Power system moving target defense method based on power flow betweenness and power flow disturbance

Abstract

The invention discloses a power system moving target defense method based on power flow betweenness and power flow disturbance, and relates to the field of power systems. Calculating to obtain a power flow betweenness and a power flow disturbance index of the normalized power system line; constructing a comprehensive index based on the power flow betweenness and the power flow disturbance index; and determining a to-be-deployed line set according to a preset device deployment number and the comprehensive index. And changing the line impedance value corresponding to the line set to obtain a target measurement matrix, calculating a measurement value residual error after the line impedance value is changed according to the original measurement matrix and the target measurement matrix, and determining an attack success rate based on a size relationship between the measurement value residual error and a detection threshold value. And deploying power system moving target defense according to a result of the attack success rate. According to the invention, the detection effectiveness and the MTD concealment are balanced. A traditional global combination search problem is converted into a linear complexity sorting problem, rapid solving is achieved, calculation efficiency is improved, and rapid generation of a hidden MTD strategy is achieved.

Description

Technical Field

[0001] This invention relates to the field of power systems, and more specifically, to a method for defending against moving targets in power systems based on power flow betweenness and power flow disturbance. Background Technology

[0002] With the rapid development of Cyber-Physical Power Systems (CPPS), the deep integration of power systems and information networks is improving operational efficiency, but it also faces increasingly severe cybersecurity threats.

[0003] Given the disadvantages of traditional passive defense, active defense methods such as Moving Target Defense (MTD) have been introduced. MTD, as an active defense technology, has been introduced into power systems to detect False Data Injection Attacks (FDIA).

[0004] However, traditional MTD deployment methods rely on global combinatorial optimization (such as maximizing the matrix rank), which leads to an exponential increase in computational complexity. Traditional heuristic algorithms require global search, are inefficient, and have long solution times, making it difficult to meet real-time defense requirements. Summary of the Invention

[0005] In view of the above problems, this invention proposes a power system moving target defense method based on power flow betweenness and power flow disturbance to overcome the shortcomings of the prior art.

[0006] This invention provides a method for defending against moving targets in a power system based on power flow betweenness and power flow disturbances, comprising: Based on the measured values ​​of the power system and the formulas for power flow betweenness and power flow disturbance index, the normalized power flow betweenness and power flow disturbance index of the power system lines are calculated. Based on the current betweenness factor and the current disturbance index, a comprehensive index is constructed; The set of lines to be deployed is determined based on the preset number of devices to be deployed and the comprehensive indicators mentioned above; By changing the line impedance values ​​corresponding to the line set, the target measurement matrix is ​​obtained; Based on the attacker's measurement values, estimated values ​​of state variables, and the target measurement matrix after the change in line impedance, the residual of the measurement values ​​after the change in line impedance is calculated, and the attack success rate is determined based on the relationship between the residual of the measurement values ​​and the detection threshold. If the attack success rate is greater than a preset value, the preset number of deployed devices is increased by 1 to obtain a new number of deployments, and the following steps are executed: determine the set of new lines to be deployed based on the new number of deployments and the comprehensive indicators; If the attack success rate is not less than a preset value, then deploy power system mobile target defense according to the preset number of deployed devices and their corresponding line sets.

[0007] Optionally, the normalized power flow betweenness numbers of the power system lines are calculated, including: Calculate the power flow betweenness of a single generating load pair; Based on the power flow betweenness of the single generating load pair, and taking into account the cumulative effect of all generating load pairs in the power grid, the power flow betweenness of the target line is defined. Using the power flow tracing method, based on the sequential and reverse allocation matrices, downstream and upstream tracing calculations are performed respectively to obtain the power flow composition in the target line; Based on the power flow composition, the power flow betweenness formula for the target line is obtained; Based on the power flow betweenness formula of the target line, the power flow betweenness of all power system lines is calculated and normalized to obtain the normalized power flow betweenness of the power system lines.

[0008] Optionally, the normalized power flow disturbance index of the power system lines is calculated, including: Calculate the average value of the system line reactance; The reactance of each power system line is modified to the target reactance in turn; Based on the target reactance, the new power flow value for each power system line is calculated. Based on the new power flow value of each power system line and its corresponding initial power flow value, calculate the sum of the absolute values ​​of power flow changes of all power system lines; Based on the sum of the absolute values ​​of power flow changes of all power system lines, the power flow disturbance index of each power system line is obtained, and then normalized to obtain the normalized power flow disturbance index of the power system line.

[0009] Optionally, calculate the power flow betweenness of a single generating load pair. The formula is as follows:

[0010] In the above formula, For generator to load The active power transmitted; For generator to load The transmitted active power at the target line The amount on, and The target routes are respectively The node numbers at both ends; The weight of the single power flow betweenness is taken from the generator. Actual output and load Actual load The smaller value in represents and The maximum available transmission power between them; Taking into account the cumulative effect of all generating load pairs in the power grid, the target line is defined. Trend betweenness as follows:

[0011] In the above formula, For the set of generator nodes; For the set of all load nodes; The power flow composition of the target line includes: the target line Flowing towards load in the tide The power of the target line The trend originated from generators power, generator to load The actual transmission power is determined by the power generation load. Provided component power; Among them, the line Flowing towards load in the tide power as follows:

[0012] In the above formula, For the target route Active power flowing in the middle; For nodes The node flow is equal to the sum of the injected or outflowing flow; For load nodes Active load; Assign matrices sequentially. For matrix The inverse is located at Element; The target line The trend originated from generators power as follows:

[0013] In the above formula, For load nodes Those who have made meritorious contributions; Assign matrices in reverse order. For matrix The inverse is located at Element; The generator to load Actual transmission power as follows:

[0014] In the above formula, For nodes The node flow is equal to the sum of the injected or outflowing flow; For matrix The inverse is located at Element; The power generation load Provided component power as follows:

[0015] Combining the expressions corresponding to the four powers in the power flow composition, the power flow betweenness formula for the target line is obtained as follows:

[0016] Based on the above formula, let... For the first The power flow betweenness of each line is used to calculate the power flow betweenness of all lines in the power system. ; The normalization process is as follows:

[0017] In the above formula, For the first Normalized power flow betweenness numbers of power system lines; This is the maximum value of the power flow betweenness of all power system lines, i.e. ; This is the minimum value of the power flow betweenness of all power system lines, i.e. .

[0018] Optionally, calculate the average value of the system line reactance:

[0019] In the above formula, This represents the average reactance of the power system lines, also known as its per-unit value. This represents the total number of lines in the power system. For the first The reactance value of a power system line, also known as its per-unit value; The first The reactance of a power system line is modified to a target reactance, the value of which is... ; The sum of the absolute values ​​of power flow changes across all power system lines is calculated as follows:

[0020] In the above formula, In order to disturb the first After the reactance value of the power system line, the first Transmission power on a power system line; In order to disturb the first Before the reactance of the power system line, the first Transmission power on a power system line; In the disturbance After determining the reactance value of each power system line, the sum of the absolute values ​​of the power flow changes of all power system lines; Based on the sum of the absolute values ​​of power flow changes across all lines, a quantitative index of disturbance impact is obtained for each line. , for the Power flow disturbance index of power system lines Normalization is as follows:

[0021] In the above formula, For the first Normalized power flow disturbance index for each power system line; This represents the maximum value of all power flow disturbance indices in the power system, i.e. ; This is the minimum value of all power flow disturbance indices in the power system, i.e. .

[0022] Optionally, based on the power flow betweenness and the power flow disturbance index, a comprehensive index is constructed, including: Based on the power flow betweenness and the power flow disturbance index, the detection effectiveness and stealth of the mobile target defense strategy are optimized in a coordinated manner, and the comprehensive index is constructed. The comprehensive indicators are as follows:

[0023] In the above formula, For the first The comprehensive defense value score of each power system line; the higher the score, the better. The higher the priority of the deployment of each power system line; The weights for the power flow betweenness are used to characterize the weights corresponding to the detection effectiveness. ; The weight of the power flow disturbance index represents the weight corresponding to the concealment. ; E i For the first Normalized power flow betweenness numbers of power system lines; S i For the first Power flow disturbance index after normalization of power system lines.

[0024] Optionally, the detection threshold is calculated by combining the chi-square distribution and a preset significance level, along with the degrees of freedom of the original measurement matrix, wherein the original measurement matrix is ​​calculated based on the measured values ​​and the DC power flow model; it includes: Treat the voltage magnitude of the reference node as 1, and set the voltage phase angle of the remaining nodes other than the reference node as 1. As a state variable of the power system, use It is expressed as follows:

[0025] The measured values ​​are the injected active and reactive power of the busbar, and the active and reactive power of the transmission line. These measured values ​​are expressed as... The DC power flow model is then expressed as a set of linear equations as follows:

[0026] In the above formula, Let the measurement noise column vector take values ​​that conform to a normal distribution; if there are a total of Each measurement value One non-reference node, and Then the measurement matrix It is represented as follows:

[0027] In the above formula, The admittance matrix of the power system; The correlation matrix of the power system; For matrix The transpose of the measurement; the detection threshold is calculated by combining the chi-square distribution and a preset significance level with the degrees of freedom of the measurement value, including: The degrees of freedom are calculated from the dimensions of the original measurement matrix. :

[0028] According to degrees of freedom First, set a significance level, then look up the chi-square distribution table to obtain the detection threshold.

[0029] Optionally, determining the set of lines to be deployed based on the preset number of devices and the comprehensive indicators includes: Based on the aforementioned comprehensive indicators, each power system line is ranked from highest to lowest according to the comprehensive indicators; The power system lines with the highest target number in the ranking are identified as the set of lines to be deployed, and this target number is the same as the preset number of equipment to be deployed.

[0030] Optionally, based on the attacker's measurement values ​​during the attack after the change in line impedance, the estimated values ​​of state variables, and the target measurement matrix, the measurement residuals after the moving target defense action are calculated, including: In the DC power flow model, calculating the estimated values ​​of the state variables is transformed into solving the following weighted minimum variance optimization problem:

[0031] In the above formula, This is the weight matrix of the measurement values, i.e., the angular covariance matrix of the measurement values; State variables The estimated value, the weight matrix of the measured value as follows:

[0032] Based on the weight matrix Original measurement matrix H Measurement values The state variables are obtained using the least squares method. The estimated value for:

[0033] The weight matrix middle, These are the measured values The reciprocal of the measurement noise variance; In the state estimation of the DC power flow model, the residual of the measured values ​​is defined as follows:

[0034] In the formula, The residual value is the measurement value. If its value is greater than the detection threshold, an alarm will be triggered. This indicates taking the 2-norm; This is an estimate of the measured value; Based on the aforementioned DC power flow model, the attacker designs an attack vector using existing raw measurement values. as follows:

[0035] In the above formula,H This refers to the original measurement matrix; The deviation injected into the state variables; After the attacker's attack is successfully executed, the estimated values ​​of the state variables are changed as follows:

[0036] In the above formula, These are estimates of the state variables after the attack; If the attacker based on The attack vector is designed, and the measurement residuals after the attack are as follows:

[0037] In the above formula, The measurement residuals after the attack; These are measurements taken after the attack, because ,but The value is zero, that is Therefore, this attack bypasses bad data detection based on measurement residuals; After changing the line impedance value corresponding to the aforementioned line set, if the attacker... If the attack vector is designed, the measurement residuals are as follows:

[0038] In the formula, The residual of the measurement value when an attack occurs after the line impedance value has changed; These are the measured values ​​when an attack occurs after a change in the line impedance. The target measurement matrix; , This is an estimated state of the line when an attack occurs after the line impedance value changes. This is the actual measured value after the line impedance value has changed; , The actual measured value after the change in line impedance. The corresponding state estimate; , This refers to the deviation value injected into the state variables after the line impedance value changes.

[0039] Optionally, the attack success rate is determined based on the relationship between the measured residual and the detection threshold, including: The process of calculating the residual of the measured value after the change of the line impedance value is repeated a preset number of times. After each calculation of the residual of the measured value, it is judged against the detection threshold. If the residual of the measured value does not exceed the detection threshold, no alarm is triggered, and the attack is confirmed to be successful; if the residual of the measured value exceeds the detection threshold, an alarm is triggered, and the attack is confirmed to be unsuccessful. The attack success rate is obtained by dividing the number of successful attacks by the preset number of attacks. Among them, the residual of the measured value when an attack occurs after the change in line impedance value. The formula states that when the line impedance value changes, the target measurement matrix differs significantly from the original measurement matrix, making... If the difference is not zero and is large, then If the detection threshold is exceeded, an alarm is triggered, indicating that the attack was unsuccessful.

[0040] The proposed method for mobile target defense in power systems based on power flow betweenness and power flow disturbance first calculates the normalized power flow betweenness and power flow disturbance indices of the power system lines; then constructs a comprehensive index based on the power flow betweenness and power flow disturbance indices; next, it determines the set of lines to be deployed based on the preset number of equipment to be deployed and the comprehensive index, and selects high-value candidate lines to deploy MTD defense.

[0041] By changing the line impedance values ​​corresponding to the line set, the target measurement matrix is ​​obtained; that is, simulating the MTD defense situation, the measurement residuals after the line impedance value is changed are calculated based on the measurement values ​​of the attacker, the estimated values ​​of the state variables, and the target measurement matrix. The attack success rate is determined based on the relationship between the measurement residuals and the detection threshold.

[0042] If the attack success rate is greater than the preset value, the preset number of deployed devices is increased by 1 to obtain a new deployment number. The following steps are then executed: Based on the new deployment number and comprehensive indicators, a new set of lines needs to be deployed. In other words, when the attack success rate is high, the preset number of deployed devices is considered insufficient to achieve a good MTD defense effect, and the number of deployed devices needs to be increased. The increased deployment number is then used as the basis for MTD defense, and the measurement residual is calculated to determine the attack success rate. This process is repeated until the attack success rate is not less than the preset value. Then, power system mobile target defense is deployed according to the preset number of deployed devices and their corresponding set of lines.

[0043] The proposed power system moving target (MTD) defense method creatively balances detection effectiveness and MTD concealment by calculating the power flow betweenness factor (WBD) of each power system line (which quantifies the effectiveness of defense) and the power flow disturbance index (which quantifies the stealth of defense). Different weights can be assigned to different defense targets. The method prioritizes the protection of power system lines, deploying MTD defense only on high-value candidate lines. This transforms the traditional global combinatorial search problem into a linear complexity ranking problem, enabling rapid solution and improving computational efficiency. It has broad application prospects and high practicality. Attached Figure Description

[0044] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1 This is a schematic diagram of the physical operation status of the transmission network CPPS in a traditional power system; Figure 2 This is a schematic diagram of the MTD structure in a traditional power system. Figure 3 This is a flowchart of a power system moving target defense method based on power flow betweenness and power flow disturbance according to an embodiment of this application; Figure 4 This is a schematic diagram of the physical topology of the IEEE 30-node transmission network used to verify the effectiveness of the power system moving target defense method proposed in this application embodiment; Figure 5 This is an embodiment of the present application. Figure 4 The physical topology of the IEEE 30-node transmission network is obtained by calculating the comprehensive indexes proposed in this invention, resulting in a comprehensive index distribution diagram. Figure 6 This is a bar chart showing the attack success rate test results in the embodiments of this application under the conditions of no MTD, using the power system moving target defense method proposed in this invention, and random MTD defense. Detailed Implementation

[0045] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present invention, and are only some, not all, embodiments of the present invention, and are not intended to limit the present invention.

[0046] The integration of communication and information processing in new power systems provides new technological means for power system perception and control. However, the deep integration of power networks and information networks also exposes the system to higher attack risks. Attacks on information networks may spill over into the power system, threatening its stable and secure operation. To address the defense challenges brought about by openness, it is necessary to develop new proactive defense technologies to ensure the security of energy networks. Traditional passive defense methods are insufficient to comprehensively address all potential attacks, and with the continuous emergence of new attack forms, researchers are increasingly turning their attention to proactive defense strategies to cope with the increasingly severe cybersecurity situation.

[0047] As the core architecture supporting the construction of new power systems, the deep coupling between the information layer and the physical layer of the power cyber-physical system allows FDIA (Factory Data Interchange) to tamper with measurement data or control commands. Figure 1 The measurement data of the information layer in the schematic diagram of the CPPS structure of the power transmission network shown in the figure, which in turn affects Figure 1 The physical operating status of the power grid CPPS is shown. Figure 1 The data center, acting as the information layer, acquires various data from the physical layer (i.e., the power grid formed by various devices in the power system) through data collection. Simultaneously, it generates various commands based on this data to achieve the goal of monitoring and controlling the physical layer. FDIA, through carefully designed data, can induce the system to issue erroneous dispatch commands, seriously affecting the safe and stable operation of the power system.

[0048] To address this challenge, Moving Target Defense (MTD) technology enhances defense capabilities by dynamically altering the system's attack surface. Its core principle involves using D-FACTS (Distributed Flexible Alternative Current Transmission Systems) equipment to actively adjust transmission line parameters, rendering attack vectors constructed by attackers based on historical system information ineffective. When the system detects a potential attack, MTD alters line impedance parameters, causing false data injection attacks based on outdated system information to expose anomalies during BDD (Bad Data Detection), thus achieving effective detection and defense against FDIA (Fault-Doubling Attack Intrusion). This proactive defense mechanism significantly improves the security capabilities of power cyber-physical systems by increasing system uncertainty and the difficulty for attackers to obtain information.

[0049] Reference Figure 2The diagram shows a power system MTD structure, with D-FACTS devices deployed on transmission lines. D-FACTS devices were originally developed to improve the efficiency and stability of power system operation. As a distributed version of traditional FACTS devices, D-FACTS achieves more flexible deployment through modular design. Its core function is to achieve precise control of system power flow by rapidly adjusting the impedance parameters of transmission lines. In traditional applications, D-FACTS is mainly used to solve power flow congestion problems in transmission networks, increase transmission capacity, dampen power oscillations, and improve voltage stability, providing a cost-effective and efficient power grid control method for power systems.

[0050] With the increasing demand for power system network security, D-FACTS devices are being applied in the field of transmission network MTD (Mean Transmission Damage Prevention). Its MTD defense principle lies in the fact that attackers need to accurately grasp the real-time impedance parameters of the power grid to construct a covert attack vector when launching FDIA (Fixed Detection and Analysis). This is achieved through... Figure 2 The diagram illustrates the deployment of D-FACTS devices on transmission lines. Defenders can dynamically adjust line impedance, rendering previously acquired system parameter information invalid. When an attacker uses outdated grid parameters to implement FDIA, the injected false data will significantly deviate from the actual system state after MTD (Mean Transmission Control) action, thus being identified by BDD (Blockchain Destruction) mechanisms. This D-FACTS-based MTD technology, by continuously altering the grid's "attack surface," maintains the normal operation of the power system while effectively disrupting the attacker's information advantage, providing the power system with proactive defense capabilities.

[0051] Further research by the inventors revealed that while the aforementioned MTD defense is effective, its computational complexity increases exponentially when dealing with large power systems due to its reliance on global combinatorial optimization (such as matrix rank maximization). Traditional heuristic algorithms require global search, resulting in low efficiency and long solution times, making them unsuitable for real-time defense requirements. Furthermore, existing mobile target defense deployment methods based on network vulnerability guidance do not consider the stealth aspect of the defense. When MTD attacks occur, they significantly impact the power flow during normal operation, making them easily detectable by attackers and revealing the attack's exposure.

[0052] To address the aforementioned problems, the inventors have creatively proposed a power system moving target defense method based on power flow betweenness and power flow disturbances. The technical solution proposed in this invention will be explained and described in detail below.

[0053] This invention proposes a power system moving target defense method based on power flow betweenness and power flow disturbance, referencing... Figure 3 The flowchart shown includes: Step 301: Calculate the normalized power flow betweenness and power flow disturbance index of the power system lines based on the measured values ​​of the power system and the formulas for power flow betweenness and power flow disturbance index.

[0054] First, based on the measured values ​​of the power system and the formulas for power flow betweenness and power flow disturbance index, it is necessary to calculate the normalized power flow betweenness and power flow disturbance index of the power system lines.

[0055] In one embodiment of the present invention, a preferred method for calculating the power flow betweenness of a normalized power system line includes: First, the power flow betweenness factor of a single generating load pair is calculated. Then, based on the power flow betweenness factor of a single generating load pair, and considering the cumulative effect of all generating load pairs in the grid, the power flow betweenness factor of the target line is defined. Next, using the power flow tracing method, based on the sequential and reverse allocation matrices, forward and reverse tracing calculations are performed respectively to obtain the power flow composition of the target line (i.e., any line in the entire power system). Based on the power flow composition, the power flow betweenness factor formula of the target line is obtained. Finally, based on the power flow betweenness factor formula of the target line, the power flow betweenness factors of all power system lines are calculated and normalized to obtain the normalized power flow betweenness factors of the power system lines. Specifically: Calculate the power flow betweenness of a single generating load pair The formula is as follows:

[0056] In the above formula, For generator to load The active power transmitted; For generator to load The transmitted active power at the target line The amount on, and The target routes are respectively The node numbers at both ends; The weight of the single power flow betweenness is taken from the generator. Actual output and load Actual load The smaller value in represents and The maximum available transmission power between them.

[0057] After obtaining the power flow betweenness of the single generating load pair, the cumulative effect of all generating load pairs in the grid is then considered to define the target line. Trend betweenness as follows:

[0058] In the above formula, For the set of generator nodes; This is the set of all load nodes.

[0059] The target line The power flow in the system consists of several power components, including: the target line. Flowing towards load in the tide The power of the target line The trend originated from generators power, generator to load The actual transmission power is determined by the power generation load. Provided component power; of which, the line Flowing towards load in the tide power as follows:

[0060] In the above formula, For the target route Active power flowing in the middle; For nodes The node flow is equal to the sum of the injected or outflowing flow; For load nodes Active load; Assign matrices sequentially. For matrix The inverse is located at Element.

[0061] Target route The trend originated from generators power as follows:

[0062] In the above formula, For load nodes Those who have made meritorious contributions; Assign matrices in reverse order. For matrix The inverse is located at Element.

[0063] dynamo to load Actual transmission power as follows:

[0064] In the above formula, For nodes The node flow is equal to the sum of the injected or outflowing flow; For matrix The inverse is located at Element.

[0065] By power generation load Provided component power as follows:

[0066] Based on the above target routes The expression corresponding to the four power components in the power flow composition can be used to obtain the target line. The formula for the power flow betweenness is as follows:

[0067] Based on the formula, for ease of expression, let's denote... For the first The power flow betweenness of each line is used to calculate the power flow betweenness of all lines in the power system. Finally, normalization is performed as follows:

[0068] In the above formula, For the first Normalized power flow betweenness numbers of power system lines; This is the maximum value of the power flow betweenness of all power system lines, i.e. ; This is the minimum value of the power flow betweenness of all power system lines, i.e. .

[0069] The above explains and illustrates how to calculate the power flow betweenness factor. Regarding power flow disturbance indices, in one embodiment of the present invention, a preferred method for calculating the normalized power flow disturbance indices of power system lines includes: First, calculate the average reactance of the system lines; then, sequentially modify the reactance of each power system line to the target reactance; next, based on the target reactance, calculate the new power flow value for each power system line; based on the new power flow value of each power system line and its corresponding initial power flow value, calculate the sum of the absolute values ​​of power flow changes for all power system lines; finally, based on the sum of the absolute values ​​of power flow changes for all power system lines, obtain the power flow disturbance index for each power system line, and perform normalization processing to obtain the normalized power flow disturbance index for the power system lines. Specifically: Calculate the average value of the system line reactance:

[0070] In the above formula, This represents the average reactance of the power system lines, also known as its per-unit value. This represents the total number of lines in the power system. For the first The reactance value of a power system line, also known as its per-unit value.

[0071] The first The reactance of a power system line is modified to a target reactance, the value of which is... In other words, during MTD defense, the reactance of each power system line is increased by 0.1 times the average reactance, which is then used as the target reactance for each power system line.

[0072] After obtaining the target reactance, the sum of the absolute values ​​of the power flow changes across all power system lines is calculated as follows:

[0073] In the above formula, In order to disturb the first After the reactance value of the power system line, the first Transmission power on a power system line; In order to disturb the first Before the reactance of the power system line, the first Transmission power on a power system line; In the disturbance The sum of the absolute values ​​of the power flow changes of all power system lines after determining the reactance value of each power system line.

[0074] Finally, based on the sum of the absolute values ​​of power flow changes across all lines, a quantitative index of the disturbance impact on each line is obtained. , for the Power flow disturbance index of power system lines Normalization is as follows:

[0075] In the above formula, For the first Normalized power flow disturbance index for each power system line; This represents the maximum value of all power flow disturbance indices in the power system, i.e. ; This is the minimum value of all power flow disturbance indices in the power system, i.e. .

[0076] As can be seen from the above explanation and description, the "certain formula" mentioned in the embodiments of the present invention does not refer to a single formula, but is formed by at least one or more formulas. For example, the power flow betweenness formula used is specifically formed by eight formulas, not a single formula.

[0077] Step 302: Construct a comprehensive index based on the tidal current betweenness and tidal current disturbance index.

[0078] After obtaining the power flow betweenness and power flow disturbance index, a comprehensive index is constructed based on these two indicators. Ideally, the detection effectiveness and stealth of the moving target defense strategy can be synergistically optimized based on the power flow betweenness and power flow disturbance index to construct a comprehensive index. This comprehensive index can be as follows:

[0079] In the above formula, For the first The comprehensive defense value score of each power system line; the higher the score, the better. The higher the priority of the deployment of each power system line; The weights for the power flow betweenness are used to characterize the weights corresponding to the effectiveness of the detection. ; The weights of the tidal current disturbance index represent the weights corresponding to its concealment. ; E i For the first Normalized power flow betweenness numbers of power system lines; S i For the first Power flow disturbance index after normalization of power system lines.

[0080] By using the above comprehensive indicators, we can balance detection effectiveness and MTD stealth, and we can also set different weights to favor different defense targets.

[0081] Step 303: Determine the set of lines to be deployed based on the preset number of equipment to be deployed and comprehensive indicators.

[0082] After establishing the comprehensive indicators, the set of lines to be deployed is determined based on the preset equipment deployment quantity and the comprehensive indicators. Since the value of the comprehensive indicators is [value missing]... The comprehensive defense value score of each power system line; the higher the score, the better. The higher the deployment priority of a power system line, the more high-value candidate lines can be selected for MTD defense deployment. Because the protection priorities of power system lines are ranked, and MTD defense is deployed only on high-value candidate lines, the traditional global combinatorial search problem can be transformed into a linear complexity ranking problem, enabling rapid solution and improving computational efficiency.

[0083] In one embodiment of the present invention, a preferred method for determining the set of lines to be deployed based on a preset number of devices and the comprehensive indicators includes: Based on comprehensive indicators, each power system line is ranked from highest to lowest according to these indicators. The top-ranked power system lines with the highest target number are identified as the set of lines to be deployed, and this target number is the same as the preset equipment deployment number. For example, if the preset equipment deployment number is 6, then the top 6 power system lines ranked from highest to lowest comprehensive indicators are identified as the set of lines to be deployed, and the preset equipment is deployed on these 6 power system lines. In this embodiment of the invention, the preset equipment is preferably the aforementioned D-FACTS equipment. Of course, it can also be any equipment currently used for MTD defense in the communications field.

[0084] Step 304: Change the line impedance value corresponding to the line set to obtain the target measurement matrix.

[0085] After the above line set is selected, MTD defense is simulated, that is, the impedance value of each power system line corresponding to the line set is changed to obtain the target measurement matrix.

[0086] Step 305: Based on the attacker's measured values, estimated values ​​of state variables, and target measurement matrix after the line impedance value changes, calculate the residual of the measured values ​​after the line impedance value changes, and determine the attack success rate based on the relationship between the residual of the measured values ​​and the detection threshold.

[0087] For the original power system, there is an original measurement matrix based on the original measurement values. That is, the original measurement matrix is ​​calculated based on the original measurement values ​​of the power system lines and the DC power flow model. The original measurement matrix can be calculated at any time during the operation of the power system. For example, it can be calculated at the beginning of the power system's operation, after a period of operation, or after MTD (Moving Target Defense) measures are implemented. However, calculating after MTD measures are implemented will prolong the execution time of the power system moving target defense method. Therefore, it is preferable not to perform the calculation during the execution of the method proposed in this invention.

[0088] For specific calculations, in the DC power flow model, the voltage magnitude of the reference node is considered to be 1, and the voltage phase angle of the remaining nodes other than the reference node is considered to be... As a state variable of the power system, use It is expressed as follows:

[0089] Generally, the measured values ​​are the injected active and reactive power of the busbar, and the active and reactive power of the transmission line. These measured values ​​are expressed as... The DC power flow model can then be represented by a set of linear equations as follows:

[0090] In the above formula, Let the measurement noise column vector take values ​​that conform to a normal distribution; if there are a total of Each measurement value One non-reference node, and Then the measurement matrix It is represented as follows:

[0091] In the above formula, The admittance matrix of the power system; The correlation matrix of the power system; For matrix The transpose of .

[0092] A preferred detection threshold is calculated by combining the chi-square distribution, a preset significance level, and the degrees of freedom of the original measurement matrix. A preferred method for calculating the detection threshold by combining the chi-square distribution table and the degrees of freedom of the measurement values ​​includes: Degrees of freedom are calculated from the dimensions of the original measurement matrix. :

[0093] According to degrees of freedom First, a predefined significance level is set, and the detection threshold is obtained by looking up the chi-square distribution table. Similarly, the timing of calculating the detection threshold is the same as that of the original measurement matrix; preferably, it should not be performed when executing the method proposed in this invention.

[0094] In the DC power flow model, state variables are... The calculation of the estimated value is transformed into solving the following weighted minimum variance optimization problem:

[0095] In the above formula, The weights of the measurements are the angular covariance matrix of the measurements. State variables The estimated value, the weight matrix of the measured value as follows:

[0096] Based on the weight matrix Original measurement matrix H Measurement values The state variables are obtained using the least squares method. The estimated value for:

[0097] The above weight matrix middle, These are the measured values The reciprocal of the measurement noise variance.

[0098] In practical applications, measurement residuals can be used to eliminate erroneous or manipulated measurement data. For state estimation of DC power flow models, the measurement residuals are defined as follows:

[0099] In the formula, The residual value is the measurement value. If its value is greater than the detection threshold, an alarm will be triggered. This indicates taking the 2-norm; This is an estimate of the measured value.

[0100] Based on the DC power flow model, attackers can design attack vectors using existing raw measurement values. as follows:

[0101] In the above formula, H This is the original measurement matrix; This refers to the deviation injected into the state variables.

[0102] After the attacker's attack is successfully executed, the estimated values ​​of the state variables are changed as follows:

[0103] In the above formula, These are the estimated values ​​of the state variables after the attack.

[0104] If the attacker based on The attack vector is designed, and the measurement residuals after the attack are as follows:

[0105] In the above formula, The measurement residuals after the attack; These are measurements taken after the attack, because ,but The value is zero, that is Therefore, the attack bypassed bad data detection based on measurement residuals and was successful.

[0106] After MTD defense, that is, after changing the line impedance value corresponding to the line set, if the attacker uses... If the attack vector is designed, the measurement residuals are as follows:

[0107] In the formula, The residual of the measurement value when an attack occurs after the line impedance value has changed; These are the measured values ​​when an attack occurs after a change in the line impedance. For the target measurement matrix; , This is an estimated state of the line when an attack occurs after the line impedance value changes. This is the actual measured value after the line impedance value has changed; , The actual measured value after the change in line impedance. The corresponding state estimate; , This represents the deviation value injected into the state variables after an attack following a change in line impedance. It is based on the residual values ​​of the measurements taken when an attack occurs after the line impedance change. From the formula, we can see that when the line impedance value changes, the target measurement matrix differs significantly from the original measurement matrix, thus making... If the difference is not zero and is large, then If the detection threshold is exceeded, an alarm is triggered, meaning the attack was unsuccessful.

[0108] The determination of attack success rate includes: The process of calculating the residual value of the measured value after the change of the line impedance is repeated a preset number of times. After each calculation of the residual value, it is compared with the detection threshold. For example, if the preset number of times is 1000, then the process of calculating the residual value of the measured value after the change of the line impedance is repeated 1000 times. After each calculation of the residual value, it is compared with the detection threshold. That is, the residual value of the measured value is compared with the detection threshold 1000 times.

[0109] For any given judgment, if the residual of the measurement value does not exceed the detection threshold, no alarm is triggered, and the attack is considered successful; if the residual of the measurement value exceeds the detection threshold, an alarm is triggered, and the attack is considered unsuccessful. The attack success rate can be obtained by dividing the number of successful attacks by the preset number.

[0110] Step 306: If the attack success rate is greater than the preset value, increase the preset number of deployed devices by 1 to obtain the new deployment number, and execute the following steps: Determine the set of new lines to be deployed based on the new deployment number and comprehensive indicators.

[0111] After obtaining the attack success rate, if the attack success rate is greater than the preset value, it is considered that the preset number of deployed devices is insufficient to achieve a good MTD defense effect, and the number of preset deployed devices needs to be increased. Therefore, the number of preset deployed devices is increased by 1 to obtain the new number of deployments, and the following steps are performed: determine the new set of lines to be deployed based on the new number of deployments and comprehensive indicators, and then use the increased number of deployments as MTD defense again, as well as calculate the new measurement residual and determine the attack success rate again. This process is repeated.

[0112] Step 307: If the attack success rate is not less than the preset value, then deploy the power system mobile target defense according to the preset number of devices and their corresponding line sets.

[0113] If, during the above process, the attack success rate is not less than the preset value, it is considered that the preset number of deployed devices is sufficient to achieve a good MTD defense effect, and there is no need to increase the preset number of deployed devices. In this case, the power system mobile target defense is deployed according to the preset number of deployed devices and their corresponding line sets.

[0114] To verify the effectiveness of the proposed power system moving target defense method based on power flow betweenness and power flow disturbance, this invention was used... Figure 4 The physical topology of the IEEE 30-node transmission network shown is used as the verification object. The comprehensive indicators of the IEEE 30-node network are calculated using the method described above, yielding the results. Figure 5 The comprehensive index distribution chart shown indicates that the higher the comprehensive index of a line, the wider the corresponding line. For example: Figure 5 The middle nodes 12-13 have the widest lines, so their corresponding comprehensive indicators are the highest, and their pre-installed equipment has the highest priority.

[0115] The significance level for attack detection was set to 0.05 (i.e., the false positive rate was 0.05), the degrees of freedom were 31, and the detection threshold was set to 52.9485. The number of lines where D-FACTS devices were deployed was set to 5 (i.e., the preset number of devices deployed was 5). Attack success rates were tested under conditions of no MTD, using the power system moving target defense method proposed in this invention, and random MTD defense. The test results are as follows: Figure 6 As shown. By Figure 6 It can be known that: Without MTD, the success rate of 10,000 attacks is close to 95%, which meets the success rate corresponding to the set threshold. Using the power system moving target defense method proposed in this invention, the success rate of 10,000 attacks is significantly lower than without MTD, hovering around 60%. Under random MTD, the number of lines deployed for MTD is the same as in the power system moving target defense method proposed in this invention, but the deployed lines are random. One hundred random MTD deployment strategies are set, and each random MTD strategy is used to attack 10,000 times. The success rates of the 100 random MTD attacks are as follows: Figure 6 As shown on the far right, the MTD strategy, since it is not limited by the attack detection success rate, exhibits a large dispersion in the attack success rate points of the random MTD, indicating that its defense performance is unstable and fluctuates significantly. Therefore, it can be seen that the power system moving target defense method based on power flow betweenness and power flow disturbance proposed in this invention has a better defense effect.

[0116] In summary, the power system moving target defense method based on power flow betweenness and power flow disturbance proposed in this invention first calculates the normalized power flow betweenness and power flow disturbance indices of the power system lines; then, it constructs a comprehensive index based on the power flow betweenness and power flow disturbance indices; next, it determines the set of lines to be deployed based on the preset number of equipment deployments and the comprehensive index, and selects high-value candidate lines for MTD defense. The target measurement matrix is ​​obtained by changing the line impedance values ​​corresponding to the line set; that is, simulating the MTD defense situation. Based on the original measurement matrix and the target measurement matrix, the measurement residuals after the change in line impedance values ​​are calculated, and the attack success rate is determined based on the relationship between the measurement residuals and the detection threshold.

[0117] If the attack success rate is greater than the preset value, the preset number of deployed devices is increased by 1 to obtain a new deployment number. The following steps are then executed: Based on the new deployment number and comprehensive indicators, a new set of lines needs to be deployed. In other words, when the attack success rate is high, the preset number of deployed devices is considered insufficient to achieve a good MTD defense effect, and the number of deployed devices needs to be increased. The increased deployment number is then used as the basis for MTD defense, and the measurement residual is calculated to determine the attack success rate. This process is repeated until the attack success rate is not less than the preset value. Then, power system mobile target defense is deployed according to the preset number of deployed devices and their corresponding set of lines.

[0118] The proposed power system moving target (MTD) defense method creatively balances detection effectiveness and MTD stealth by calculating the power flow betweenness factors (representing the effectiveness of quantitative defense) and power flow disturbance indices (representing the stealth of quantitative defense) of each power system line. Different weights can be assigned to different defense targets. The protection priority of power system lines is ranked, and MTD defense is deployed only on high-value candidate lines. This transforms the traditional global combinatorial search problem into a linear complexity ranking problem, enabling rapid solution and improving computational efficiency. Furthermore, the aforementioned MTD defense has minimal impact on the power flow during normal operation, making it less likely to be detected by attackers. It effectively incorporates stealth into the rapid deployment strategy of MTD, achieving rapid generation of stealthy MTD strategies, and possesses broad application prospects and high practicality.

[0119] Although preferred embodiments of the present invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the present invention.

[0120] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0121] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A method for defending against moving targets in a power system based on power flow betweenness and power flow disturbance, characterized in that, include: Based on the measured values ​​of the power system and the formulas for power flow betweenness and power flow disturbance index, the normalized power flow betweenness and power flow disturbance index of the power system lines are calculated. Based on the current betweenness factor and the current disturbance index, a comprehensive index is constructed; The set of lines to be deployed is determined based on the preset number of devices to be deployed and the comprehensive indicators mentioned above; By changing the line impedance values ​​corresponding to the line set, the target measurement matrix is ​​obtained; Based on the attacker's measurement values, estimated values ​​of state variables, and the target measurement matrix after the change in line impedance, the residual of the measurement values ​​after the change in line impedance is calculated, and the attack success rate is determined based on the relationship between the residual of the measurement values ​​and the detection threshold. If the attack success rate is greater than a preset value, the preset number of deployed devices is increased by 1 to obtain a new number of deployments, and the following steps are executed: determine the set of new lines to be deployed based on the new number of deployments and the comprehensive indicators; If the attack success rate is not less than a preset value, then deploy power system mobile target defense according to the preset number of deployed devices and their corresponding line sets.

2. The power system moving target defense method according to claim 1, characterized in that, Calculating the normalized power flow betweenness numbers of power system lines includes: Calculate the power flow betweenness of a single generating load pair; Based on the power flow betweenness of the single generating load pair, and taking into account the cumulative effect of all generating load pairs in the power grid, the power flow betweenness of the target line is defined. Using the power flow tracing method, based on the sequential and reverse allocation matrices, downstream and upstream tracing calculations are performed respectively to obtain the power flow composition in the target line; Based on the power flow composition, the power flow betweenness formula for the target line is obtained; Based on the power flow betweenness formula of the target line, the power flow betweenness of all power system lines is calculated and normalized to obtain the normalized power flow betweenness of the power system lines.

3. The method for defending against moving targets in a power system according to claim 2, characterized in that, The calculation of the normalized power flow disturbance indices for power system lines includes: Calculate the average value of the system line reactance; The reactance of each power system line is modified to the target reactance in turn; Based on the target reactance, the new power flow value for each power system line is calculated. Based on the new power flow value of each power system line and its corresponding initial power flow value, calculate the sum of the absolute values ​​of power flow changes of all power system lines; Based on the sum of the absolute values ​​of power flow changes of all power system lines, the power flow disturbance index of each power system line is obtained, and then normalized to obtain the normalized power flow disturbance index of the power system line.

4. The power system moving target defense method according to claim 2, characterized in that, Calculate the power flow betweenness of a single generating load pair The formula is as follows: In the above formula, For generator to load The active power transmitted; For generator to load The transmitted active power at the target line The amount on, and The target routes are respectively The node numbers at both ends; The weight of the single power flow betweenness is taken from the generator. Actual output and load Actual load The smaller value in represents and The maximum available transmission power between them; Taking into account the cumulative effect of all generating load pairs in the power grid, the target line is defined. Trend betweenness as follows: In the above formula, For the set of generator nodes; For the set of all load nodes; The power flow composition of the target line includes: the target line Flowing towards load in the tide The power of the target line The trend originated from generators power, generator to load The actual transmission power is determined by the power generation load. Provided component power; Among them, the line Flowing towards load in the tide power as follows: In the above formula, For the target route Active power flowing in the middle; For nodes The node flow is equal to the sum of the injected or outflowing flow; For load nodes Active load; Assign matrices sequentially. For matrix The inverse is located at Element; The target line The trend originated from generators power as follows: In the above formula, For load nodes Those who have made meritorious contributions; Assign matrices in reverse order. For matrix The inverse is located at Element; The generator to load Actual transmission power as follows: In the above formula, For nodes The node flow is equal to the sum of the injected or outflowing flow; For matrix The inverse is located at Element; The power generation load Provided component power as follows: Combining the expressions corresponding to the four powers in the power flow composition, the power flow betweenness formula for the target line is obtained as follows: Based on the above formula, let... For the first The power flow betweenness of each line is used to calculate the power flow betweenness of all lines in the power system. ; The normalization process is as follows: In the above formula, For the first Normalized power flow betweenness numbers of power system lines; This is the maximum value of the power flow betweenness of all power system lines, i.e. ; This is the minimum value of the power flow betweenness of all power system lines, i.e. .

5. The method for defending against moving targets in a power system according to claim 3, characterized in that, Calculate the average value of the system line reactance: In the above formula, This represents the average reactance of the power system lines, also known as its per-unit value. This represents the total number of lines in the power system. For the first The reactance value of a power system line, also known as its per-unit value; The first The reactance of a power system line is modified to a target reactance, the value of which is... ; The sum of the absolute values ​​of all power system line flow changes is calculated as follows: In the above formula, In order to disturb the first After the reactance value of the power system line, the first Transmission power on a power system line; In order to disturb the first Before the reactance of the power system line, the first Transmission power on a power system line; In the disturbance After determining the reactance value of each power system line, the sum of the absolute values ​​of the power flow changes of all power system lines; Based on the sum of the absolute values ​​of power flow changes across all lines, a quantitative index of disturbance impact is obtained for each line. , for the Power flow disturbance index of power system lines Normalization is as follows: In the above formula, For the first Normalized power flow disturbance index for each power system line; This represents the maximum value of all power flow disturbance indices in the power system, i.e. ; This is the minimum value of all power flow disturbance indices in the power system, i.e. .

6. The method for defending against moving targets in a power system according to claim 1, characterized in that, Based on the aforementioned power flow betweenness and the aforementioned power flow disturbance index, a comprehensive index is constructed, including: Based on the power flow betweenness and the power flow disturbance index, the detection effectiveness and stealth of the mobile target defense strategy are optimized in a coordinated manner, and the comprehensive index is constructed. The comprehensive indicators are as follows: In the above formula, For the first The comprehensive defense value score of each power system line; the higher the score, the better. The higher the priority of the deployment of each power system line; The weights for the power flow betweenness are used to characterize the weights corresponding to the detection effectiveness. ; The weight of the power flow disturbance index represents the weight corresponding to the concealment. ; E i For the first Normalized power flow betweenness numbers of power system lines; S i For the first Power flow disturbance index after normalization of power system lines.

7. The method for defending against moving targets in a power system according to claim 1, characterized in that, The detection threshold is calculated by combining the chi-square distribution, a preset significance level, and the degrees of freedom of the original measurement matrix. The original measurement matrix is ​​calculated based on the measured values ​​and the DC power flow model; it includes: Treat the voltage magnitude of the reference node as 1, and set the voltage phase angle of the remaining nodes other than the reference node as 1. As a state variable of the power system, use It is expressed as follows: The measured values ​​are the injected active and reactive power of the busbar, and the active and reactive power of the transmission line. These measured values ​​are expressed as... The DC power flow model is then expressed as a set of linear equations as follows: In the above formula, Let the measurement noise column vector take values ​​that conform to a normal distribution; if there are a total of Each measurement value One non-reference node, and Then the measurement matrix It is represented as follows: In the above formula, The admittance matrix of the power system; The correlation matrix of the power system; For matrix The transpose of the measurement; the detection threshold is calculated by combining the chi-square distribution and a preset significance level with the degrees of freedom of the measurement value, including: The degrees of freedom are calculated from the dimensions of the original measurement matrix. : According to degrees of freedom First, set a significance level, then look up the chi-square distribution table to obtain the detection threshold.

8. The method for defending against moving targets in a power system according to claim 1, characterized in that, The set of lines to be deployed, determined based on the preset number of devices and the aforementioned comprehensive indicators, includes: Based on the aforementioned comprehensive indicators, each power system line is ranked from highest to lowest according to the comprehensive indicators; The power system lines with the highest target number in the ranking are identified as the set of lines to be deployed, and this target number is the same as the preset number of equipment to be deployed.

9. The method for defending against moving targets in a power system according to claim 1, characterized in that, Based on the attacker's measurement values ​​during the attack after the change in line impedance, the estimated values ​​of state variables, and the target measurement matrix, the measurement residuals after the moving target defense action are calculated, including: In the DC power flow model, calculating the estimated values ​​of the state variables is transformed into solving the following weighted minimum variance optimization problem: In the above formula, This is the weight matrix of the measurement values, i.e., the angular covariance matrix of the measurement values; State variables The estimated value, the weight matrix of the measured value as follows: Based on the weight matrix Original measurement matrix H Measurement values The state variables are obtained using the least squares method. The estimated value for: The weight matrix middle, These are the measured values The reciprocal of the measurement noise variance; In the state estimation of the DC power flow model, the residual of the measured values ​​is defined as follows: In the formula, The residual value is the measurement value. If its value is greater than the detection threshold, an alarm will be triggered. This indicates taking the 2-norm; This is an estimate of the measured value; Based on the aforementioned DC power flow model, the attacker designs an attack vector using existing raw measurement values. as follows: In the above formula, H This refers to the original measurement matrix; The deviation injected into the state variables; After the attacker's attack is successfully executed, the estimated values ​​of the state variables are changed as follows: In the above formula, These are estimates of the state variables after the attack; If the attacker based on The attack vector is designed, and the measurement residuals after the attack are as follows: In the above formula, The measurement residuals after the attack; These are measurements taken after the attack, because ,but The value is zero, that is Therefore, this attack bypasses bad data detection based on measurement residuals; After changing the line impedance value corresponding to the aforementioned line set, if the attacker... If the attack vector is designed, the measurement residuals are as follows: In the formula, The residual of the measurement value when an attack occurs after the line impedance value has changed; These are the measured values ​​when an attack occurs after a change in the line impedance. The target measurement matrix; , This is an estimated state of the line when an attack occurs after the line impedance value changes. This is the actual measured value after the line impedance value has changed; , The actual measured value after the change in line impedance. The corresponding state estimate; , This refers to the deviation value injected into the state variables after the line impedance value changes.

10. The method for defending against moving targets in a power system according to claim 9, characterized in that, Based on the relationship between the measured residual and the detection threshold, the attack success rate is determined, including: The process of calculating the residual of the measured value after the change of the line impedance value is repeated a preset number of times. After each calculation of the residual of the measured value, it is judged against the detection threshold. If the residual of the measured value does not exceed the detection threshold, no alarm is triggered, and the attack is confirmed to be successful; if the residual of the measured value exceeds the detection threshold, an alarm is triggered, and the attack is confirmed to be unsuccessful. The attack success rate is obtained by dividing the number of successful attacks by the preset number. Among them, the residual of the measured value when an attack occurs after the change in line impedance value. The formula states that when the line impedance value changes, the target measurement matrix differs significantly from the original measurement matrix, making... If the difference is not zero and is large, then If the detection threshold is exceeded, an alarm is triggered, indicating that the attack was unsuccessful.

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