A power distribution network resilience evaluation verification method, system, device and medium based on multi-dimensional fault injection

Abstract

The present application relates to the technical field of power distribution network resilience evaluation, and discloses a power distribution network resilience evaluation verification method, system, device and medium based on multi-dimensional fault injection, which comprises the following steps: constructing a multi-dimensional fault model library; based on a preset test target, selecting a target fault scene from the model library and generating a fault injection strategy; executing the strategy on a hardware-in-the-loop simulation platform, and collecting system operation data in real time; calculating a performance index curve representing the overall power supply level of the power distribution network over time, and quantitatively calculating a plurality of resilience evaluation indexes; based on the resilience evaluation indexes, performing comparative analysis, identifying key scenes that significantly affect the resilience of the power distribution network, and adjusting the fault injection strategy in subsequent tests to realize closed-loop evaluation and verification of the resilience of the power distribution network. The present application not only evaluates the degree of performance loss, but also focuses on recovery speed and recovery efficiency to identify weak links affecting recovery and provide a scientific basis for formulating resilience improvement measures.

Description

Technical Field

[0001] This invention relates to the field of distribution network resilience assessment technology, and in particular to a method, system, equipment and medium for distribution network resilience assessment and verification based on multi-dimensional fault injection. Background Technology

[0002] As a crucial link connecting the main grid and users, the distribution network faces multiple threats to its safe and stable operation, including extreme weather and cyberattacks. Therefore, resilience assessment is essential. Currently, this mainly relies on software simulation methods. By constructing simplified power grid equipment models and control strategy models, preset fault scenarios are simulated, and the system's disturbance rejection capability is evaluated based on static indicators such as load loss output from the simulation.

[0003] However, with the increasing complexity and coupling of disturbance types, existing assessment methods are often limited to the analysis of single-type physical faults, making it difficult to realistically reproduce complex scenarios where multiple disturbances such as information interruption and control failure coexist and influence each other. This leads to discrepancies between assessment results and the diverse risks actually faced by the power grid. Furthermore, pure software simulation cannot accurately reflect the dynamic response characteristics and actual defects of real protection devices, automation terminals, and other hardware, causing a disconnect between the simulation environment and the real operating environment, reducing the credibility and guiding value of assessment conclusions. Moreover, it often focuses on the degree of system performance degradation after a fault occurs, lacking dynamic tracking and quantitative analysis of the speed and efficiency of the entire system self-healing and recovery process, making it difficult to comprehensively reveal existing problems. Summary of the Invention

[0004] In view of the aforementioned existing problems, the present invention is proposed.

[0005] Therefore, this invention provides a method and system for evaluating and verifying the resilience of distribution networks based on multi-dimensional fault injection, which solves the problems of current evaluation methods, such as limited fault scenarios, lack of realistic verification environments, disconnect between simulation and reality, and failure to quantify recovery capabilities. To solve the above-mentioned technical problems, the present invention provides the following technical solution: In a first aspect, the present invention provides a method for evaluating and verifying the resilience of a distribution network based on multi-dimensional fault injection, comprising: Based on historical data of distribution network faults, a multi-dimensional fault model library is constructed. Based on the preset test objectives, target fault scenarios are selected from the fault model library, and a fault injection strategy including fault selection, injection timing and injection strength is generated. The fault injection strategy is executed on a hardware-in-the-loop simulation platform, which includes a real-time digital simulator that runs a power distribution network simulation model and at least one type of actual power distribution equipment connected through a standard interface. Real-time monitoring and acquisition of system operation data of the hardware-in-the-loop simulation platform before and after fault injection; Based on the system operation data, the performance index characteristic of the overall power supply level of the distribution network is calculated as a function of time, and multiple resilience assessment indicators are quantitatively calculated based on the performance index change curve. Comparative analysis based on the aforementioned resilience assessment indicators identifies key fault scenarios, key equipment, and bottlenecks in the recovery process that significantly impact the resilience of the distribution network. Based on the identification results, the fault injection strategy in subsequent tests is adjusted to achieve closed-loop assessment and verification of the distribution network resilience.

[0006] As a preferred embodiment of the distribution network resilience assessment and verification method based on multi-dimensional fault injection described in this invention, the method includes: constructing a multi-dimensional fault model library based on historical distribution network fault data, comprising: For each fault scenario, a multi-dimensional fault descriptor is defined, which includes fault identifier, fault type, spatial location, time parameter, and severity coefficient. Establish a fault correlation matrix to characterize the triggering dependencies or independence relationships between different fault scenarios, so as to support the generation of cascading faults or concurrent multi-fault scenarios that conform to the actual physical logic.

[0007] As a preferred embodiment of the distribution network resilience assessment and verification method based on multi-dimensional fault injection described in this invention, the method includes: generating a fault injection strategy comprising fault selection, injection timing, and injection strength, including: Based on the test objectives, a set of faults to be injected is determined from the fault model library using a fault selection method. Configure the start time and duration of the injection for each fault in the fault set; Based on the fault correlation matrix, configure the event trigger interval for faults with triggering dependencies; Adjust the severity coefficient in the fault descriptor to set the fault injection strength.

[0008] As a preferred embodiment of the distribution network resilience assessment and verification method based on multi-dimensional fault injection described in this invention, wherein: executing the fault injection strategy on a hardware-in-the-loop simulation platform includes: The generated injection strategy is encoded into a sequence of fault instructions; If a physical layer fault is simulated when the injection time specified in the instruction sequence is reached, the parameters of the corresponding component in the power distribution network simulation model are modified. If a fault is simulated at the information layer, the programmable network devices deployed in the communication link will be interrupted or interfered with data communication. If the simulated control layer fails, simulated signals are injected into the input and output circuits of the actual power distribution equipment or its internal configuration parameters are modified.

[0009] As a preferred embodiment of the distribution network resilience assessment and verification method based on multi-dimensional fault injection described in this invention, the method involves: calculating the time-varying curves of performance indicators characterizing the overall power supply level of the distribution network based on the system operation data; and quantifying and calculating multiple resilience assessment indicators based on the performance indicator variation curves, including: Based on system operation data, the total power supply rate of the system is calculated as the performance indicator. The characteristic stages of the performance index change curve are extracted, including the steady-state operation stage, the performance degradation stage, the worst operation stage, and the performance recovery stage. Based on the aforementioned characteristic stages, toughness indices are calculated, including performance loss, recovery time, recovery rate, and toughness coefficient. The performance loss is determined based on the area of ​​the performance curve below the initial level during the performance degradation phase and the initial recovery phase; the recovery time is the time required for performance to recover to a preset ratio from the occurrence of the fault; the recovery rate is the average recovery slope during the performance recovery phase; and the resilience coefficient is a composite index that comprehensively reflects the performance loss and the recovery rate.

[0010] As a preferred embodiment of the distribution network resilience assessment and verification method based on multi-dimensional fault injection described in this invention, the method involves: comparative analysis based on the resilience assessment indicators to identify key fault scenarios, key equipment, and bottlenecks in the recovery process that significantly impact the resilience of the distribution network, including: The resilience coefficients corresponding to each failure scenario are statistically analyzed, the resilience impact of each failure scenario compared to the baseline scenario without failure is calculated, and the scenarios are sorted according to the resilience impact to determine the key failure scenarios. Statistically analyze the frequency of failures and the average performance loss caused by each actual power distribution equipment or simulation model component during testing, calculate the equipment importance, and identify key equipment. Analyze the data from the performance recovery phase, break it down into multiple sub-phases, and identify the sub-phase with the longest duration as the bottleneck in the recovery process.

[0011] As a preferred embodiment of the distribution network resilience assessment and verification method based on multi-dimensional fault injection described in this invention, the method includes: adjusting the fault injection strategy in subsequent tests based on the identification results, including: Based on the ranking of the key fault scenarios, the probability of their corresponding fault models being extracted in subsequent fault selection steps is increased. For the identified bottlenecks in the recovery process, specific test scenarios that cause the corresponding bottleneck links to fail or be restricted are designed and injected into the fault injection strategy.

[0012] Secondly, the present invention provides a distribution network resilience assessment and verification system based on multi-dimensional fault injection, comprising: The fault model library construction module is used to build a multi-dimensional fault model library based on historical fault data of the distribution network. The fault injection control module is used to select target fault scenarios from the fault model library based on preset test targets, and generate a fault injection strategy that includes fault selection, injection timing and injection strength. The hardware-in-the-loop simulation module is used to execute the fault injection strategy on the hardware-in-the-loop simulation platform, which includes a real-time digital simulator that runs a power distribution network simulation model and at least one type of actual power distribution equipment connected through a standard interface. The performance monitoring module is used to monitor and collect system operation data of the hardware-in-the-loop simulation platform in real time before and after fault injection. The resilience assessment module is used to calculate the performance index change curve over time, which characterizes the overall power supply level of the distribution network, based on the system operation data, and to quantify and calculate multiple resilience assessment indicators based on the performance index change curve. The intelligent analysis module is used to perform comparative analysis based on the resilience assessment indicators to identify key fault scenarios, key equipment, and bottlenecks in the recovery process that have a significant impact on the resilience of the distribution network. The feedback optimization module is used to adjust the fault injection strategy in subsequent tests based on the identification results, so as to achieve closed-loop evaluation and verification of the distribution network resilience.

[0013] Thirdly, the present invention provides a computer device, comprising: Memory and processor; The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions. When the computer-executable instructions are executed by the processor, they implement the steps of a distribution network resilience assessment and verification method based on multi-dimensional fault injection.

[0014] Fourthly, the present invention provides a computer-readable storage medium storing computer-executable instructions that, when executed by a processor, implement the steps of the aforementioned method for evaluating and verifying the resilience of a distribution network based on multi-dimensional fault injection.

[0015] Compared with existing technologies, the beneficial effects of this invention are as follows: By establishing a multi-dimensional fault model library covering physical layer faults, information layer faults, and control layer faults, this invention can support flexible combinations of single fault and multi-fault coupled scenarios, and set various strategies to inject faults into the system, realistically simulating various threat scenarios such as typhoons, ice storms, network attacks, and equipment aging, to comprehensively discover resilience performance under complex disturbances. By connecting actual power distribution automation equipment, protection devices, and distributed power controllers to a real-time digital simulator through standard communication interfaces, a hardware-software integrated verification platform is constructed. This platform retains the real characteristics of actual equipment while possessing the flexibility and security of simulation testing, resulting in evaluation results that are closer to actual operating conditions. Furthermore, a resilience assessment index system covering the entire process before, during, and after a fault is constructed. This system not only assesses the degree of performance loss but also focuses on recovery speed and efficiency to identify weak links affecting recovery, providing a scientific basis for the formulation of resilience improvement measures. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a schematic diagram of the overall process of a distribution network resilience assessment and verification method based on multi-dimensional fault injection, as described in one embodiment of the present invention. Detailed Implementation

[0018] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0019] Example 1, referring to Figure 1 As an embodiment of the present invention, a method for evaluating and verifying the resilience of a distribution network based on multi-dimensional fault injection is provided, comprising: S100: Construct a multi-dimensional fault model library based on historical data of distribution network faults; S200: Based on the preset test target, select the target fault scenario from the fault model library and generate a fault injection strategy that includes fault selection, injection timing and injection strength. S300: Execute the fault injection strategy on a hardware-in-the-loop simulation platform, the hardware-in-the-loop simulation platform including a real-time digital simulator that runs a power distribution network simulation model and at least one type of actual power distribution equipment connected through a standard interface. S400: Real-time monitoring and acquisition of system operation data of the hardware-in-the-loop simulation platform before and after fault injection. S500: Based on the system operation data, calculate the performance index change curve over time that characterizes the overall power supply level of the distribution network, and quantify and calculate multiple resilience assessment indicators based on the performance index change curve. S600: Based on the aforementioned resilience assessment indicators, a comparative analysis is conducted to identify key fault scenarios, key equipment, and bottlenecks in the recovery process that have a significant impact on the resilience of the distribution network. S700: Based on the identification results, adjust the fault injection strategy in subsequent tests to achieve closed-loop assessment and verification of the distribution network resilience.

[0020] Specifically, current assessments of the coupled effects of various faults in distribution networks—such as typhoons causing line faults that may be accompanied by chain reactions like communication outages and automation equipment failures—cannot accurately reflect the true resilience of the system under complex disturbances, resulting in poorly targeted emergency plans. Furthermore, the actual performance of distribution automation terminals, protection devices, and distributed power controllers under fault conditions often differs from theoretical models. For instance, communication delays, device crashes, and malfunctions frequently occur in actual equipment, but these are difficult to accurately simulate in a pure simulation environment and thus cannot guide the resilience improvement of actual systems. Moreover, it is impossible to identify key factors affecting recovery speed, such as backup power startup time and topology reconfiguration speed.

[0021] Therefore, based on the various fault scenario parameters predefined in steps S100-S700, fault types and parameters are selected from the model library according to the test strategy, and fault signals are injected into the hardware-in-the-loop simulation platform through a dedicated interface. The simulation platform consists of a real-time digital simulator and actual power distribution equipment. The simulator runs an electromagnetic transient model of the power distribution network, and the actual equipment, including protection devices, automation terminals, and distributed power controllers, is connected to the simulator through standard interfaces. After fault injection, operating parameters such as voltage, current, switch status, and load data are collected in real time to form a system performance time series. Based on the monitoring data, the performance curve decline and recovery process is calculated, resilience indicators are quantified using mathematical methods, and the evaluation results are deeply analyzed to identify weak links and generate improvement suggestions. The analysis results are used to adjust the fault injection strategy, achieve iterative optimization of the test scheme, and ultimately form a complete resilience assessment and verification closed loop.

[0022] Example 2, refer to Figure 1As an embodiment of the present invention, based on the above embodiment, a method for evaluating and verifying the resilience of a distribution network based on multi-dimensional fault injection is provided. The method includes: S100: Construct a multi-dimensional fault model library based on historical data of distribution network faults; It should be noted that the fault model library is the foundation of the entire verification system, storing detailed parameters of various faults that the distribution network may suffer.

[0023] In this embodiment of the application, step S100 involves constructing a multi-dimensional fault model library based on historical data of distribution network faults, including the following steps A1-A2: A1: Define a multi-dimensional fault descriptor for each fault scenario. The fault descriptor includes fault identifier, fault type, spatial location, time parameter, and severity coefficient. Specifically, the five-tuple of the fault descriptor can be represented as: (1) In the formula, For the first One fault scenario descriptor; Assign fault identification numbers; For fault type codes; The coordinates of the fault location in space; A set of failure time parameters; This represents the severity coefficient of the fault.

[0024] For example, a fault identifier such as "a three-phase short-circuit fault at kilometer 5 of a 10 kV line, with a transition resistance of 0.5 ohms, occurring 120 seconds after the simulation started, lasting 0.15 seconds" would be used. F001, fault type Three-phase short circuit, location coordinates Marking point 5 km along line A, time parameters Including a start time of 120 seconds and an end time of 120.15 seconds, severity coefficient. It is 0.9.

[0025] Specifically, fault types can be categorized into three main types based on their impact level: physical layer faults, information layer faults, and control layer faults. Physical layer faults include physical damage to equipment such as line breaks, transformer short circuits, and switch malfunctions. Each fault can be described using parameters such as fault location, fault type, fault impedance, and time of occurrence. Information layer faults include communication interruptions, data packet loss, and information errors, and can be described using parameters such as communication link identifier, interruption duration, and packet loss rate. Control layer faults include protection malfunctions, automation failures, and control command errors, and can be described using parameters such as device number, failure mode, and duration.

[0026] A2: Establish a fault correlation matrix to characterize the triggering dependency or independence relationships between different fault scenarios, so as to support the generation of cascading faults or concurrent multi-fault scenarios that conform to the actual physical logic. Specifically, the fault correlation matrix can be represented as follows: (2) In the formula, For elements of the fault correlation matrix, and These are the fault numbers. When Time indicates fault The occurrence of this will trigger a fault. ,when This indicates that the two faults are independent. For example, a typhoon causes a line to break (fault). This may also cause a break in the communication fiber optic cable (fault). ), then the corresponding matrix element By using the correlation matrix, the system can automatically generate cascading failure scenarios that conform to actual physical laws.

[0027] S200: Based on the preset test target, select the target fault scenario from the fault model library and generate a fault injection strategy that includes fault selection, injection timing and injection strength. In this embodiment of the application, step S200 generates a fault injection strategy that includes fault selection, injection timing, and injection strength, including the following steps B1-B4: B1: Based on the test objective, determine the set of faults to be injected from the fault model library using a fault selection method; Specifically, the type of fault to be injected is determined based on the test objective.

[0028] In one alternative implementation, in B1, for the target being resilience benchmark testing, the system extracts faults from the model library according to the probability of fault occurrence; for the target being extreme scenario testing, the system selects high-severity multi-fault coupling scenarios; for the target being weak link detection, the system uses a traversal method to sequentially inject faults at different locations.

[0029] In another alternative implementation, based on the above implementation, the fault selection method in B1 can be a variety of fault selection methods such as deterministic selection, random sampling, and genetic algorithm optimization.

[0030] B2: Configure the start time and duration for each fault in the fault set; Specifically, for a single fault, the time of occurrence and duration of the fault can be set directly.

[0031] B3: Based on the fault correlation matrix, configure the event trigger interval for faults with triggering dependencies; Specifically, for multi-fault scenarios, it is necessary to consider the time intervals and causal relationships between faults. This is based on the fault correlation matrix from the first step. When a fault is detected After it occurs, the propagation time is delayed. Automatically triggers associated faults The propagation time is determined by the physical mechanism of the fault. For example, the delay caused by control failure due to communication interruption is usually a few seconds to tens of seconds.

[0032] B4: Adjust the severity coefficient in the fault descriptor to set the fault injection strength; Specifically, in B4, for short-circuit faults, the short-circuit current is changed by adjusting the transition resistance; for communication faults, the communication quality is changed by adjusting the packet loss rate and delay; and for control faults, the control reliability is changed by adjusting the failure probability and duration. Furthermore, it supports a stepped increase in intensity, gradually escalating from minor disturbances to severe faults, comprehensively examining the system's resilience under different disturbance intensities.

[0033] S300: Execute the fault injection strategy on a hardware-in-the-loop simulation platform, the hardware-in-the-loop simulation platform including a real-time digital simulator that runs a power distribution network simulation model and at least one type of actual power distribution equipment connected through a standard interface. Specifically, the hardware-in-the-loop simulation platform in S300 is the core execution environment of the system, consisting of a real-time digital simulator and actual power distribution equipment.

[0034] In one alternative implementation, the real-time digital simulator uses a commercial platform such as RTDS or RT-LAB to run an electromagnetic transient simulation model of the power distribution network, simulating the electrical characteristics of primary equipment such as power distribution lines, transformers, and loads. The simulation step size can be set to 50 microseconds to ensure accurate calculation of the electromagnetic transient process.

[0035] Based on the above implementation methods, the actual power distribution equipment includes three categories: protection devices, distribution automation terminals, and distributed power controllers. Protection devices connect to the simulator via current transformer and voltage transformer interfaces, receiving simulated current and voltage signals output by the simulator, executing actual protection logic judgments and tripping outputs, and feeding back the tripping signal to the simulator to trigger the circuit breaker model's operation. Distribution automation terminals connect to the simulator's SCADA simulation module via an Ethernet interface, receiving telemetry data and uploading remote signaling information, and executing remote control commands to control the switch states in the simulation model. Distributed power controllers connect to the simulator via power amplifiers; the control signals output by the controllers are amplified and injected into the simulator's distributed power model to achieve real-time adjustment of active and reactive power.

[0036] In this embodiment of the application, the execution of the fault injection strategy on the hardware-in-the-loop simulation platform in step S300 includes the following steps C1-C4: C1: Encode the generated injection strategy into a fault instruction sequence; Specifically, the generated injection strategy is encoded into a fault instruction sequence. Each instruction includes fields such as fault identifier, target device, injection time, and injection parameters obtained from S100. The instruction sequence can be sent to the hardware-in-the-loop simulation platform through a dedicated fault injection channel. After receiving the instruction, the platform injects the corresponding fault into the specified device or simulation model at the specified time.

[0037] It should be noted that this centralized control method can ensure precise synchronization of fault injection from multiple devices, with a time accuracy down to the millisecond level.

[0038] C2: If a physical layer fault is simulated when the injection time specified in the instruction sequence is reached, the parameters of the corresponding component in the power distribution network simulation model are modified. For example, physical layer faults directly affect the power grid model of the simulator. For instance, a line break fault is achieved by changing the impedance parameters of the corresponding line in the simulation model, modifying the line impedance during normal operation to a maximum value to simulate an open circuit state.

[0039] C3: If a fault is simulated in the information layer, the programmable network device deployed in the communication link will be interrupted or interfered with data communication. For example, information layer faults affect communication links. For instance, a communication interruption fault is achieved by blocking Ethernet packets between the power distribution automation terminal and the SCADA system. The system deploys a programmable switch on the communication link and discards packets with specific source or destination addresses according to the fault injection instructions generated by S200.

[0040] C4: If the simulation control layer fails, then inject analog signals into the input and output circuits of the actual power distribution equipment or modify its internal configuration parameters.

[0041] For example, a control layer fault can affect the control device. For instance, a protection maloperation fault can be caused by injecting a false trigger signal into the trip output circuit of the protection device, or by modifying the internal registers of the protection device to change the protection setting value to simulate a setting error.

[0042] It should be noted that the S300 simulation platform runs the distribution network model in real time. The simulator updates the network state every calculation step and outputs electrical signals and communication information to the actual equipment through the interface. The actual equipment executes control and protection functions based on the received information, and its output signals are fed back to the simulator in real time, affecting the operating state of the network model, forming a real-time closed-loop interaction between hardware and software. When the fault injection controller issues a fault command, the simulation platform executes the corresponding fault action at a specified time, and the operating state of the entire system changes accordingly, providing a real observation object for subsequent performance monitoring.

[0043] S400: Real-time monitoring and acquisition of system operation data of the hardware-in-the-loop simulation platform before and after fault injection; Specifically, the key performance indicators of the real-time acquisition simulation platform in S400 can be mainly divided into four categories: electrical quantity data, switch status data, load power supply data, and equipment action data.

[0044] Electrical data acquisition comes from the simulator's measurement output, including the three-phase voltage amplitude, phase angle, and frequency of each bus, and the three-phase current, active power, and reactive power of each line. The acquisition frequency is set to 20 times per second to capture transient processes such as voltage dips and frequency fluctuations. The system processes the acquired voltage data in real time, calculates the voltage deviation of each bus, and determines voltage quality by comparing the measured voltage of the bus with the rated voltage. When the measured voltage of a bus is lower than 90% of the rated voltage, the bus voltage is considered unqualified; when it is lower than 70%, it is considered a severe voltage drop. By statistically analyzing the number of buses with unqualified voltage at each time point, a time series of voltage quality indicators is generated.

[0045] Switch status data is acquired from the switch model in the simulator and status feedback from actual circuit breakers, recording the open / closed states of all circuit breakers, disconnectors, and sectionalizing switches, as well as the times when these states change. The system establishes a switch action sequence table, recording the time of each switch action, switch number, action type (open or close), and trigger reason (protection trip, automatic reclosing, manual remote control, etc.). By analyzing the switch action sequence, the system can reconstruct the complete process of fault isolation and power restoration.

[0046] Load power supply data is acquired from the load model of the simulator, recording the power supply status and power output of each load node. System definition... The power supply rate of each load node is the ratio of actual power supplied to rated load power. A power supply rate less than 1 indicates that the load is not fully powered, and a power supply rate of 0 indicates a complete power outage. The system calculates the total power supply rate in real time, which serves as a core indicator for measuring the overall performance of the system.

[0047] All collected data is timestamped to ensure time synchronization across different sources, with synchronization accuracy guaranteed to be within 1 millisecond using GPS clocks. The raw data is preprocessed and stored in a time-series database, providing a complete data foundation for subsequent resilience assessments. The monitoring module transmits key performance indicators to the resilience assessment module via real-time data streams, and the assessment module calculates quantitative resilience indicators based on these indicators.

[0048] S500: Based on the system operation data, calculate the performance index change curve over time that characterizes the overall power supply level of the distribution network, and quantify and calculate multiple resilience assessment indicators based on the performance index change curve. In this embodiment of the application, step S500 calculates the time-varying curves of performance indicators characterizing the overall power supply level of the distribution network based on the system operation data, and quantifies and calculates multiple resilience assessment indicators based on the performance indicator changing curves, including the following steps D1-D3: D1: The total power supply rate of the system is calculated based on the system operation data and used as the performance indicator. Specifically, system performance is defined as total power supply rate, which is the sum of the actual power supplied by all load nodes divided by the sum of the rated power of all loads. This can be expressed as: (3) In the formula, for Total power supply of the system at any time This represents the total number of load nodes. For the first Each load node Actual power supply at any given time For the first Rated power of each load node. Performance during normal operation. When the value is close to 1, performance degrades after a fault occurs, but gradually recovers during fault isolation and power restoration. The evaluation module samples performance values ​​at 1-second intervals to form a performance time series.

[0049] D2: Extract the characteristic stages from the performance index change curve, including the steady-state operation stage, the performance degradation stage, the worst-case operation stage, and the performance recovery stage; It should be noted that during the steady-state operation phase, from the start of the simulation until the occurrence of the fault, the performance remains at the initial level. (Typically 1); the performance degradation phase begins from the moment the failure occurs. When performance drops to its lowest point During this phase, the system is impacted by a fault, causing partial load power loss; the worst operating phase begins from... When the recovery measures begin to take effect During this phase, performance remains at its lowest level. The performance recovery phase begins When performance recovers to an acceptable level During this phase, power supply is gradually restored through measures such as fault isolation, topology reconfiguration, and distributed power supply support.

[0050] D3: Based on the aforementioned characteristic stages, calculate the resilience indicators, including performance loss, recovery time, recovery rate, and resilience coefficient; The performance loss is determined based on the area of ​​the performance curve below the initial level during the performance degradation phase and the initial recovery phase; the recovery time is the time required for performance to recover to a preset ratio from the occurrence of the fault; the recovery rate is the average recovery slope during the performance recovery phase; and the resilience coefficient is a composite index that comprehensively reflects the performance loss and the recovery rate.

[0051] Specifically, the performance loss is defined as the area between the performance curve and the initial performance level, divided by the product of the initial performance level and the evaluation time, expressed as: (4) In the formula, This refers to the performance loss. This represents the initial performance level. for The system performance at time t is calculated using formula (3); The time when the fault occurred; This is used to assess the end point of failure. This indicator reflects the overall impact of the failure on the system, and its value ranges from 0 to 1, with a smaller value indicating better resilience.

[0052] Recovery time is defined as the time required from the occurrence of a failure to the recovery of performance to 90% of its initial level, and can be expressed as: (5) In the formula, Recovery time; The time when the fault occurred; for System performance at any given time; This represents the initial performance level. Recovery time directly reflects the system's ability to recover quickly; the shorter the time, the better the resilience.

[0053] Recovery rate is defined as the ratio of performance improvement during the performance recovery phase to recovery time, and can be expressed as: (6) In the formula, For recovery rate; This represents the initial performance level. This is the lowest performance value; The recovery time is calculated using formula (5). This indicator reflects the efficiency of the recovery measures; a higher rate indicates a stronger recovery capability.

[0054] The toughness coefficient, taking into account both performance loss and recovery ability, can be defined as: (7) In the formula, It is the toughness coefficient; The performance loss is calculated using formula (4); The recovery rate is calculated using formula (6); This represents the initial performance level. A higher toughness coefficient indicates a higher level of system toughness; this indicator unifies performance resistance and recovery capability into a single quantitative metric.

[0055] Furthermore, the S500 calculates the above four indicators in real time and generates a resilience assessment report that includes performance curves, indicator values, and key event time points. The report data is then transmitted to the intelligent analysis module for in-depth analysis. By comparing resilience indicators under different failure scenarios, the system can identify the failure types and weak points that have the greatest impact on resilience.

[0056] S600: Based on the aforementioned resilience assessment indicators, a comparative analysis is conducted to identify key fault scenarios, key equipment, and bottlenecks in the recovery process that have a significant impact on the resilience of the distribution network. In this embodiment of the application, step S600 involves comparative analysis based on the resilience assessment indicators to identify key fault scenarios, key equipment, and bottlenecks in the recovery process that significantly impact the resilience of the distribution network, including the following steps E1-E3: E1: Calculate the resilience coefficients corresponding to each failure scenario, determine the resilience impact of each failure scenario compared to the baseline scenario without failure, and sort them according to the resilience impact to identify the key failure scenarios. Specifically, in E1, for each fault scenario i, its corresponding resilience coefficient is recorded. The toughness impact of each fault is calculated using formula (7). (8) In the formula, For fault The degree of influence of toughness; This is the initial toughness coefficient under fault-free conditions; For fault The resilience coefficient under a given scenario. A higher impact indicates a more severe weakening of the system's resilience by the fault. For example, the system can sort all fault scenarios from highest to lowest impact, identifying the top 10% of faults with the most severe impact as the focus of resilience improvement efforts.

[0057] E2: Statistically analyze the frequency of failures and the average performance loss caused by each actual power distribution equipment or simulation model component during testing, calculate the equipment importance, and identify key equipment. Specifically, in E2, device importance can be expressed as: (9) In the formula, For the first The importance of each device; This represents the number of times the equipment failed during the test. The average performance loss caused by the failure of this equipment can be calculated by averaging the results of multiple calculations using formula (4). Equipment of high importance will have serious consequences if it fails, requiring a focus on strengthening reliability and redundancy.

[0058] E3: Analyze the data of the performance recovery phase, break it down into multiple sub-phase times, and compare them to find the sub-phase with the longest time as the bottleneck of the recovery process.

[0059] In one optional implementation, E3 records the recovery measures taken and their execution times in each failure scenario, including fault isolation time, topology reconfiguration time, load shifting time, and distributed power supply startup time. By comparing the performance curves with and without a particular recovery measure, the contribution of that measure to resilience improvement is quantitatively evaluated. For example, the resilience coefficients under fast fault isolation and slow isolation scenarios can be compared. The result is obtained by formula (7) to quantify the resilience enhancement effect of rapid isolation.

[0060] In one alternative implementation, E3 can analyze data from the performance recovery phase to identify bottlenecks limiting recovery speed. For example, if recovery time is primarily consumed during the topology reconfiguration phase in multiple tests, then slow topology reconfiguration speed is determined to be the system bottleneck; if recovery time is primarily consumed during the backup power startup phase, then slow backup power startup is determined to be the bottleneck. The system uses time decomposition analysis to determine the total recovery time. The result is obtained by formula (7). It is decomposed into multiple sub-stages such as fault detection time, fault isolation time, reconfiguration decision time, and switching operation time. The sub-stage with the longest time consumption is identified as the bottleneck.

[0061] It should be noted that the S600 can automatically generate resilience improvement recommendation reports based on the above analysis results. These reports include high-risk faults that require special attention, key equipment that needs enhanced reliability (i.e., equipment importance ranking), recovery measures that need optimization, and bottlenecks that need improvement. For example, if the analysis finds that a fault on a certain line has the highest impact, it is recommended to add a tie switch to that line; if the topology reconfiguration speed is found to be slow, it is recommended to optimize the reconfiguration algorithm or add automated terminals. These recommendations are then passed on as feedback to subsequent steps and system maintenance personnel.

[0062] S700: Based on the identification results, adjust the fault injection strategy in subsequent tests to achieve closed-loop assessment and verification of the distribution network resilience.

[0063] In this embodiment of the application, step S700, based on the identification result, adjusts the fault injection strategy in subsequent tests, including the following steps F1-F2: F1: Based on the ranking of the key fault scenarios, increase the probability of their corresponding fault models being extracted in subsequent fault selection steps; Specifically, in F1, the fault selection strategy is adjusted based on the calculated fault impact ranking results. For example, for fault scenarios with high impact, their extraction probability in subsequent tests is increased to ensure that high-risk scenarios are fully validated. The system maintains a fault probability distribution; initially, all faults are extracted with equal probability. After several rounds of testing, the probability distribution is updated based on the accumulated impact data, defining the... The probability of sampling after updating a fault is: (10) In the formula, For fault The updated extraction probability; For fault The degree of influence of toughness The total number of faults in the fault model library. This is a smoothing constant (usually set to 0.01) to prevent the probability of low-impact failures from dropping to zero. It increases the probability of high-impact failures to 3 to 5 times that of low-impact failures, allowing more testing resources to be allocated to critical scenarios.

[0064] F2: For the identified bottlenecks in the recovery process, design specific test scenarios that cause the corresponding bottleneck links to fail or be restricted, and inject them into the fault injection strategy.

[0065] Specifically, based on the identification of weaknesses, targeted stress testing plans are designed. For example, if analysis reveals that the system's resilience coefficient is low under multi-fault coupling scenarios... A significant decrease in performance will lead to an increase in the proportion of multi-fault combination tests, and a gradual increase in the number of simultaneous faults, from two faults to three or four, to probe the resilience limits of the system. If the analysis finds that a certain type of recovery measure is ineffective, test scenarios will be designed to assume that the measure fails, such as testing the system resilience under the assumption that the topology reconstruction algorithm has failed, to verify whether there is an effective backup recovery path.

[0066] The effectiveness of the improvement plan is verified based on the results of the recovery measure effectiveness analysis. For example, when system maintenance personnel implement resilience enhancement measures based on analysis recommendations, such as adding a tie switch, optimizing the reconfiguration algorithm, or configuring energy storage devices, a comparative test plan is automatically designed to test the system's resilience indicators before and after the improvement under the same fault scenario, quantitatively evaluating the actual effect of the improvement measures. For instance, after adding a tie switch, the recovery time is compared before and after adding the switch under the same line fault scenario. (Calculated from Formula 5) and performance loss (Calculated by Formula 4) If the recovery time is shortened by more than 30% and the performance loss is reduced by more than 20%, then the improvement measures are verified to be effective.

[0067] The S700 may also include an adjusted testing strategy, including an updated fault extraction probability. The new fault combination schemes are converted into new fault injection command sequences and sent to the S200 fault injection controller to initiate the next round of testing. Through multiple iterations, the system gradually covers all critical fault scenarios, comprehensively verifying the system's resilience under various disturbances, while also verifying the effectiveness of various resilience enhancement measures. The iteration process continues until all high-risk fault scenarios have been fully tested, all weak links have been specifically strengthened, and the system's resilience level reaches the design target.

[0068] In summary, this invention realizes a complete process from fault model establishment, fault injection execution, system response monitoring, resilience index assessment, weak link identification to test plan optimization. The first step, the fault model library, provides the system with the foundation of fault scenarios, namely: fault descriptors and correlation matrices; the second step, the fault injection controller flexibly generates test strategies; the third step, the hardware-in-the-loop simulation platform realistically executes faults and generates system responses; the fourth step, the performance monitoring module comprehensively collects response data; the fifth step, the resilience assessment module quantifies resilience levels through computational quantitative analysis; and the sixth step, through analysis and calculation, uncovers the root causes of problems and finally provides feedback for continuous improvement of the test plan.

[0069] Example 3, referring to Tables 1 and 3, provides an application scheme for a distribution network resilience assessment and verification method based on multi-dimensional fault injection, to verify the feasibility and effectiveness of the present invention.

[0070] This simulation example is based on a typical 10 kV distribution network in a certain city. This network includes two 110 kV substations, five 10 kV feeders with a total line length of 68 km, a total load capacity of 25 MW, and is connected to 4.5 MW of distributed photovoltaic power and 2 MW of energy storage devices. A detailed electromagnetic transient model of the distribution network is built on an RTDS real-time digital simulator. Three actual protection devices, five distribution automation terminals, and two photovoltaic inverter controllers are connected to the simulator to construct a hardware-in-the-loop simulation platform. Twenty typical fault scenarios are selected from the fault model library for testing, including single device failure, communication failure, and multiple fault coupling. Each scenario is tested three times, for a total of 60 fault injection tests. During the test, data such as voltage, current, switch status, and load power supply are collected in real time at a sampling frequency of 20 Hz. Each test lasts for 600 seconds, and a total of 720,000 sets of data are collected.

[0071] Table 1: Comparison of resilience indicators under different failure scenarios

[0072] As shown in Table 1, the resilience coefficients for single-fault scenarios (S01-S04) range from 4.87 to 5.59, indicating relatively quick system recovery. However, the performance loss in multi-fault coupled scenarios (S05-S06) exceeds 0.2, with recovery times exceeding 180 seconds, and the resilience coefficient drops to around 2, showing a significant decrease in resilience. While the performance loss in communication interruption fault (S03) is small, the recovery time is as long as 125 seconds because the system needs to wait for communication to be restored before performing automatic reconfiguration, resulting in a low recovery rate. The recovery rates for transformer faults (S02) and protection maloperation (S04) are relatively high, exceeding 0.006, because the system is equipped with a backup transformer and manual recovery measures, enabling rapid load transfer.

[0073] Table 2: Ranking of Equipment Importance

[0074] Equipment importance analysis shows that the main line L01 has the highest importance score of 1.496 because it carries 40% of the system load, and a failure on this line would cause a large-scale power outage. The main transformer T01 and the main line L02 rank second and third in importance, respectively, and are critical nodes in the system. The communication master station DTU01 ranks fourth in importance; although it experiences fewer failures, each failure has a large impact. Branch line L03 experiences more failures, but each failure has a smaller impact, ranking fifth in importance. Based on the importance ranking, it is recommended to prioritize improving the reliability of L01, T01, and L02. For example, adding parallel lines to L01, configuring dual protection for T01, and adding a tie switch to L02.

[0075] Table 3: Verification of the effectiveness of resilience enhancement measures

[0076] The results of resilience enhancement measures demonstrate that all improvements significantly increased the system's resilience coefficient. Communication redundancy backup showed the most significant effect, increasing the resilience coefficient by 307.4% and reducing recovery time by 72.0%, as the communication recovery time decreased from 125 seconds to 5 seconds, greatly accelerating the automatic reconfiguration speed. Rapid energy storage support measures reduced the recovery time in transformer fault scenarios from 78 seconds to 42 seconds, increasing the resilience coefficient by 36.1%. The energy storage device started up within 2 seconds and provided 2 MW of power support, effectively reducing the performance drop. Distributed collaborative control improved the resilience coefficient from 2.20 to 4.28 in multi-fault coupled scenarios. Through coordinated control of photovoltaics, energy storage, and loads, local power supply was maintained during partial line faults, avoiding large-scale power outages. Adding tie switches and optimizing the reconfiguration algorithm reduced recovery time by 37.8% and 36.3%, respectively, verifying the important role of grid reinforcement and intelligent control in improving resilience.

[0077] Example 4 illustrates a schematic scheme for a distribution network resilience assessment and verification method based on multi-dimensional fault injection. It should be noted that the technical solution of this distribution network resilience assessment and verification system based on multi-dimensional fault injection belongs to the same concept as the technical solution of the distribution network resilience assessment and verification method based on multi-dimensional fault injection described above. Details not described in detail in the technical solution of the distribution network resilience assessment and verification system based on multi-dimensional fault injection in this embodiment can be found in the description of the technical solution of the distribution network resilience assessment and verification method based on multi-dimensional fault injection described above.

[0078] This embodiment also provides a distribution network resilience assessment and verification system based on multi-dimensional fault injection, including: a fault model library construction module, used to construct a multi-dimensional fault model library based on historical fault data of the distribution network; The fault injection control module is used to select target fault scenarios from the fault model library based on preset test targets, and generate a fault injection strategy that includes fault selection, injection timing and injection strength. The hardware-in-the-loop simulation module is used to execute the fault injection strategy on the hardware-in-the-loop simulation platform, which includes a real-time digital simulator that runs a power distribution network simulation model and at least one type of actual power distribution equipment connected through a standard interface. The performance monitoring module is used to monitor and collect system operation data of the hardware-in-the-loop simulation platform in real time before and after fault injection. The resilience assessment module is used to calculate the performance index change curve over time, which characterizes the overall power supply level of the distribution network, based on the system operation data, and to quantify and calculate multiple resilience assessment indicators based on the performance index change curve. The intelligent analysis module is used to perform comparative analysis based on the resilience assessment indicators to identify key fault scenarios, key equipment, and bottlenecks in the recovery process that have a significant impact on the resilience of the distribution network. The feedback optimization module is used to adjust the fault injection strategy in subsequent tests based on the identification results, so as to achieve closed-loop evaluation and verification of the distribution network resilience.

[0079] This embodiment also provides a computer device applicable to a distribution network resilience assessment and verification method based on multi-dimensional fault injection, comprising: a memory and a processor; the memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to implement the distribution network resilience assessment and verification method based on multi-dimensional fault injection as proposed in the above embodiment.

[0080] This embodiment also provides a storage medium storing a computer program that, when executed by a processor, implements a method for assessing and verifying the resilience of a distribution network based on multi-dimensional fault injection, as proposed in the above embodiments.

[0081] The storage medium proposed in this embodiment belongs to the same inventive concept as the method for implementing a distribution network resilience assessment and verification based on multi-dimensional fault injection proposed in the above embodiments. Technical details not described in detail in this embodiment can be found in the above embodiments, and this embodiment has the same beneficial effects as the above embodiments.

[0082] From the above description of the implementation methods, those skilled in the art will clearly understand that the present invention can be implemented using software and necessary general-purpose hardware. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as a computer floppy disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk, or optical disk, etc., including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods of the various embodiments of the present invention.

[0083] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for evaluating and verifying the resilience of distribution networks based on multi-dimensional fault injection, characterized in that, include: Based on historical data of distribution network faults, a multi-dimensional fault model library is constructed. Based on the preset test objectives, target fault scenarios are selected from the fault model library, and a fault injection strategy including fault selection, injection timing and injection strength is generated. The fault injection strategy is executed on a hardware-in-the-loop simulation platform, which includes a real-time digital simulator that runs a power distribution network simulation model and at least one type of actual power distribution equipment connected through a standard interface. Real-time monitoring and acquisition of system operation data of the hardware-in-the-loop simulation platform before and after fault injection; Based on the system operation data, the performance index characteristic of the overall power supply level of the distribution network is calculated as a function of time, and multiple resilience assessment indicators are quantitatively calculated based on the performance index change curve. Comparative analysis based on the aforementioned resilience assessment indicators identifies key fault scenarios, key equipment, and bottlenecks in the recovery process that significantly impact the resilience of the distribution network. Based on the identification results, the fault injection strategy in subsequent tests is adjusted to achieve closed-loop assessment and verification of the distribution network resilience.

2. The method for evaluating and verifying the resilience of a distribution network based on multi-dimensional fault injection as described in claim 1, characterized in that, Based on historical data of distribution network faults, a multi-dimensional fault model library is constructed, including: For each fault scenario, a multi-dimensional fault descriptor is defined, which includes fault identifier, fault type, spatial location, time parameter, and severity coefficient. Establish a fault correlation matrix to characterize the triggering dependencies or independence relationships between different fault scenarios, so as to support the generation of cascading faults or concurrent multi-fault scenarios that conform to the actual physical logic.

3. The distribution network resilience assessment and verification method based on multi-dimensional fault injection as described in claim 2, characterized in that, Generate a fault injection strategy that includes fault selection, injection timing, and injection strength, including: Based on the test objectives, a set of faults to be injected is determined from the fault model library using a fault selection method. Configure the start time and duration of the injection for each fault in the fault set; Based on the fault correlation matrix, configure the event trigger interval for faults with triggering dependencies; Adjust the severity coefficient in the fault descriptor to set the fault injection strength.

4. The distribution network resilience assessment and verification method based on multi-dimensional fault injection as described in claim 3, characterized in that, Executing the fault injection strategy on the hardware-in-the-loop simulation platform includes: The generated injection strategy is encoded into a sequence of fault instructions; If a physical layer fault is simulated when the injection time specified in the instruction sequence is reached, the parameters of the corresponding component in the power distribution network simulation model are modified. If a fault is simulated at the information layer, the programmable network devices deployed in the communication link will be interrupted or interfered with data communication. If the simulated control layer fails, simulated signals are injected into the input and output circuits of the actual power distribution equipment or its internal configuration parameters are modified.

5. The distribution network resilience assessment and verification method based on multi-dimensional fault injection as described in claim 4, characterized in that, Based on the system operation data, the performance indicators characterizing the overall power supply level of the distribution network are calculated as time-varying curves. Based on these performance indicator curves, multiple resilience assessment indicators are quantitatively calculated, including: Based on system operation data, the total power supply rate of the system is calculated as the performance indicator. The characteristic stages of the performance index change curve are extracted, including the steady-state operation stage, the performance degradation stage, the worst operation stage, and the performance recovery stage. Based on the aforementioned characteristic stages, toughness indices are calculated, including performance loss, recovery time, recovery rate, and toughness coefficient. The performance loss is determined based on the area of ​​the performance curve below the initial level during the performance degradation phase and the initial recovery phase; the recovery time is the time required for performance to recover to a preset ratio from the occurrence of the fault; the recovery rate is the average recovery slope during the performance recovery phase; and the resilience coefficient is a composite index that comprehensively reflects the performance loss and the recovery rate.

6. The distribution network resilience assessment and verification method based on multi-dimensional fault injection as described in claim 5, characterized in that, Based on the aforementioned resilience assessment indicators, a comparative analysis is conducted to identify key fault scenarios, key equipment, and bottlenecks in the recovery process that significantly impact the resilience of the distribution network, including: The resilience coefficients corresponding to each failure scenario are statistically analyzed, the resilience impact of each failure scenario compared to the baseline scenario without failure is calculated, and the scenarios are sorted according to the resilience impact to determine the key failure scenarios. Statistically analyze the frequency of failures and the average performance loss caused by each actual power distribution equipment or simulation model component during testing, calculate the equipment importance, and identify key equipment. Analyze the data from the performance recovery phase, break it down into multiple sub-phases, and identify the sub-phase with the longest duration as the bottleneck in the recovery process.

7. The method for evaluating and verifying the resilience of a distribution network based on multi-dimensional fault injection as described in claim 6, characterized in that, Based on the identification results, the fault injection strategy in subsequent tests will be adjusted, including: Based on the ranking of the key fault scenarios, the probability of their corresponding fault models being extracted in subsequent fault selection steps is increased. For the identified bottlenecks in the recovery process, specific test scenarios that cause the corresponding bottleneck links to fail or be restricted are designed and injected into the fault injection strategy.

8. A distribution network resilience assessment and verification system based on multi-dimensional fault injection, using the method described in any one of claims 1-7, characterized in that, include: The fault model library construction module is used to build a multi-dimensional fault model library based on historical fault data of the distribution network. The fault injection control module is used to select target fault scenarios from the fault model library based on preset test targets, and generate a fault injection strategy that includes fault selection, injection timing and injection strength. The hardware-in-the-loop simulation module is used to execute the fault injection strategy on the hardware-in-the-loop simulation platform, which includes a real-time digital simulator that runs a power distribution network simulation model and at least one type of actual power distribution equipment connected through a standard interface. The performance monitoring module is used to monitor and collect system operation data of the hardware-in-the-loop simulation platform in real time before and after fault injection. The resilience assessment module is used to calculate the performance index change curve over time, which characterizes the overall power supply level of the distribution network, based on the system operation data, and to quantify and calculate multiple resilience assessment indicators based on the performance index change curve. The intelligent analysis module is used to perform comparative analysis based on the resilience assessment indicators to identify key fault scenarios, key equipment, and bottlenecks in the recovery process that have a significant impact on the resilience of the distribution network. The feedback optimization module is used to adjust the fault injection strategy in subsequent tests based on the identification results, so as to achieve closed-loop evaluation and verification of the distribution network resilience.

9. A computer device, characterized in that, include: Memory and processor; The memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions. When the computer-executable instructions are executed by the processor, they implement the steps of the distribution network resilience assessment and verification method based on multi-dimensional fault injection as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, It stores computer-executable instructions, which, when executed by a processor, implement the steps of the distribution network resilience assessment and verification method based on multi-dimensional fault injection as described in any one of claims 1 to 7.

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