CN115801546B - Power distribution network information physical system reliability assessment method considering information disturbance - Google Patents

Abstract

The invention discloses a distribution network information physical system reliability assessment method considering information disturbance, comprising the following steps: S1, establishing a distribution network CPS reliability model; S2, solving the corresponding correlation matrix in the reliability model; S3, Solve the minimum cut set of the cyber-physical system of the distribution network from the correlation matrix: S4, and calculate the reliability index of the cyber-physical system of the distribution network. The present invention considers the complexity of the structure and characteristics of the CPS of the distribution network, and adopts the method of combining the fault tree and the Petri net to model the reliability of the system when establishing the reliability model, and realizes the modeling of the physical system and the information system The combination of the two methods can give full play to the advantages of fault tree modeling and greatly improve the efficiency and accuracy of solving system reliability. Only by partially modifying the correlation matrix of the Petri network diagram, the topology structure After the change, the reliability index is calculated for the system. Therefore, it is suitable for popularization and application.

Description

A reliability assessment method for cyber-physical system of distribution network considering information disturbance

Technical Field

The present invention belongs to the technical field of distribution network reliability assessment, and in particular, relates to a distribution network information-physical system reliability assessment method taking information disturbance into consideration.

Background Art

With the widespread application of information technology, traditional distribution networks have gradually developed into cyber-physical systems with a high degree of cyber-physical integration. Among them, the physical system provides energy support for the information system, while the information system provides 3C (Communication, Computation, Control) technical support for the physical system to achieve the coordinated interaction between information flow and energy flow. However, compared with the reliability assessment of traditional distribution networks, the characteristics of the physical system in the distribution network CPS that is highly dependent on the information system make it face many new challenges when conducting reliability assessment of the system. On the one hand, the interaction mechanism of cyber-physics is more vague, and the complexity of the analysis of distribution network CPS is significantly increased. On the other hand, the cyber-physical infrastructure is highly dependent, and information attacks and information system failures will have potential negative impacts on the reliability of distribution network CPS operation. In recent years, malicious network attacks have occurred continuously, affecting the operation status of the system, and then affecting the stable development of urban economy and society. The reason for the significant losses is that the system status changes are not judged in time and reasonable measures are not taken. The external security threats to the network system are mainly cyber attacks, and the internal threats are mainly network component failures. Therefore, it is urgent to analyze the impact of various information disturbances such as external threats and internal threats on the reliability of distribution network CPS. Since the research on distribution network reliability is very mature, the focus of distribution network CPS reliability analysis is to clarify the coupling mechanism between the physical system and the information system, how to evaluate the system reliability after considering the impact of information disturbance on the system state, and the update of relevant evaluation methods and reliability indicators.

Although the relevant research on information disturbance has gradually deepened, most of them still use the traditional distribution network reliability assessment method, and do not reflect the impact of information disturbance on system reliability in the indicators. The indicators used for reliability assessment of distribution network CPS also mostly use traditional distribution network reliability indicators. Therefore, the relevant research still has the following deficiencies: On the one hand, due to the continuous deepening of the research on information-physical interaction, the consequences of information failures have been refined, which requires that the impact of information disturbance on the system state and thus the impact on system reliability be reflected in the indicators. Therefore, it is necessary to appropriately expand the scope of the original indicator assessment; on the other hand, from the perspective of information-physical fusion, there is a lack of reliability indicators that can comprehensively and quantitatively evaluate the reliability of information-physical systems, and it is impossible to scientifically measure the impact of information disturbance on the system. It is necessary to break through the limitations of traditional distribution network reliability assessment indicators from the perspective of information-physical fusion.

At the same time, in terms of reliability modeling, as the scale of the system continues to expand, the method of modeling using fault trees alone is more complicated to analyze during modeling, and the problem of state combination space explosion is prone to occur during solution. In addition, the calculation is too complicated when the minimum cut set is directly solved by the fault tree. In terms of reliability assessment, when the simulation method is used to evaluate the reliability of the model, the credibility is closely related to the number of samples selected during sampling, and the simulation time is too long, which is difficult to meet the requirements of online evaluation. In terms of reliability assessment indicators, most of the existing indicators use traditional distribution network reliability assessment indicators, which are difficult to meet the reliability assessment requirements of information-physical systems, and the impact of information disturbances on system reliability is not reflected in the indicators. There is a lack of reliability indicators that can conduct comprehensive and quantitative evaluation of the reliability of information-physical systems.

Summary of the invention

The purpose of the present invention is to provide a distribution network cyber-physical system reliability assessment method taking into account information disturbances. Aiming at the impact of various information disturbances on the system state and reliability, a generalized distribution network CPS reliability assessment index taking into account information disturbances is defined, which can accurately assess the system reliability under the influence of information disturbances.

To achieve the above purpose, the technical solution adopted by the present invention is as follows:

A reliability assessment method for a distribution network cyber-physical system considering information disturbances comprises the following steps:

S1, establish the distribution network CPS reliability model:

S1.1, determine the fault top event based on the topological structure and coupling relationship of the distribution network cyber-physical system;

S1.2, analyze the causes of load failure, establish and simplify the load fault tree model;

S1.3, conduct qualitative analysis on the load fault tree model and transform the load fault tree model into a corresponding Petri net model;

S2, solve the corresponding correlation matrix in the reliability model:

S2.1, obtain the input matrix and output matrix of the Petri net model according to the Petri net structure;

S2.2, solve the incidence matrix based on the input matrix and the output matrix;

S3, solve the minimum cut set of the distribution network cyber-physical system by the incidence matrix:

S3.1, find the event top library and input event;

S3.2, determine whether the event is an intermediate place, if not, the place is a bottom place, if yes, return to step S3.1;

S3.3, expand all the bases, obtain the cut sets and simplify them into the minimum cut sets;

S4, calculate the reliability index of the distribution network cyber-physical system:

S4.1, solve the probability of occurrence of the top fault event based on the minimum cut set;

S4.2, solve the probability of each load point being in a network attack state;

S4.3, calculate the annual failure rate and annual average power outage time of each load point, and obtain various reliability indicators based on this;

S4.4, calculate the reliability indicators of the generalized distribution network cyber-physical system considering information disturbances and evaluate the system reliability.

Furthermore, in step S2.2, based on the Petri net model, a four-tuple matrix is defined:

为库所的集合，

，代表故障树中线路、变压器、开关元件、服务器、交换机及IED故障；

为变迁的集合，

表示故障树中故障传递过程；

为有向弧，是输入函数与输出函数的集合，表示故障的传输方向；

为系统初始令牌；in,

is the collection of places,

, represents the line, transformer, switch element, server, switch and IED faults in the fault tree;

For the collection of changes,

Represents the fault transmission process in the fault tree;

is a directed arc, which is a set of input functions and output functions, indicating the transmission direction of the fault;

It is the system initial token;

The Petri net model is represented as an n- row and m- column matrix:

A =

in,

为Petri网的输出矩阵的元素，

为Petri网的输入矩阵的元素，矩阵A即为四元组矩阵

的关联矩阵。In the formula,

is the element of the output matrix of the Petri net,

is the element of the input matrix of the Petri net, and the matrix A is a four-tuple matrix

The correlation matrix of .

Furthermore, in step S4.1, the occurrence probability of the minimum cut set is used to determine the occurrence probability of the top fault event, and the mathematical expression is:

为最小割集，

、

为第

、f、e个割集发生的概率；m为最小割集个数的最大值。Where P ( T ) is the probability of the top fault event T occurring,

is the minimum cut set,

,

For the

The probability of occurrence of , f , and e cut sets; m is the maximum number of minimum cut sets.

Furthermore, in step S4.2, the probability of the load point being in a network attack state is calculated as follows:

Assuming that the number of switches, IED devices and servers in the minimum cut set of a load point l fault is a , b and c respectively, the probability p _l that the load point is in a network attack state is:

P _l = 1-

Where: The probability that the load point is in normal operation is (1- p _l ).

Furthermore, in step S4.3, the obtained reliability indicators include:

：反映因物理元件故障直接导致或通过信息扰动引起的控制失效导致负荷削减的频率，该指标定义为：1) Generalized system average power outage frequency index

: Reflects the frequency of load shedding due to control failure caused directly by physical component failure or through information disturbance. This indicator is defined as:

表示负荷点数目；

表示第

个负荷点用户数；

表示由于物理元件故障直接导致负荷点削减次数；

表示信息元件自身故障引起的控制失效导致负荷点削减次数；

表示由于网络攻击IED引起的控制失效导致负荷点削减次数；Where:

Indicates the number of load points;

Indicates

Number of users at each load point;

Indicates the number of load point cuts caused directly by physical component failures;

Indicates the number of load point reductions caused by control failures caused by failures of the information element itself;

It indicates the number of load point reductions caused by control failures caused by cyber attacks on IEDs;

：反映系统因物理元件故障直接导致或通过信息扰动引起的控制失效导致的负荷削减的年平均持续时间，该指标定义为：2) Generalized system average power outage duration indicator

: Reflects the annual average duration of load reduction caused by control failure directly caused by physical component failure or through information disturbance. This indicator is defined as:

表示由于物理元件故障直接导致的负荷点年停电时间；

表示信息元件自身故障引起的控制失效导致的负荷点年停电时间；

表示由于网络攻击IED引起的控制失效导致的负荷点年停电时间；Where:

It indicates the annual power outage time of the load point directly caused by the failure of physical components;

Indicates the annual power outage time of the load point caused by control failure due to the failure of the information component itself;

It represents the annual power outage time of load points caused by control failure due to cyber attack on IED;

，反映系统因物理元件故障直接导致或通过信息扰动引起的控制失效导致的期望的缺供电量，该指标定义为；3) Expected general power shortage

, reflects the expected power shortage caused by the control failure of the system directly caused by physical component failure or through information disturbance. This indicator is defined as;

表示由于物理元件故障直接导致的缺供电量期望值；

表示信息元件自身故障引起的控制失效导致的缺供电量期望值；

表示由于网络攻击IED引起的控制失效导致的缺供电量期望值；Where:

It indicates the expected value of power shortage caused directly by the failure of physical components;

Indicates the expected value of power shortage caused by control failure due to the fault of the information element itself;

It represents the expected value of power shortage caused by control failure due to cyber attack on IED;

，反映系统中用户不停电小时数与用户要求的总供电时间之比，该指标定义为：4) Generalized power supply availability index

, reflects the ratio of the number of hours without power outages for users in the system to the total power supply time required by users. This indicator is defined as:

。

.

Compared with the prior art, the present invention has the following beneficial effects:

(1) The present invention considers the complexity of the structure and characteristics of the distribution network CPS. When establishing the reliability model, the fault tree and Petri net are combined to model the reliability of the system, realizing the unification of the physical system and the information system in modeling. The combination of the two methods can give full play to the modeling advantages of the fault tree, greatly improve the efficiency and accuracy of solving the system reliability, and save time. The accessibility of the Petri net can determine whether the system can run to a specified state under a given initial state. Only by partially modifying the association matrix of the Petri net diagram, the reliability index of the system after the topology structure changes can be calculated. The reliability evaluation index of the generalized distribution network information-physical system considering information interference is defined, which can more accurately characterize the system reliability.

(2) Aiming at the impact of various information disturbances on system status and reliability, the present invention defines a generalized distribution network CPS reliability evaluation index considering information disturbances, which can accurately evaluate the system reliability under the influence of information disturbances.

(3) The present invention adopts an analytical method to evaluate the reliability of the system. The system association matrix is written according to the system reliability model, and the minimum cut set is obtained from the association matrix. Then, the reliability index of the system is obtained according to the minimum cut set, thereby realizing the accurate calculation of the reliability index.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a schematic diagram of the traditional distribution network CPS structure.

FIG. 2 is a schematic diagram of an information-physical interface IED model in the prior art.

FIG3 is a block diagram of the reliability evaluation method in the present invention.

FIG. 4 is a schematic diagram of the steps of fault tree analysis in the present invention.

FIG5 is a schematic diagram of a typical power distribution system structure in the present invention.

FIG6 is a fault tree of load point B in an embodiment of the present invention.

FIG. 7 is a Petri net representation of logic “AND, OR, NOT” in an embodiment of the present invention, wherein (a) logic “AND”, (b) logic “OR”, and (c) logic “NOT”.

FIG. 8 is a Petri net diagram of a load point B fault in an embodiment of the present invention.

FIG. 9 shows the initial values assigned to the L2 library in an embodiment of the present invention.

FIG. 10 is a diagram showing the operation results when L2 fails in an embodiment of the present invention.

FIG. 11 is a schematic diagram of the structure of a CPS system of a distribution network in an embodiment of the present invention.

FIG. 12 is a topological diagram of an information system in an embodiment of the present invention.

FIG. 13 is a diagram showing the changing trend of the average power outage frequency of the system under different failure rates in an embodiment of the present invention.

FIG. 14 is a reliability index under different attack targets in an embodiment of the present invention.

FIG. 15 is a bar graph showing the impact of attacking an IED on GSAIDI according to an embodiment of _the present invention.

FIG. 16 is a bar graph showing the impact of attacking an IED on _{the GEENS} according to an embodiment of the present invention.

FIG. 17 is a bar graph showing the impact of attacking two IEDs on GSAIDI according to an embodiment of _the present invention.

FIG. 18 is a bar graph showing the impact of attacking two IEDs on GEENS according to an embodiment of _the present invention.

FIG. 19 is a schematic diagram of the access network structure in an embodiment of the present invention.

FIG. 20 is a reliability index curve diagram of different access network structures in an embodiment of the present invention.

FIG. 21 is a fault tree model of load point 1 in an embodiment of the present invention.

FIG. 22 is a Petri net model diagram of load point 1 failure in an embodiment of the present invention.

DETAILED DESCRIPTION

The present invention is further described below in conjunction with the accompanying drawings and embodiments. The embodiments of the present invention include but are not limited to the following embodiments.

The invention discloses a reliability assessment method for a distribution network information-physical system considering information disturbance, which is mainly used to break through the limitations of traditional distribution network reliability assessment indicators from the perspective of information-physical integration. In the distribution network CPS, the physical system is mainly composed of traditional components such as overhead lines, disconnectors, transformers, etc., which provide energy support for the information system; while the information system mainly includes components such as servers, switches, and intelligent terminal devices (Intelligent Electronic Device, IED) to monitor, control and protect the physical system. The structure of the distribution network CPS is shown in Figure 1. The information-physical system is a combination of the physical layer, the communication layer and the decision-making layer. The physical layer is composed of traditional power system equipment required for power generation, transmission and distribution. The introduction of sensors and communication networks further increases the possibility of reliable and efficient operation of the power system, and the communication layer makes it possible to make real-time decisions using real-time data from the physical layer.

The schematic diagram of the IED model is shown in Figure 2. IED is an interface device that connects the information system and the physical system. It consists of fault monitoring units, relay protection units, and control units. The function of IED is to monitor and collect the real-time status of the power grid, and transmit it to the main station server through the communication network. The main station server makes decisions and dispatches according to the collected data, handles various accidents, and sends control signals to the IED device. At this time, IED conveys the instructions to the primary device through various interactions, thereby effectively coupling the physical system and information system of the distribution network.

The reliability assessment method of the distribution network CPS proposed in the present invention is shown in Figure 3. The fault tree and Petri net are combined for modeling; the influence of information disturbance on the system state is considered to define the reliability index; and the minimum cut set method in the analytical method is used for reliability assessment.

In the reliability modeling of distribution network CPS, since the fault tree model has clear and vivid causal relationships, it can make a comprehensive and concise description of the various causes and logical relationships that lead to accidents, so it can clearly and accurately analyze the causes of load failures in the system. However, for complex systems, there are many steps to compile a fault tree, and the compiled fault tree is also relatively large. In addition, the calculation is relatively complex, which brings difficulties to the given and quantitative analysis; and the fault tree model is a static analysis model and cannot study the dynamic process of the reliability of the system under investigation. The main advantage of Petri nets is that they can handle practical phenomena such as concurrency, synchronization, asynchrony, parallelism, and non-determinism that are difficult to solve with general methods. It has simple and well-defined syntax and semantics, and can describe different abstract levels of a system. Using the reachability of Petri nets, it can be determined whether the system can run to a specified state under a given initial state, and the fault tree can be easily represented by Petri nets. Therefore, the present invention uses a combination of fault trees and Petri nets to model the system when modeling the reliability of the system.

A fault tree is a logic diagram that uses event symbols, transfer symbols, and logic gate symbols to describe the causal relationship of events. Fault tree analysis mainly analyzes the causes of failures of various components in the distribution network CPS, thereby determining all combinations of fault causes and the probability of occurrence. The analysis steps of the fault tree are shown in Figure 4.

The steps of constructing a fault tree of the present invention are: firstly, determining the top fault event, i.e., the situation that the system least wants to happen; then analyzing all possible causes that lead to the top fault event, analyzing the logical relationship between the causes and connecting them with logic gates; then analyzing whether the input events directly connected to the top fault event can be further decomposed, and if so, treating them as input events of the next level events, decomposing until all input events cannot be decomposed any further, and the events that cannot be decomposed any further are bottom events.

The typical power distribution system is shown in Figure 5. This power distribution system is a typical radial power distribution system, which consists of two feeders, three trunk lines L1, L2 and L3, and three branch lines L4, L5 and L6. The trunk lines are separated by disconnectors, and T is a tie switch.

Assuming that the top fault event is the fault of load point B, the possible causes of the top fault event are: failure of the main line L2, failure of the branch line L5, and disconnection of the disconnector. Since the failure of the main line L1 and the main line L3 is the cause of the disconnection of the disconnector, and as long as one of all the possible causes occurs, load point B will inevitably fail. Therefore, without considering the failure of the circuit breaker and the tie switch, the fault tree of load point B is shown in Figure 6.

In the figure, L2 and L5 represent the failure of the main line L2 and the branch line L5 respectively; L1 and L3 represent the disconnection of the disconnector caused by the main lines L1 and L3 respectively. Figure 6 can clearly show all possible causes of the load B failure in the typical radial distribution system of Figure 4. The Petri net model of the system can be obtained by analyzing the fault tree, and then a series of reliability indicators can be solved.

Although the network structure of Petri nets is static, the tokens therein can flow in the network according to the defined occurrence rules, so Petri nets are dynamically executable. Therefore, it is feasible to use Petri nets to model information-physical systems with event-driven characteristics.

The present invention adopts a combination of fault tree and Petri net to model the reliability of distribution network CPS, converts the fault tree model into a Petri net model, and defines a four-tuple matrix based on the Petri net model:

为库所的集合，

，代表故障树中线路、变压器、开关元件、服务器、交换机及IED故障；

为变迁的集合，

表示故障树中故障传递过程；

为有向弧，是输入函数与输出函数的集合，表示故障的传输方向；

为系统初始令牌。in,

is the collection of places,

, represents the line, transformer, switch element, server, switch and IED faults in the fault tree;

For the collection of changes,

Represents the fault transmission process in the fault tree;

is a directed arc, which is a set of input functions and output functions, indicating the transmission direction of the fault;

The system initial token.

The fault tree is the logical relationship of fault propagation in the system, which can be easily converted into a Petri net representation. The Petri net representation of the logic "AND, OR, NOT" when the fault tree is converted into a Petri net is shown in Figure 7. According to the logic conversion rules, the fault tree model of load B in Figure 6 is converted into a Petri net model as shown in Figure 8.

The advantages of combining the fault tree and Petri net modeling methods are as follows:

(1) The model is comprehensive and accurate

Combining the two methods for modeling can give full play to the advantages of fault tree modeling. The fault tree has clear and vivid causal relationships, and can make a comprehensive and concise description of the various causes and logical relationships that lead to the fault. It can perform both qualitative analysis and quantitative analysis and system evaluation. Using this fault analysis approach, when modeling the reliability of the distribution network CPS, it can provide a comprehensive and accurate description of the various causes of the fault.

(2) High solution efficiency

For an example with 5 layers and 7 bottom events, it takes 8 steps to solve the minimum cut set through the fault tree, while it only takes 3 steps to solve the minimum cut set using the Petri net. Therefore, this paper adopts the method of first converting the fault tree model into a Petri net and then solving the minimum cut set to effectively improve the efficiency of the system. In addition, the distribution network CPS adds an information system to monitor and control the physical system on the basis of the traditional distribution network, making the system structure more complex. At this time, if only the fault tree model is used to calculate the minimum cut set of the system, the calculation is very complicated and takes a lot of time. Therefore, the combination of the two methods can greatly improve the efficiency and accuracy of the system reliability solution and save time.

(3) Image of the fault transmission process

The reachability of Petri nets can be used to determine whether the system can run to a specified state under a given initial state. Using this feature of Petri nets, the PIPE software can assign an initial identifier to any library in the diagram when defining the initial state. By running the Petri net, the token transfer process, that is, the fault transfer process, can be clearly seen. At the same time, the final library can be immediately obtained, that is, the result caused by the fault, which provides convenience for system fault analysis and reliability calculation. The initial identifier assigned to the L2 library in the Petri net shown in Figure 8 is shown in Figure 9, indicating that L2 has a fault at this time. At this time, running the program, the running result shown in Figure 10 is obtained, showing the fault of load point B.

The structure of Petri net can be represented by a matrix, which can introduce linear algebra methods to analyze the properties of Petri net. The Petri net model is represented as a u- row v- column matrix:

A =

in,

为Petri网的输出矩阵中的元素，

为Petri网的输入矩阵中的元素，矩阵A即为四元组

的关联矩阵。图8所示Petri网的输出矩阵

和输入矩阵

分别为：In the formula,

is the element in the output matrix of the Petri net,

is the element in the input matrix of the Petri net, and the matrix A is a quaternion

The output matrix of the Petri net shown in Figure 8

and the input matrix

They are:

和输入矩阵

可求得该Petri网对应的关联矩阵为：According to, the output matrix

and the input matrix

The correlation matrix corresponding to the Petri net can be obtained as:

In the system shown in Figure 5, due to a fault or other reasons, the disconnector DS2 is opened (such as L3 fault), and the trunk line L3 and its load are powered by feeder 2. When evaluating the reliability of the system at this time, if only fault tree modeling is used, the system structure needs to be re-analyzed and the fault tree model needs to be established. However, if the fault tree and Petri net are combined for modeling, only the output matrix and input matrix need to be changed to:

Then the minimum cut set can be solved. This method can greatly save modeling time and improve modeling efficiency. Especially for distribution network CPS, the addition of information system makes the system structure more complex and the interaction between parts is more frequent. The combination of fault tree and Petri net can greatly improve the efficiency of modeling and make modeling more accurate.

The minimum cut set analysis method mainly seeks the minimum cut set for the load points in the network and calculates the reliability index, which can reflect the minimum fault composition mode of system failure, and is a necessary condition for system failure. Based on the minimum cut set, the reliability analysis of the system can be conveniently performed. Since Petri nets have the characteristics of accessibility and boundedness, they can better describe various common phenomena in complex systems, and there are very rich analysis methods. Among them, the association matrix analysis method is suitable for large-scale Petri net models with high complexity. On the basis of the Petri net model, the present invention calculates the topological relationship embodied in the Petri net model and converts it into the form of an association matrix, solves the minimum cut set by the association matrix, and finally solves the probability of occurrence of the top fault event according to the failure rate of each component in the minimum cut set, and then solves the system reliability index.

来表示，而信息元件网络攻击成功率用P _atk 来表示。由于针对IED设备的网络攻击对系统影响最大，故本发明以IED网络攻击为例进行分析计算，其他信息元件网络攻击计算同IED网络攻击。根据两种安全威胁的特征及影响，将系统状态分为正常运行状态和网络攻击状态，信息元件故障在两种状态都可能随时发生。The external security threat in information disturbance is mainly network attack, which usually exploits the security weakness of the element and tampers the original data by injecting false data. The internal threat is mainly the failure of the element itself. Since the failure rate of the information element itself is an inherent property of the element and will not change with external factors, the present invention uses the failure rate of the information element

The success rate of network attacks on information components is represented by P _atk . Since network attacks on IED devices have the greatest impact on the system, the present invention uses IED network attacks as an example for analysis and calculation. The calculation of network attacks on other information components is the same as that of IED network attacks. According to the characteristics and impacts of the two security threats, the system state is divided into normal operation state and network attack state. Information component failures may occur at any time in both states.

Specifically, the occurrence probability of the minimum cut set is used to determine the occurrence probability of the top fault event, and the mathematical expression is:

为最小割集，

、

为第

、f、e个割集发生的概率；m为最小割集个数的最大值。Where P ( T ) is the probability of the top fault event T occurring,

is the minimum cut set,

,

For the

The probability of occurrence of , f , and e cut sets; m is the maximum number of minimum cut sets.

In step S4.2, the probability of a load point being in a network attack state is calculated as follows:

Assuming that the number of switches, IED devices and servers in the minimum cut set of a load point l fault is a , b and c respectively, the probability p _l that the load point is in a network attack state is:

p _l = 1-

为网络攻击IED设备的成功概率，该负荷点处于正常运行状态的概率为(1-p _l ) 。Where:

is the success probability of a network attack on the IED device, and the probability that the load point is in normal operation is (1- p _l ).

、停电时间

、和失负荷量

分别为：Number of load outages caused by information component failures

, power outage time

, and load loss

They are:

；

;

；

;

分别表示IED设备、交换机和服务器的元件故障率；

分别表示单台IED设备、交换机和服务器的年故障时间；

表示负荷点l的平均负荷。Where:

They represent the component failure rates of IED devices, switches, and servers, respectively;

Represents the annual failure time of a single IED device, switch and server respectively;

Represents the average load at load point l .

、停电时间

和失负荷量

分别为：Number of load outages caused by cyber attacks

, power outage time

and load loss

They are:

表示最小割集中遭受网络攻击的IED设备数量。Where:

Represents the number of IED devices that are attacked by the network in the minimum cut set.

（次/a）、年平均停电时间

指标为基础，得到的各可靠性指标包括：In order to take into account the impact of information disturbance on system reliability, this paper takes into account the load reduction caused by information component failure and network attack on the basis of the traditional distribution network reliability evaluation index system, defines the generalized distribution network CPS reliability evaluation index considering information disturbance, and characterizes the changes in system reliability caused by control failure due to physical component failure and information interference.

(times/ a ), annual average power outage time

Based on the indicators, the reliability indicators obtained include:

：反映因物理元件故障直接导致或通过信息扰动引起的控制失效导致负荷削减的频率，该指标定义为：1) Generalized system average power outage frequency index

: Reflects the frequency of load shedding due to control failure caused directly by physical component failure or through information disturbance. This indicator is defined as:

表示负荷点数目；

表示第

个负荷点用户数；

表示由于物理元件故障直接导致负荷点削减次数；

表示信息元件自身故障引起的控制失效导致负荷点削减次数；

表示由于网络攻击IED引起的控制失效导致负荷点削减次数；Where:

Indicates the number of load points;

Indicates

Number of users at each load point;

Indicates the number of load point cuts caused directly by physical component failures;

Indicates the number of load point reductions caused by control failures caused by failures of the information element itself;

It indicates the number of load point reductions caused by control failures caused by cyber attacks on IEDs;

：反映系统因物理元件故障直接导致或通过信息扰动引起的控制失效导致的负荷削减的年平均持续时间，该指标定义为：2) Generalized system average power outage duration indicator

: Reflects the annual average duration of load reduction caused by control failure directly caused by physical component failure or through information disturbance. This indicator is defined as:

表示由于物理元件故障直接导致的负荷点年停电时间；

表示信息元件自身故障引起的控制失效导致的负荷点年停电时间；

表示由于网络攻击IED引起的控制失效导致的负荷点年停电时间；Where:

It indicates the annual power outage time of the load point directly caused by the failure of physical components;

Indicates the annual power outage time of the load point caused by control failure due to the failure of the information component itself;

It represents the annual power outage time of load points caused by control failure due to cyber attack on IED;

，反映系统因物理元件故障直接导致或通过信息扰动引起的控制失效导致的期望的缺供电量，该指标定义为；3) Expected general power shortage

, reflects the expected power shortage caused by the control failure of the system directly caused by physical component failure or through information disturbance. This indicator is defined as;

表示由于物理元件故障直接导致的缺供电量期望值；

表示信息元件自身故障引起的控制失效导致的缺供电量期望值；

表示由于网络攻击IED引起的控制失效导致的缺供电量期望值；Where:

It indicates the expected value of power shortage caused directly by the failure of physical components;

Indicates the expected value of power shortage caused by control failure due to the fault of the information element itself;

It represents the expected value of power shortage caused by control failure due to cyber attack on IED;

，反映系统中用户不停电小时数与用户要求的总供电时间之比，该指标定义为：4) Generalized power supply availability index

, reflects the ratio of the number of hours without power outages for users in the system to the total power supply time required by users. This indicator is defined as:

。

.

Therefore, the reliability assessment process proposed in this invention can be summarized into the following four stages:

S1, establish the distribution network CPS reliability model:

S1.1, determine the fault top event based on the topological structure and coupling relationship of the distribution network cyber-physical system;

S1.2, analyze the causes of load failure, establish and simplify the load fault tree model;

S1.3, conduct qualitative analysis on the load fault tree model and transform the load fault tree model into a corresponding Petri net model;

S2, solve the corresponding correlation matrix in the reliability model:

S2.1, obtain the input matrix and output matrix of the Petri net model according to the Petri net structure;

S2.2, solve the incidence matrix based on the input matrix and the output matrix;

S3, solve the minimum cut set of the distribution network cyber-physical system by the incidence matrix:

S3.1, find the event top library and input event;

S3.2, determine whether the event is an intermediate place, if not, the place is a bottom place, if yes, return to step S3.1;

S3.3, expand all the bases, obtain the cut sets and simplify them into the minimum cut sets;

S4, calculate the reliability index of the distribution network cyber-physical system:

S4.1, solve the probability of occurrence of the top fault event based on the minimum cut set;

S4.2, solve the probability of each load point being in a network attack state;

S4.3, calculate the failure rate and annual average power outage time of each load point, and based on this, calculate various reliability indicators;

S4.4, calculate the reliability indicators of the generalized distribution network cyber-physical system considering information disturbances and evaluate the system reliability.

Specifically, this embodiment uses an improved IEEE RBTS BUS2 system to verify the above method, as shown in Figure 11. The system is an improved distribution network CPS based on the IEEE RBTS BUS2 system and configured with a corresponding information system. The information system in this embodiment adopts a star topology, and the data adopts EPON communication. Optical fibers, a control center server, several switches, and IEDs that control each switch element are laid along the primary grid of the distribution network, as shown in Figure 12. The reliability parameters of the physical system are shown in Tables 1 to 3, and the failure rate and repair time of each component in the information system are shown in Table 4.

元件可靠性原始数据surface

Component reliability raw data

Where: λ _P is the permanent failure rate; r is the mean fault repair time; r _P is the backup replacement time; s is the switch switching time.

Table 2 RBTS-BUS2 feeder type and length

Table 3 Load point user types and peak loads

Table 4 Failure rate and repair time of each component of the information system

In order to simplify the calculation, this embodiment makes some general assumptions. During the study, it is considered that the other two important systems of the power system, namely the power generation system and the transmission system, and the initial power supply are reliable; each component is independent, and only the steady-state impact of the fault is considered; the impact of other factors such as weather is not considered, and only the power outage caused by equipment failure is considered; after the interconnection switch fails, the load of the intact section can be fully transferred.

Taking the load point LP1 fault as an example, a fault tree as shown in Figure 21 can be established. According to the transformation rules between the fault tree and the Petri net model, the fault tree model shown in Figure 21 is transformed into the Petri net model shown in Figure 22. The minimum cut sets of each load point are calculated as shown in Table 5.

Table 5 Minimum cut sets for each load point

为评估信息系统对物理系统可靠性的影响，可分以下两个场景进行研究：

To evaluate the impact of information systems on the reliability of physical systems, the following two scenarios can be studied:

Scenario 1: Consider the impact of information systems.

Scenario 2: Information systems are considered completely reliable.

The reliability indicators of the two scenarios are calculated respectively, and the results of scenario 2 are compared with those of the prior art. The calculation results are shown in Table 6.

Table 6 Comparison of reliability index results

From the calculation results of the method proposed in the present invention in Table 6, it can be seen that the deviation of G _SAIFI is 0.09%, the deviation of G _SAIDI is 0.07%, the deviation of G _EENS is 0.05%, and the deviation of G _ASAI is 0. The calculation results are highly consistent, indicating that the method proposed in the present invention is reasonable and effective.

From the results in Table 6, it can be seen that after considering the impact of the information system, the system reliability indicators G _SAIFI , G _SAIDI , and G _EENS have increased significantly compared with scenario 1, indicating that after considering the impact of the information system, the system's power outage frequency and power outage time and the system's power shortage expectation have increased to a certain extent. The reason for this result is that considering the impact of the information system increases the uncertainty of the system, and the failure of the information system will also affect the reliability of the system, resulting in a decrease in system reliability. Therefore, although the information system helps to improve the efficiency of the fault management process, the reliability impact caused by it should not be ignored, especially in the future when the coupling between information and physical systems is deepening, which also reflects the importance of considering the information system for distribution network reliability assessment.

The impact of information component failure rate on the reliability of distribution network CPS is analyzed as follows:

In order to study the influence of various information components on system reliability under different failure rates, this paper considers the influence of a single failure of an information component on the reliability of the distribution network CPS (selecting a certain component as an unreliable component, while other components are considered to be completely reliable). The failure rate of each type of information component is gradually increased or decreased by a certain proportion, and the failure rate of other equipment remains unchanged. The average value of multiple calculation results is calculated. Through the change of the index, the change trend of the system reliability index G _SAIDI of various information components under different failure rates can be obtained, as shown in Figure 13.

It can be seen that the impact of changes in the failure rate of different devices on the reliability of the distribution network CPS is different. The impact of single information component failure on CPS reliability is ranked as follows: IED device > switch > server. Among them, compared with IED and switch, server failure changes have less impact on reliability. The main reason is that at this stage, servers have sufficient protection measures, which greatly reduces the failure rate of servers. Therefore, server interruptions have little impact on the reliability of the distribution network CPS. The main functions of IED devices are data collection and instruction execution. Whether IED fails or not affects the transmission performance of the information system. Its failure will directly cause the failure of the components in the physical system connected to it to fail. Therefore, reducing the failure rate of IED is of great significance to improving power supply reliability and provides a reference for system investment.

The impact of cyber attacks on the reliability of distribution network CPS is analyzed as follows:

In the distribution network CPS, the potential main attack points are the servers in the control center and the intelligent electronic devices connected through switches. The network attack scenarios are as follows:

The distribution network is operating normally, and the cyber attacker attacks the IED device

① If the IED fails, the cyber attack will not affect the system reliability;

② If IEDs are attacked during normal operation, the consequences are related to the number and location of the attacked IEDs.

The distribution network is operating normally, and the network attacker attacks the main station server

① If the information system fails completely, the main site server cannot be attacked;

② If part of the information system fails, the attacker can use the master station to control the IED;

③If the information system is normal, the attacked main station may cause the entire system to crash.

In order to analyze the impact of different network attack targets on system reliability, the following three scenarios can be divided into for research. The results are shown in Figure 14.

Scenario 3: The target of the attack is the main server.

Scenario 4: The target of the attack is an IED.

Scenario 5: The attack targets two IEDs.

As can be seen from Figure 14, the impact of the network attack target on the system reliability is one IED>two IEDs>distribution master station, which means that for information systems, choosing a method with a higher success rate to attack the network will cause greater economic losses to the system. In order to study the impact of a specific IED attack on the system reliability, various scenarios of one IED and two IEDs being attacked by the network are calculated based on the normal operation of the physical system. The scenario types are shown in Table 7, and the results are shown in Figures 15 to 18.

Table 7 Classification of cyber attack schemes for IEDs

It can be seen from Figures 15 and 16 that compared with the reliability index without considering network attacks, the reliability index of the system increases to varying degrees when attacking one IED, indicating that attacking one IED will reduce the reliability of the system. In addition, when the physical system is operating normally, the fewer switches on the bus where the IED control switch is located and the fewer IEDs connected, the smaller the impact on the reliability of the system.

It can be seen from Figures 17 and 18 that, compared with the reliability index without considering the network attack, the reliability index of the system increases to varying degrees when attacking two IEDs, indicating that attacking two IEDs will reduce the reliability of the system, and for the network attack on two IEDs, the longer the distance between the two IEDs in the attacked IED combination, the greater the impact on reliability. Based on this, it can provide a reference for the investment of defense resources.

The impact of access network structure on the reliability of distribution network CPS is analyzed as follows:

The network topology of the information system is also an important factor affecting the reliability of the distribution network CPS. Therefore, this paper studies the impact of various access network structures such as bus, star, tree, and mesh on the reliability of the distribution network CPS. The schematic diagram of each access network structure is shown in Figure 19. The results of the impact of different access network structures on system reliability indicators are shown in Figure 20.

From the results in Figure 20, we can see that the G _SAIDI and G _EENS indicators of the mesh structure are the smallest and the system reliability is the highest, because it has more redundant communication lines as backup, which improves the reliability of the system. Secondly, the G _SAIDI and G _EENS indicators of the star structure are slightly higher than those of the mesh structure, but compared with the other structures, the change range of its reliability indicators is smaller. Therefore, it is necessary to select a suitable access network structure according to the reliability requirements.

When calculating the reliability index of different access network structures, the superiority of the fault tree and Petri net combination method in this paper is also reflected. Only the association matrix of the Petri net needs to be changed to continue the calculation, which greatly improves the efficiency of reliability assessment.

The above embodiment is only one of the preferred implementation modes of the present invention and should not be used to limit the protection scope of the present invention. Any changes or modifications that are made to the main design concept and spirit of the present invention and have no substantive significance, and the technical problems they solve are still consistent with the present invention, should be included in the protection scope of the present invention.

Claims (5)

1. A reliability assessment method for a distribution network cyber-physical system considering information disturbance, characterized in that it comprises the following steps: S1, establish the distribution network CPS reliability model: S1.1, determine the fault top event based on the topological structure and coupling relationship of the distribution network cyber-physical system; S1.2, analyze the causes of load failure, establish and simplify the load fault tree model; S1.3, conduct qualitative analysis on the load fault tree model and transform the load fault tree model into a corresponding Petri net model; S2, solve the corresponding correlation matrix in the reliability model: S2.1, obtain the input matrix and output matrix of the Petri net model according to the Petri net structure; S2.2, solve the incidence matrix based on the input matrix and the output matrix; S3, solve the minimum cut set of the distribution network cyber-physical system by the incidence matrix: S3.1, find the event top library and input event; S3.2, determine whether the event is an intermediate place, if not, the place is a bottom place, if yes, return to step S3.1; S3.3, expand all the bases, obtain the cut sets and simplify them into the minimum cut sets; S4, calculate the reliability index of the distribution network cyber-physical system: S4.1, solve the probability of occurrence of the top fault event based on the minimum cut set; S4.2, solve the probability of each load point being in a network attack state; S4.3, calculate the annual failure rate and annual average power outage time of each load point, and obtain various reliability indicators based on this; wherein the reliability indicators include a generalized system average power outage frequency indicator that reflects the frequency of load reduction caused by control failure directly caused by physical component failure or through information disturbance

; Generalized system average outage duration indicator reflecting the annual average duration of load reduction caused by control failure directly caused by physical component failure or through information disturbance

; Reflects the expected power shortage caused by the control failure of the system directly caused by physical component failure or through information disturbance.

; A generalized power supply availability index that reflects the ratio of the number of hours without power outages for users in the system to the total power supply time required by users

; S4.4, calculate the reliability indicators of the generalized distribution network cyber-physical system considering information disturbances and evaluate the system reliability. 2. A reliability assessment method for a distribution network cyber-physical system considering information disturbance according to claim 1, characterized in that, in step S2.2, based on a Petri net model, a four-tuple matrix is defined:

in,

is the collection of places,

, represents the line, transformer, switch element, server, switch and IED faults in the fault tree;

For the collection of changes,

Represents the fault transmission process in the fault tree;

is a directed arc, which is a set of input functions and output functions, indicating the transmission direction of the fault;

It is the system initial token; The Petri net model is represented as a u- row v- column matrix: A =

in,

In the formula,

is the element in the output matrix of the Petri net,

is the element in the input matrix of the Petri net, and the matrix A is the four-tuple matrix

The correlation matrix of . 3. A reliability assessment method for a distribution network cyber-physical system considering information disturbance according to claim 2, characterized in that, in step S4.1, the probability of occurrence of the minimum cut set is used to determine the probability of occurrence of the top fault event, and the mathematical expression is: P ( T ) = P ( K ₁

K ₂

K _m

=

+

+…+

Where P ( T ) is the probability of the top fault event T occurring,

,

For the

The probability of occurrence of , f , and e cut sets; m is the maximum number of minimum cut sets. 4. According to a method for evaluating the reliability of a distribution network cyber-physical system considering information disturbances according to claim 3, it is characterized in that, in step S4.2, the probability of a load point being in a network attack state is calculated as follows: Assuming that the number of switches, IED devices and servers in the minimum cut set of a load point l fault is a , b and c respectively, the probability p _l that the load point is in a network attack state is: p _l = 1-

Where:

is the success probability of a network attack on an IED device, and the probability that the load point is in normal operation is (1- p _l ); Among them, the number of load power outages caused by information component failures

, power outage time

and load loss

They are:

;

;

Where:

They represent the component failure rates of IED devices, switches, and servers, respectively;

Represents the annual failure time of a single IED device, switch and server respectively;

represents the average load at load point l ; Number of load outages caused by cyber attacks

, power outage time

, and load loss

They are:

+(

Where:

Represents the number of IED devices that are attacked by the network in the minimum cut set. 5. A reliability assessment method for a distribution network cyber-physical system considering information disturbance according to claim 4, characterized in that in step S4.3, the obtained reliability indicators include: 1) Generalized system average power outage frequency index

: Reflects the frequency of load shedding due to control failure caused directly by physical component failure or through information disturbance. This indicator is defined as:

Where:

Indicates the number of load points;

represents the number of users at load point l ;

Indicates the number of load point cuts caused directly by physical component failures;

Indicates the number of load point reductions caused by control failures caused by failures of the information element itself;

It indicates the number of load point reductions caused by control failures caused by cyber attacks on IEDs; 2) Generalized system average power outage duration indicator

: Reflects the annual average duration of load reduction caused by control failure directly caused by physical component failure or through information disturbance. This indicator is defined as:

Where:

It indicates the annual power outage time of the load point directly caused by the failure of physical components;

Indicates the annual power outage time of the load point caused by control failure due to the failure of the information component itself;

It represents the annual power outage time of load points caused by control failure due to cyber attack on IED; 3) Expected general power shortage

, reflects the expected power shortage caused by the control failure of the system directly caused by physical component failure or through information disturbance. This indicator is defined as:

Where:

It indicates the expected value of power shortage caused directly by the failure of physical components;

Indicates the expected value of power shortage caused by control failure due to the fault of the information element itself;

It represents the expected value of power shortage caused by control failure due to cyber attack on IED; 4) Generalized power supply availability index

, reflects the ratio of the number of hours without power outages for users in the system to the total power supply time required by users. This indicator is defined as:

.

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