtaining three-layer topology data containing intra-layer topology connections and inter-layer coupling associations. Step S2: Based on the three-layer topology data, establish a closed-loop interactive system that includes information flow transmission, control decision-making, and energy flow regulation. The real-time operating data of the power layer is converted into information flow through the measurement equipment and transmitted to the control center. The control center generates regulation commands and transmits them to the power layer through the information layer to perform energy flow adjustment. The mutual conversion and real-time response characteristics between energy flow and information flow are plotted in real time to obtain the dynamic interactive characteristic data of CPPS. Step S3: Based on the three-layer topology data and the dynamic interaction characteristic data, identify the key network modules that support the core functions of the system in the CPPS topology, select the module types that appear frequently and have statistical significance as optimization objects, and obtain the set of key modules and their parameterized description data. Step S4: Based on the set of key phantoms and their parameterized description data, with the goal of minimizing the risk of fault propagation, establish the objective function and constraints for phantom optimization, optimize the density, distribution and topological embedding position of the key phantoms, and obtain the optimal phantom configuration scheme. Step S5: Update the three-layer CPPS topology model based on the optimal phantom configuration scheme, and simulate fault propagation by setting typical fault scenarios. Compare the system operating status before and after optimization to verify the effect of phantom optimization on the robustness of CPPS.

2. The method for improving the robustness of a power cyber-physical system based on phantom optimization and flow dynamic interaction as described in claim 1, characterized in that, In step S1, the power layer uses an undirected graph. Characterization, in which For a set of power nodes, The set of power links; the power layer association matrix The element is defined as: ； in, For link Real-time transmission power, This represents the maximum transmission capacity of the link. The information layer uses directed graphs Characterization, in which For a set of information nodes, The information link set; the information layer association matrix The element is defined as: ； in, For link Real-time transmission latency, The maximum allowable latency of the link. For bit error rate, For bandwidth utilization; The cross-layer coupling matrix The elements are in tuples Describe the power supply support strength, monitoring coverage, and control response rate between power nodes and information nodes.

3. The method for improving the robustness of a power cyber-physical system based on phantom optimization and flow dynamic interaction as described in claim 1, characterized in that, In step S2, the closed-loop interaction process of the energy flow and information flow includes: The observation status of the information node on the power node is represented by the following formula: ； in, It is a 0-1 variable, with 1 representing an information node. For power nodes Observable, with 0 representing unobservable; , These are binary parameters, with values ​​of 1 indicating information nodes. , Configure the measurement equipment; a value of 0 indicates that it is not configured. For power link set The elements in the table represent power nodes. and The connection relationship, A set of information nodes; The adjustment of power layer energy flow corresponding to the control command is characterized by the adjustment of generator output as follows: ； in, For power generation nodes In the stage The output value; For the stage Power generation node Corresponding information nodes The working status indicates whether the control commands are effectively transmitted; , Respectively, power generation nodes Minimum and maximum output limits; For power generation nodes The output value in the previous stage.

4. The method for improving the robustness of a power cyber-physical system based on phantom optimization and flow dynamic interaction according to claim 3, characterized in that, In step S2, the dynamic interaction characteristic data is quantitatively described by response latency and interaction accuracy: Define total response delay Total time spent from information flow generation to energy flow adjustment: ； in, The transmission delay from energy flow to information flow, To delay decision-making in the control center, The transmission delay from information flow to energy flow; Define comprehensive interaction precision for: ； in, To improve the efficiency of information flow generation, The energy flow adjustment accuracy is the deviation rate between the target value of the control command and the actual change in energy flow.

5. The method for improving the robustness of a power cyber-physical system based on phantom optimization and flow dynamic interaction according to claim 1, characterized in that, In step S3, the key network module includes a three-node closed-loop subgraph and a four-node star subgraph; Frequency of occurrence of phantoms Calculate using the following formula: ； in, This represents the actual number of occurrences of the target subgraph. This represents the total number of nodes in the CPPS topology. The number of nodes in the module. From Select from nodes The number of combinations of nodes; The statistical significance score of the subplots was quantified using the Z-score method. : ； in, This represents the average frequency of occurrence of this subgraph in the random topology. The standard deviation is denoted as ; when When this occurs, the subgraph is identified as a key motif with statistical significance.

6. The method for improving the robustness of a power cyber-physical system based on phantom optimization and flow dynamic interaction according to claim 1, characterized in that, In step S3, the parameterized description data of the key motif includes: phantom density coefficient Characterizing the motif within a unit topological region The number of configurations is defined as: ； in, For the model The actual number of configurations, For the motif within this topological region The maximum number that can be configured; Distribution rationality coefficient The coverage of the quantification model in high-fault areas is defined as: ； in, For the phantom in the high-incidence area of ​​failure The number of configurations, For the model Total number of configurations; Local connectivity enhancement coefficient Differentiated definitions based on phantom type: ； in, This represents the number of actually available communication paths in a three-node closed-loop subgraph. The number of nodes in a four-node star subplot to configure measurement devices; Interaction Adaptability Coefficient The ability of a quantization module to support the interaction of energy flow and information flow is defined as: ； in, For the model The surrounding interaction latency deviation, This represents the maximum allowable interaction latency of the system.

7. The method for improving the robustness of a power cyber-physical system based on phantom optimization and flow dynamic interaction according to claim 1, characterized in that, In step S4, the objective function is to minimize the comprehensive value of fault propagation risk: ； in, This is the comprehensive risk value for fault propagation, with a value range of [0,1]. The smaller the value, the lower the probability of fault propagation. This represents the total number of nodes in the CPPS topology. For the set of key motifs; , , , respectively the phantom The density coefficient, distribution rationality coefficient, local connectivity enhancement coefficient, and interaction adaptation coefficient; The constraints include: Cost constraints in phantom configuration: ； in, For a single phantom Configuration cost, Choose a variable for the motif type. This represents the maximum allowable configuration cost threshold for the system. Topology compatibility constraints: ； in, The determinant of the topological correlation matrix of the motif embedding region is given. The minimum topological connectivity threshold; Interactive data adaptation constraints: ； in, The minimum interaction adaptation threshold.

8. The method for improving the robustness of a power cyber-physical system based on phantom optimization and flow dynamic interaction according to claim 7, characterized in that, In step S4, a distributed two-layer cooperative competitive optimization algorithm is used to solve the objective function and constraints. The algorithm includes: The local competition layer is used to perform multi-directional independent search through a hybrid selection operator, motif crossover operator, and motif mutation operator, and to optimize the population by combining an artificial immune framework to generate an approximately optimal motif configuration scheme. The global competition layer is used to receive the best individuals uploaded by each local process through asynchronous queue communication, update the global population using a fusion operator, perform additional iterative optimization, and output the globally optimal motif configuration scheme.

9. The method according to claim 1, characterized in that, In step S5, the typical fault scenarios include transmission line faults, information node failures, and cross-layer coupling link interruptions. By comparing the load failure rate, node survival rate, and fault propagation range of the system before and after motif optimization under the same fault scenario, the effect of motif optimization on the robustness of CPPS is evaluated.

10. A robustness enhancement system for a power cyber-physical system based on phantom optimization and flow dynamic interaction, characterized in that, The system is used to implement the robustness improvement method for power cyber-physical systems based on phantom optimization and flow dynamic interaction as described in any one of claims 1 to 9, specifically including: The topology modeling module is used to construct a three-layer CPPS topology model consisting of a power layer, an information layer, and cross-layer coupling. It uses a power layer correlation matrix to describe the node connection relationship within the power layer, a information layer correlation matrix to describe the node connection relationship within the information layer, and a cross-layer coupling matrix to quantify the cross-layer dependency relationship between power nodes and information nodes, thus obtaining three-layer topology data that includes intra-layer topology connections and inter-layer coupling associations. The dynamic interactive simulation module is used to establish a closed-loop interactive system based on the three-layer topology data, including information flow transmission, control decision and energy flow regulation. The real-time operation data of the power layer is converted into information flow through the measurement equipment and transmitted to the control center. The control center generates regulation commands and transmits them to the power layer through the information layer to perform energy flow adjustment. The module also displays the mutual conversion and real-time response characteristics between energy flow and information flow in real time, thus obtaining the dynamic interactive characteristic data of CPPS. The motif optimization module is used to identify key network motifs supporting the core functions of the CPPS topology based on the three-layer topology data and the dynamic interaction characteristic data, and to select motif types that appear frequently and have statistical significance as optimization objects, thereby obtaining a set of key motifs and their parameterized description data. The fault inference module is used to establish the objective function and constraints for the optimization of the key phantoms based on the set of key phantoms and their parameterized description data, with the goal of minimizing the risk of fault propagation. It optimizes the density, distribution and topological embedding position of the key phantoms to obtain the optimal phantom configuration scheme. The robustness evaluation module is used to update the three-layer CPPS topology model based on the optimal phantom configuration scheme, and to simulate fault propagation by setting typical fault scenarios. The module compares the system operating status before and after optimization to verify the effect of phantom optimization on the robustness of CPPS.

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