A Method for Assessing and Improving the Resilience of a Distribution Cyber-Physical System under Disasters

Abstract

The present invention discloses a method for evaluating and enhancing the resilience of a distribution information - physical system under disasters, belonging to the field of coordinated control and optimal operation of power systems. By using Monte Carlo simulation sampling, damaged scenarios of urban power grids under disasters are randomly generated. Based on the scenarios, a multi - period dynamic joint resilience evaluation model of the distribution network information - physical system is established, and resilience evaluation indicators are introduced to evaluate the resilience of the power grid. Considering the recovery requirements of the power network load and communication system resources, resources such as distributed units and energy storage devices in the distribution network are utilized to cooperate with mobile emergency power supplies and mobile communication vehicles for strategy optimization. Moreover, the resilience of the distribution network information - physical system under different configurations is evaluated, and the optimal strategy for enhancing the resilience of the distribution network information - physical system is solved. By establishing a multi - period resilience evaluation model of the distribution network under extreme disaster scenarios, combining various resource configurations, and promoting the enhancement of power grid resilience on the basis of considering the coupling of the information network, it has high application value.

Description

Technical Field

[0001] The present invention relates to the field of coordinated regulation and optimal operation of power systems, and particularly to a method for evaluating and enhancing the resilience of a distribution cyber-physical system under disasters. Background Art

[0002] Under the background of the intelligent and informatized transformation of power systems, promoting the resilience assessment and improvement of distribution networks in the increasingly frequent extreme disaster scenarios is a challenging task.

[0003] When extreme disasters occur, power systems are prone to occur mass failures, which will lead to large-scale power outages, seriously threatening social economy and residents' lives. To promote the distribution cyber-physical system to cope with extreme disasters at a higher resilience level, it is necessary to coordinate various resources, optimize the system operation state. Considering the characteristics of low probability and high impact of extreme disasters and the background of the rapid development of new energy, the optimal dispatching should give priority to reducing the load shedding loss, and coordinate the use of various resources to effectively improve the system resilience. Therefore, a two-way dynamic model of the distribution cyber-physical system is established based on complex network theory, and the system damage scenarios are established by the Monte Carlo simulation method. With the goal of minimizing the system load shedding, the output of distributed generators and energy storage devices in the system is adjusted, and mobile emergency power supplies and mobile communication vehicles are called to maintain the state of the distribution cyber-physical system. The resilience evaluation index is introduced to quantitatively analyze the system resilience. Whether for power system operators or grid users, reducing the impact of disasters and promoting the distribution network to resume normal operation as soon as possible after encountering extreme disasters is particularly important. Therefore, the resilience assessment and optimal load shedding model of the distribution network considering the coupling of information networks for urban operation services has important research significance. Summary of the Invention

[0004] The purpose of the present invention is to overcome the deficiencies of the prior art and provide a method for evaluating and enhancing the resilience of a distribution cyber-physical system under disasters.

[0005] The purpose of the present invention is realized by the following technical solutions:

[0006] A method for evaluating and enhancing the resilience of a distribution cyber-physical system under disasters, comprising the following steps:

[0007] Step 1: Establish a two-way dynamic model of the distribution cyber-physical system based on complex network theory, including: a distribution network model, an information network model, and a two-way connection model. The distribution network model abstracts the substation distribution equipment as nodes and the branch connection lines as edges; the information network model abstracts the sensor communication equipment as nodes and the optical fibers as edges; based on the distribution network model and the information network model, the two-way connection model is a two-way network architecture and model in which power nodes provide energy flow to information nodes and information nodes provide information flow to power nodes;

[0008] Step 2: Generate a set of damaged scenarios of the distribution network under large-scale extreme disasters through the Monte Carlo simulation method, and establish a scenario basis for the state evolution of the distribution network within the current period to obtain the dataset required for statistical analysis;

[0009] Step 3: Establish an optimal load shedding model considering system resources such as distributed units and energy storage device systems. The model aims to minimize the system load shedding, takes into account the importance of loads, and considers the constraints of the distribution network, the information network, and the two-network coupling constraints;

[0010] Step 4: Use the Gurobi solver to solve the bidirectional dynamic model of the distribution network cyber-physical system and the optimal load shedding model, calculate the resilience evaluation index to quantitatively analyze the grid resilience, according to the node vulnerability reflected by the evaluation results, combined with the node importance, use TOPSIS analysis based on the entropy weight method to obtain the comprehensive coefficient, and solve the optimal load shedding model, and compare and analyze the system resilience before and after the weighted coefficient correction;

[0011] Step 5: To effectively guide the restoration problem of the distribution network cyber-physical system, use mobile emergency power supplies and mobile communication vehicles as controllable emergency power supplies for the power grid and local area emergency wireless communication for the information network respectively, conduct post-disaster maintenance on the distribution network cyber-physical system, and quantitatively analyze the resilience improvement effect with resilience indicators.

[0012] Furthermore, the bidirectional dynamic model of the distribution network cyber-physical system established in Step 1 based on complex network theory includes a distribution network model, an information network model, and a bidirectional connection model, which are specifically as follows:

[0013] The distribution network model abstracts substations, generator distribution equipment as nodes, and branch connection lines, circuit breakers as edges to characterize the distribution network. The distribution network node set , edge set and node adjacency matrix are as follows:

[0014] ;

[0015] ;

[0016] A P = [ A P , 1 , 1 A P , 1 , 2 ⋯ A P , 1 , N A P , 2 , 1 ⋱ ⋯ ⋮ ⋮ ⋮ ⋱ ⋮ A P , N , 1 ⋯ ⋯ A P , N , N ] ;

[0017] Among them, is the number of distribution network nodes; if there is an edge between node and node , then , otherwise it is 0; if and node and node If there is an edge between them, then , otherwise it is 0;

[0018] The information network model abstracts sensors, data storage devices, and communication devices as nodes, and cables and optical fibers as edges to characterize the information network. The information network node set , edge set and node adjacency matrix are as follows:

[0019] ;

[0020] ;

[0021] A C = [ A C , 1 , 1 A C , 1 , 2 ⋯ A C , 1 , M A C , 2 , 1 ⋱ ⋯ ⋮ ⋮ ⋮ ⋱ ⋮ A C , M , 1 ⋯ ⋯ A C , M , M ] ;

[0022] Among them, is the number of information network nodes; if there is an edge between node and node , then , otherwise it is 0; if and there is an edge between node and node , then , otherwise it is 0;

[0023] The support matrix for the power node to provide energy flow support to the information node is as follows:

[0024] V PC = [ V PC , 1 , 1 V PC , 1 , 2 ⋯ V PC , 1 , M V PC , 2 , 1 ⋱ ⋯ ⋮ ⋮ ⋮ ⋱ ⋮ V PC , N , 1 ⋯ ⋯ V PC , N , M ] ;

[0025] Among them, if the distribution network node can provide energy flow to the information network node , then , otherwise it is 0;

[0026] The support matrix for the information node to provide information flow support to the power node is as follows:

[0027] V CP = [ V CP , 1 , 1 V CP , 1 , 2 ⋯ V CP , 1 , N V CP , 2 , 1 ⋱ ⋯ ⋮ ⋮ ⋮ ⋱ ⋮ V CP , M , 1 ⋯ ⋯ V CP , M , N ] ;

[0028] Among them, if the information network node can provide information flow to the distribution network node , then , otherwise it is 0;

[0029] If the distribution network and the information network are bidirectionally coupled, then , if the two networks are not bidirectionally coupled, then and Determined separately according to the actual situation; further, this two-way connection model is: the topological matrix of the distribution network cyber-physical system:

[0030] V CPS = [ A P V PC V CP A C ] .

[0031] Furthermore, in step 2, a scenario basis for the state evolution of the distribution network in the current period is established, and the Monte Carlo simulation method generates a set of distribution network damage scenarios as follows:

[0032] Based on the known failure probabilities, the state of system components is determined by randomly sampling the probabilities of component states, and then all component states are combined to obtain the system state; without considering the mutual influence between component states, there is:

[0033] ;

[0034] where, represents the state of the th component; is the failure probability of the th component; is a random number uniformly distributed over ; for a system composed of components, its state vector is:

[0035] ;

[0036] Furthermore, in step 3, an optimal load shedding model considering the importance of loads is established, and the model objective is to minimize the system load shedding. The objective function is as follows:

[0037] ;

[0038] where, is the time index; is the total operating cost of the system; is the load shedding cost;

[0039] The load shedding cost is as follows:

[0040] ;

[0041] where, is the distribution network node index; is the set of devices connecting the nodes; is the unit load shedding penalty coefficient reflecting the importance of the load; is the load shedding power.

[0042] Further, in step 3, an optimal load shedding model considering the importance of load is established. The system contains distributed units and energy storage device resources. The model considers the constraints of the distribution network, the information network, and the coupling constraints between the two networks. The specific distribution network constraints are as follows:

[0043] Node power balance constraint:

[0044] ;

[0045] ;

[0046] ;

[0047] ;

[0048] Among them, is the set of all child nodes with node as the starting node; is the set of distribution network lines; and are respectively the active power and reactive power of the line with node as the starting node at time and are respectively the active power and reactive power of power line at time and are respectively the active power and reactive power transmitted from the superior power grid to the distribution network at time and are respectively the predicted values of the active load and reactive load at node at time is the magnitude of the active power of the load shed connected to system node at time, that is, the active load loss; and are respectively the active power output and reactive power output of the gas turbine unit at node at time and are respectively the active power output and reactive power output of the wind turbine unit at node at time and are respectively the charge and discharge power of the energy storage device at node at time and are respectively Time node The active power output and reactive power output of the mobile emergency power supply at the time node; and respectively represent the minimum and maximum values of the variable; binary variable represents the power line at time. If , it means that the line is not damaged and in a closed state, otherwise it means that the line is damaged or in an open state.

[0049] AC power flow constraint:

[0050] ;

[0051] ;

[0052] Among them, and are respectively the voltage of the time node and the node ; is the reference node voltage; is the line resistance; is the line reactance, is a sufficiently large number;

[0053] Load shedding upper and lower limit constraint:

[0054] ;

[0055] Distributed gas turbine unit constraint:

[0056] ;

[0057] ;

[0058] ;

[0059] ;

[0060] ;

[0061] ;

[0062] ;

[0063] ;

[0064] Among them, and are the minimum and maximum outputs of the gas turbine unit at node ; the binary variable represents the operating state of the gas turbine unit at node at time . If , it means the gas turbine unit starts at time , otherwise it means shutdown; and are the upward and downward ramp rates of the gas turbine unit respectively; and are the start-up and shutdown counting times of the gas turbine unit at time respectively; and are the minimum start-up and shutdown times of the unit at node respectively; and are the heat consumptions for starting and stopping the unit once respectively;

[0065] Distributed wind turbine unit constraints:

[0066] ;

[0067] ;

[0068] where is the predicted output of the wind turbine unit at node at time ; and are the minimum and maximum reactive power outputs of the wind turbine unit at node respectively;

[0069] Energy storage constraints:

[0070] ;

[0071] ;

[0072] ;

[0073] ;

[0074] ;

[0075] where the binary variables and represent the charge and discharge states of the energy storage device at node at time respectively; and are respectively Time node The charging and discharging power of energy storage at the location; and are respectively the minimum and maximum values of the charging of the energy storage device at node ; and are respectively the minimum and maximum values of the discharging of the energy storage device at node ; is the energy storage capacity at the time node ; and are respectively the minimum and maximum values of the energy storage at node ; and are respectively the charging and discharging efficiencies of the energy storage device;

[0076] Topological constraints:

[0077] ;

[0078] ;

[0079] ;

[0080] Among them, is the total number of nodes in the distribution network; the binary variable indicates whether node is the root node. If , then node is the root node, otherwise it is not; and are respectively the active powers of the virtual branches with node as the receiving end and the sending end;

[0081] Furthermore, in step 3, an optimal load shedding model considering the importance of loads is established. The system contains distributed units and energy storage device resources. The model considers distribution network constraints, information network constraints, and two-network coupling constraints. Among them, the information network constraints are specifically as follows:

[0082] Node flow balance constraint:

[0083] ;

[0084] Among them, is the node set of the information network; is the communication node index; is the communication source node index; is the fiber optic communication link index; and respectively represent the information link The sender and receiver; Is the node index for configuring the wireless communication vehicle; And Respectively represent the sender and receiver of the wireless communication link ; Is the information flow on the source node; Is the information flow on the information link; Indicates whether the communication node is connected to the control master station. If , it means At time, the communication node Is connected to the control master station, otherwise it is not; Represents the information flow of wireless communication; the number 1 represents the requirements of each node;

[0085] Communication link availability constraint:

[0086] ;

[0087] ;

[0088] ;

[0089] Among them, Is the total number of communication nodes in the information network; Indicates whether the communication link is available. If , it means the communication link fails, otherwise it means the communication link is normal.

[0090] Furthermore, in step 3, an optimal load shedding model considering the importance of load is established. The system contains distributed units and energy storage device resources. The model considers distribution network constraints, information network constraints, and two-network coupling constraints. The two-network coupling constraints are specifically as follows:

[0091] Distributed unit coupling constraint:

[0092] ;

[0093] ;

[0094] ;

[0095] ;

[0096] Among them, And Are respectively the control states of the corresponding communication nodes for the gas turbine unit and wind turbine unit in the distribution network; Represents the information requirements of the communication node for controlling the gas turbine unit or wind turbine unit. If , it means The momentary communication node is connected to the control master station. The corresponding unit control status variable value is 1, indicating that the unit is in a controllable state; otherwise, it is uncontrollable.

[0097] Energy storage device coupling constraint:

[0098] ;

[0099] ;

[0100] ;

[0101] Among them, is the control status of the corresponding communication node for charging and discharging the distribution network energy storage device; represents the information requirement of the communication node for controlling the energy storage device. If , it means The momentary communication node is connected to the control master station. The corresponding energy storage control status variable value is 1, indicating controllability; otherwise, it is uncontrollable.

[0102] Furthermore, the resilience evaluation index established in step 4 is as follows:

[0103] Load shedding probability :

[0104] ;

[0105] Among them, is the number of Monte Carlo simulation sampling times; is the node The number of samples of load shedding occurring within the research period;

[0106] Average node load loss level :

[0107] ;

[0108] Among them, is the set of all nodes in the distribution network; is The magnitude of the active power of the load cut off connected to the system node at time, that is, the active load loss.

[0109] Furthermore, according to the node vulnerability reflected by the evaluation results in step 4, the TOPSIS analysis based on the entropy weight method is used to correct the weighting coefficient. The steps of the TOPSIS analysis based on the entropy weight method are specifically:

[0110] Step 4.1: The TOPSIS model generally operates based on all indicators being of the extremely large type. Therefore, first determine the type of each indicator and perform data positive transformation according to the indicator type; the probability of load shedding and the average load shedding level are both of the extremely large type. The larger their values, the higher the vulnerability of the load node. Prioritizing the protection of nodes with high vulnerability helps reduce the degree of system damage; while the load shedding penalty coefficient based on load classification , which reflects whether the impact on social life caused by the abnormality of this node is significant, is also of the extremely large type. Vulnerability and load shedding penalty coefficient comprehensively represent the importance of the node in the system. The matrix obtained after data positive transformation is denoted as the positive transformation matrix :

[0111] X = [ x 1 , 1 x 2 , 1 ⋮ x 32 , 1 x 1 , 2 x 2 , 2 ⋮ x 32 , 2 x 1 , 3 x 2 , 3 ⋮ x 32 , 3 ] ;

[0112] Step 4.2: Since the dimensions of the indicators are different, standardize to eliminate the influence of dimensions so that different indicators can be compared and analyzed on the same scale; establish the standardized matrix , each element in

[0113] ;

[0114] Step 4.3: Calculate the proportion of the th indicator occupied by the st sample, and regard it as the probability used in the relative entropy calculation. The matrix formed by the above probabilities is denoted as the probability matrix , ;

[0115] Step 4.4: Assume that represents a certain situation in which the event may occur, represents the probability of this situation occurring, and define . Because , so ; if the possible situations of the event are respectively , define the information entropy of the event as , and its calculation formula is H ( x ) = ∑ i = 1 n [ p ( x i ) I ( x i )] =− ∑ i = 1 n [ p ( x i )ln( p ( x i ))] . The essence of information entropy is the expected value of the amount of information; when , takes the maximum value. At this time, . In order to make the information entropy fall within the [ 0 , 1 ] interval, take Divided by ; Then for the th index, the calculation formula of information entropy is , Since there may be values of 0 in the probability matrix, set to 0;

[0116] Step 4.5: Calculate the information utility value ; The information utility value reflects the discrimination ability of the index, that is, the greater the information utility value, the stronger the discrimination ability of the index, the more information it carries, and the greater the contribution to the comprehensive evaluation. Therefore, its weight is also greater; According to the formula, it can also be known that the information entropy is greater, indicating that the th index has less information;

[0117] Step 4.6: Normalize the information utility value and calculate the entropy weight of each index ;

[0118] Step 4.7: Define the maximum value and the minimum value corresponding to each index, that is , , , Define the distance between the th node and the maximum value, and the distance from the minimum value, where is an element of the standardized matrix;

[0119] Step 4.8: Calculate the scores before and after normalization; When not normalized, the score of the th node is , and the larger the smaller, that is, the closer to the maximum value, the higher the score of the node importance; To eliminate the influence of different dimensions and numerical ranges, ensure the fairness and comparability of each index in the decision-making, and improve the accuracy of the calculation and the robustness of the model, normalize the score .

[0120] Furthermore, in step 5, the mobile emergency power supply and the mobile communication vehicle are respectively used as the controllable emergency power supply of the power grid and the local area emergency wireless communication of the information network. The constraints satisfied by the two emergency resources are specifically as follows:

[0121] Mobile emergency power supply constraint:

[0122] ;

[0123] ;

[0124] ;

[0125] Among them, and are respectively the active power output and reactive power output of the mobile emergency power supply at the time node ; and are the upper limits of the output of the mobile emergency power supply at node ; the binary variable indicates the configuration status of the mobile emergency power supply at the time node ; is the number of mobile emergency power supplies in the distribution network;

[0126] Constraints of mobile emergency communication vehicles:

[0127] ;

[0128] ;

[0129] Among them, is the total number of communication nodes in the information network; indicates whether a mobile emergency communication vehicle is configured at node , if it means there is a configuration, otherwise there is no configuration; represents the information flow of wireless communication; is the number of emergency communication vehicles equipped in the information network.

[0130] The beneficial effects of the present invention are:

[0131] (1) By using the Monte Carlo simulation method to randomly generate fault scenarios, the subjectivity and particularity of artificially setting fault situations are avoided, and the overall distribution of statistical data is fully reflected by generating a large number of scenarios;

[0132] (2) The proposed optimal load shedding model takes into account that the impact of power outages that may be caused by extreme weather on the public is difficult to fully measure by economic losses, aims to minimize the system load shedding, and the resilience evaluation index focuses on studying the load loss of the power system under extreme disasters;

[0133] (3) The cyber-physical system of the distribution network is configured with distributed units and energy storage devices, and can call mobile emergency power supplies and mobile communication vehicles, which conforms to the current world energy transformation and the development trend of the diversification of power system configurations in China, and provides a solution for building a safe and stable new power system;

[0134] (4) The method for improving resilience considers the load priority, introduces the load shedding penalty coefficient as the weight coefficient of the power grid load, characterizes the importance of the load, gives priority to meeting the power supply requirements of important loads, and reduces the amount of important load shedding in the power system;

[0135] (5) Based on the TOPSIS analysis of the entropy weight method, the entropy weight method calculates the entropy values of each index, assigns weights to the three vulnerability indexes and the original load shedding penalty coefficient, and obtains the corrected comprehensive importance score, reducing the deviation of subjective weight assignment and making the weight distribution more objective. In the face of uncertainty and incomplete information, the TOPSIS model based on the entropy weight method can provide relatively stable and reliable decision-making support;

[0136] (6) By optimizing the dispatch of controllable resources in the cyber-physical system of the distribution network under extreme disasters, the problem of serious losses caused by extreme weather to the distribution network is solved, and the resilience of the distribution network to extreme disasters is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0137] Figure 1 It is a flow schematic diagram of a method for evaluating the resilience of a cyber-physical system of a distribution network under extreme disasters and improving multi-source coordinated resilience according to the present invention;

[0138] Figure 2 It is a performance change curve diagram of the distribution network under extreme disasters according to the present invention;

[0139] Figure 3 It is a calculation flow chart of the TOPSIS analysis based on the entropy weight method according to the present invention;

[0140] Figure 4 It is the distribution of the load node weights of the distribution network before and after correction according to the present invention;

[0141] Figure 5 It is a topology diagram of the cyber-physical system of the distribution network according to an embodiment of the present invention;

[0142] Figure 6 It is a curve diagram of the predicted demand for active power load and reactive power load of the system in Case 1 according to the present invention;

[0143] Figure 7 It is a diagram of the output of the mobile emergency power supply within the dispatching period in Case 4 according to the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0144] Next, the technical solutions of the present invention will be clearly and completely described in conjunction with the embodiments. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0145] Power system resilience is proposed and applied as a concept to measure the resistance and recovery ability of the power grid after being severely disturbed. When faults such as line disconnection or loss of generating units occur under extreme weather, if the generating capacity of the remaining units can be redistributed to meet the system load supply and line constraint conditions, then the distribution network does not need to shed load at this time. Otherwise, the system fails and some loads must be reduced, and the output of the remaining units and the power supply of equipment are adjusted according to the importance of the loads to minimize the system loss in the fault state, and the line power flow will be redistributed at this time. The coupling of the information network increases the safe operation risk of the distribution network cyber-physical system, and large-scale unexpected faults are likely to occur under the huge destructive power of extreme disasters, leading to a power supply crisis. At the same time, the damage of the communication system will affect the monitoring and control effect of the power grid, and the maintenance of the communication network helps to obtain the information of the distribution network and better control the power equipment. Therefore, the problems of security risks and lack of coordinated scheduling mechanism brought about by the deep coupling between the power system and the communication system need to be solved urgently.

[0146] The present invention is based on the construction of a resilience evaluation method and a multi-source coordinated optimization scheduling model for a distribution network cyber-physical system. Figure 1 For the specific implementation flowchart of the method, as Figure 1 shown, different from directly controlling power equipment without considering the damage of the communication system in the traditional way, the present invention makes full use of resources such as distributed units, energy storage devices, mobile emergency power supplies, and mobile communication vehicles to jointly maintain information for the power and communication coupling network, comprehensively improve the system resilience, and the construction method includes the following steps:

[0147] Step 1: Establish a two-way dynamic model of the distribution network cyber-physical system based on complex network theory. Specifically, it is a distribution network model with distribution equipment such as substations and generating units as nodes and branch connection lines, circuit breakers, etc. as edges; an information network model with communication equipment such as sensors and data storage devices as nodes and cables, optical fibers, etc. as edges; including a two-way connection network architecture and model in which the power node provides an energy flow to the information node and the information node provides an information flow to the power node.

[0148] The distribution network model is as follows:

[0149] Abstract the distribution equipment such as substations and generating units as nodes, and abstract the branch connection lines, circuit breakers, etc. as edges to characterize the distribution network. The distribution network node set , edge set and node adjacency matrix are as follows:

[0150] ;

[0151] ;

[0152] A P = [ A P , 1 , 1 A P , 1 , 2 ⋯ A P , 1 , N A P , 2 , 1 ⋱ ⋯ ⋮ ⋮ ⋮ ⋱ ⋮ A P , N , 1 ⋯ ⋯ A P , N , N ] ;

[0153] Among them, is the number of nodes in the distribution network; if there is a connection edge between node and node , then , otherwise it is 0; if and there is a connection edge between node and node , then , otherwise it is 0.

[0154] The information network model is as follows:

[0155] Abstract communication devices such as sensors and data storage devices as nodes, and abstract cables, optical fibers, etc. as connection edges to characterize the information network. The information network node set , connection edge set and node adjacency matrix are as follows:

[0156] ;

[0157] ;

[0158] A C = [ A C , 1 , 1 A C , 1 , 2 ⋯ A C , 1 , M A C , 2 , 1 ⋱ ⋯ ⋮ ⋮ ⋮ ⋱ ⋮ A C , M , 1 ⋯ ⋯ A C , M , M ] ;

[0159] Among them, is the number of nodes in the information network; if there is a connection edge between node and node , then , otherwise it is 0; if and there is a connection edge between node and node , then , otherwise it is 0.

[0160] The two-way connection network model is as follows:

[0161] The two-way connection between the distribution network and the information network is reflected in that various monitoring and control devices of the power system rely on the communication system to transmit real-time data, that is, information nodes provide information flow to power nodes; at the same time, the communication system requires the power provided by the power system to maintain operation, that is, power nodes provide energy flow to information nodes.

[0162] The support matrix for power nodes to provide energy flow to information nodes is as follows:

[0163] V PC = [ V PC , 1 , 1 V PC , 1 , 2 ⋯ V PC , 1 , M V PC , 2 , 1 ⋱ ⋯ ⋮ ⋮ ⋮ ⋱ ⋮ V PC , N , 1 ⋯ ⋯ V PC , N , M ] ;

[0164] Among them, if a distribution network node can provide an energy flow to an information network node , then , otherwise it is 0.

[0165] The support matrix for the information node to provide an information flow to the power node is as follows:

[0166] V CP = [ V CP , 1 , 1 V CP , 1 , 2 ⋯ V CP , 1 , N V CP , 2 , 1 ⋱ ⋯ ⋮ ⋮ ⋮ ⋱ ⋮ V CP , M , 1 ⋯ ⋯ V CP , M , N ] ;

[0167] Among them, if an information network node can provide an information flow to a distribution network node , then , otherwise it is 0.

[0168] If the distribution network and the information network are bidirectionally coupled, then , if the two networks are not bidirectionally coupled, then and are determined according to the actual situation respectively. Further, the topology matrix of the distribution network cyber-physical system is as follows:

[0169] V CPS = [ A P V PC V CP A C ] ;

[0170] Step 2: Generate a set of damaged scenarios of the distribution network under large-scale extreme disasters through the Monte Carlo simulation method, and establish the scenario basis for the state evolution of the distribution network in the current period to obtain the data volume required for statistical analysis.

[0171] The set of damaged scenarios of the distribution network generated by the Monte Carlo simulation method is as follows:

[0172] Based on the known failure probabilities, the states of system components are determined by randomly sampling the probabilities of component states, and then the states of all components are combined to obtain the system state. Without considering the mutual influence between component states, there is:

[0173] ;

[0174] Among them, represents the state of the th component; is the failure probability of the th component; is a random number obeying uniform distribution.

[0175] For a system composed of components, its state vector is:

[0176] .

[0177] Step 3: Establish an optimal load shedding model considering system resources such as distributed units and energy storage devices. The model aims to minimize system load shedding, takes into account the importance of loads, and considers distribution network constraints, information network constraints, and the coupling constraints between the two networks.

[0178] The system load shedding cost is calculated by setting a load shedding penalty coefficient and representing the load priority with a weight coefficient to prioritize the power supply requirements of important loads. Adjust the resource allocation to minimize the total system load shedding cost, improve system resilience, and the optimization objective function is as follows:

[0179] ;

[0180] where is the time index; is the total operating cost of the system; is the load shedding cost.

[0181] Load shedding cost is as follows:

[0182] ;

[0183] where is the distribution network node index; is the set of devices connecting nodes; is the unit load shedding penalty coefficient; is the load shedding power.

[0184] The constraint conditions are considered from the perspectives of the distribution network, information network, and the coupling between the two networks. In terms of the distribution network, they include node power balance constraints, AC power flow constraints, load shedding upper and lower limits constraints, distributed unit constraints, energy storage constraints, and topology constraints; in terms of the information network, they include node flow balance constraints and communication link availability constraints; in terms of the coupling between the two networks, they include distributed unit coupling constraints and energy storage device coupling constraints.

[0185] Node power balance constraint:

[0186] ;

[0187] ;

[0188] ;

[0189] ;

[0190] where is the set of all child nodes starting from node ; is the line set of the distribution network; and are respectively the active power and reactive power of the line starting from node at a certain moment; and are respectively the active power and reactive power of the power line at a certain moment; and are respectively the active power and reactive power transmitted from the superior power grid to the distribution network at a certain moment; and are respectively the predicted values of the active load and reactive load at the position of node at a certain moment; is the magnitude of the active power of the load cut off at the load connected to the system node at a certain moment, that is, the active load loss; and are respectively the active power output and reactive power output of the gas turbine unit at node at a certain moment; and are respectively the active power output and reactive power output of the wind turbine unit at node at a certain moment; and are respectively the charge and discharge power of the energy storage device at node at a certain moment; and are respectively the active power output and reactive power output of the mobile emergency power supply at node at a certain moment; and respectively represent the minimum and maximum values of the variable; the binary variable represents the state of the power line at a certain moment. If , it means that the line is not damaged and is in the closed state, otherwise it means that the line is damaged or in the open state.

[0191] AC power flow constraint:

[0192] ;

[0193] ;

[0194] Among them, and are respectively Time node And node voltage; Is the reference node voltage; Is the line resistance; Is the line reactance, Is a sufficiently large number.

[0195] Load shedding upper and lower limit constraints:

[0196] ;

[0197] Distributed gas unit constraints:

[0198] ;

[0199] ;

[0200] ;

[0201] ;

[0202] ;

[0203] ;

[0204] ;

[0205] ;

[0206] Among them, And Are respectively the minimum and maximum outputs of the gas unit at node ; The binary variable Indicates the working state of the gas unit at node At time . If , it means the gas unit starts at time , otherwise it means shutdown; And Are respectively the upper and lower ramp rates of the gas unit ; And Are respectively the start-up and shutdown counting times of the gas unit at time ; And Are respectively the minimum start-up and shutdown times of the unit at node ; And Are respectively the heat consumed for starting and shutting down the unit once.

[0207] Distributed wind turbine constraints:

[0208] ;

[0209] ;

[0210] Among them, is the predicted output of the wind turbine at time node ; and are respectively the minimum and maximum reactive power outputs of the wind turbine at node .

[0211] Energy storage constraints:

[0212] ;

[0213] ;

[0214] ;

[0215] ;

[0216] ;

[0217] Among them, the binary variables and respectively represent the charge and discharge states of the energy storage device at time node ; and are respectively the charge and discharge powers of the energy storage at time node ; and are respectively the minimum and maximum values of the energy storage device charging at node ; and are respectively the minimum and maximum values of the energy storage device discharging at node ; is the capacity of the energy storage at time node ; and are respectively the minimum and maximum values of the energy storage at node ; and are respectively the charge and discharge efficiencies of the energy storage device.

[0218] Topological constraints:

[0219] ;

[0220] ;

[0221] ;

[0222] Among them, is the total number of nodes in the distribution network; the binary variable indicates whether node is a root node. If , then node is a root node; otherwise, it is not; and are the active powers of the virtual branches with node as the receiving end and the sending end, respectively.

[0223] Node flow balance constraint:

[0224] ;

[0225] Among them, is the node set of the information network; is the communication node index; is the communication source node index; is the fiber optic communication link index; and represent the sending end and the receiving end of the information link , respectively; is the node index for configuring the wireless communication vehicle; and represent the sending end and the receiving end of the wireless communication link , respectively; is the information flow on the source node; is the information flow on the information link; indicates whether the communication node is connected to the control master station. If , it means that at time the communication node is connected to the control master station; otherwise, it is not; represents the information flow of the wireless communication; the number 1 represents the demand of each node.

[0226] Communication link availability constraint:

[0227] ;

[0228] ;

[0229] ;

[0230] Among them, is the total number of communication nodes in the information network; Indicates whether the communication link is available. If , it indicates that the communication link fails; otherwise, it indicates that the communication link is normal.

[0231] Distributed unit coupling constraints:

[0232] ;

[0233] ;

[0234] ;

[0235] ;

[0236] Among them, and are the control states of the corresponding communication nodes for the gas units and wind turbine units in the distribution network respectively; Indicates the information requirements of the communication node for controlling the gas unit or wind turbine unit. If , it indicates that At the moment, the communication node is connected to the control master station, and the corresponding unit control state variable value is 1, that is, the unit is in a controllable state; otherwise, it is uncontrollable.

[0237] Energy storage device coupling constraints:

[0238] ;

[0239] ;

[0240] ;

[0241] Among them, is the control state of the corresponding communication node for charging and discharging the energy storage device in the distribution network; Indicates the information requirements of the communication node for controlling the energy storage device. If , it indicates that At the moment, the communication node is connected to the control master station, and the corresponding energy storage control state variable value is 1, that is, it is controllable; otherwise, it is uncontrollable.

[0242] Step 4: Use the Gurobi solver to solve the two-way dynamic model and the optimal load shedding model of the distribution network cyber-physical system, calculate the resilience evaluation index to quantitatively analyze the grid resilience, and according to the node vulnerability reflected by the evaluation result, combined with the node importance, use TOPSIS analysis based on the entropy weight method to obtain the comprehensive coefficient, and solve the optimal load shedding model to compare and analyze the system resilience before and after the weighted coefficient correction.

[0243] The resilience evaluation index is as follows:

[0244] After extreme disasters occur, it is very likely that mass failures will occur in the distribution network, which will lead to large-scale power outages, and the system performance will drop sharply. During the development of the disaster, the system enters a derated operation state. As the impact of extreme disasters decreases, the system enters the repair state and gradually returns to its original normal operation state. As shown in Figure 2 the "resilience trapezoid" can be used to reflect the performance changes of the power system when it is affected by extreme disasters. Therefore, in addition to failures caused by the direct impact of extreme disasters on system components themselves, indirect damage caused by mass failures may also occur. Define the frequency of load shedding at a node in the Monte Carlo simulation as the load shedding probability :

[0245] ;

[0246] where is the number of sampling times in the Monte Carlo simulation; is the node the number of samples of load shedding that occur at node

[0247] For two nodes with the same total load loss, due to the significant difference in the number of load losses, the amount of load loss per time may be significantly different, that is, the degree of impact on the stable operation of the system once the node is abnormal is different, and the node resilience level is different. Therefore, for the total load loss of the node, it is necessary to calculate the average value according to the number of load shedding times in all Monte Carlo simulations to calculate the average load loss level of each node :

[0248] ;

[0249] where is the set of all nodes in the distribution network; is the active power of the load cut off at the system node at time

[0250] Resilience assessment helps to identify the vulnerable links and potential risks of the system, providing a scientific basis and direction for decision-makers to prioritize the handling of the most critical risks and vulnerabilities to improve the overall resilience of the system. During the post-disaster recovery stage, it is necessary to focus on ensuring the power supply of important loads such as hospitals and government agencies. For this reason, each node is assigned a weight according to its importance, defined as the unit load shedding penalty coefficient and then combined with the above two resilience indicators reflecting node vulnerability to obtain a new weighted coefficient.

[0251] In a cyber-physical system, the power grid and the information network are interdependent and interact with each other. Faults in information lines and equipment lead to changes in network topology, which may cause information transmission delays and losses, disrupt the normal monitoring of power equipment, and thus plunge into a "blind regulation" state. Abnormalities in the power grid will also interfere with the stable operation of the information network. Therefore, the controllability of the information network, that is, whether the information nodes are connected to the control center, affects the system resilience to a certain extent.

[0252] The present invention uses TOPSIS analysis based on the entropy weight method to correct the weighted coefficient, obtains a comprehensive index from the node load shedding probability, average load shedding level, and unit load shedding penalty coefficient, and corrects the weighted coefficient according to the analysis process as Figure 3 shown.

[0253] The TOPSIS analysis based on the entropy weight method obtains a comprehensive coefficient, and the specific steps are as follows:

[0254] First of all, the TOPSIS model generally operates on the basis that all indicators are extremely large indicators. Therefore, first judge the type of each indicator and perform data positive normalization according to the indicator type. The load shedding probability and the average load shedding level are both extremely large indicators. The larger the value, the higher the vulnerability of the node. Prioritizing the protection of nodes with high vulnerability is conducive to reducing the degree of system damage; while the load shedding penalty coefficient based on load classification , which reflects whether the impact on social life caused by the abnormality of the node is significant, is also an extremely large indicator. The vulnerability and the load shedding penalty coefficient comprehensively characterize the importance of the node in the system. The matrix obtained after data positive normalization is denoted as the positive normalization matrix :

[0255] X = [ x 1 , 1 x 2 , 1 ⋮ x 32 , 1 x 1 , 2 x 2 , 2 ⋮ x 32 , 2 x 1 , 3 x 2 , 3 ⋮ x 32 , 3 ] ;

[0256] Since the dimensions of the indicators are different, standardization is performed to eliminate the influence of dimensions so that different indicators can be compared and analyzed on the same scale. Establish a standardized matrix , each element in which is ;

[0257] Secondly, calculate the proportion of the th indicator for the th sample, and regard it as the probability used in the relative entropy calculation. The matrix formed by the above probabilities is denoted as the probability matrix , ;

[0258] Suppose represents the event A certain situation that may occur represents the probability of this situation occurring and is defined as because so . If the possible situations of event are respectively , define the information entropy of event as , and its calculation formula is H ( x ) = ∑ i = 1 n [ p ( x i ) I ( x i )] =− ∑ i = 1 n [ p ( x i )ln( p ( x i ))] . The essence of information entropy is the expected value of the amount of information. When , takes the maximum value. At this time . In order to make the information entropy lie in the [ 0 , 1 ] interval, divide by . Then for the th item of the index, the calculation formula of information entropy is . Since there may be values of 0 in the probability matrix, set to 0;

[0259] Next, calculate the information utility value . The information utility value reflects the discrimination ability of the index, that is, the larger the information utility value, the stronger the discrimination ability of the index, the more information it carries, and the greater the contribution to the comprehensive evaluation. Therefore, its weight is also larger. According to the formula, it can also be known that the information entropy is larger, indicating that the information of the th item of the index is less;

[0260] Then, normalize the information utility value and calculate the entropy weight of each index ;

[0261] Define the maximum value and the minimum value corresponding to each index, that is , , . Define the distance of the th node from the maximum value, and the distance from the minimum value, where is the element of the standardized matrix;

[0262] Finally, calculate the scores before and after normalization. When not normalized, the score of the th node, and , The larger The smaller it is, that is, the closer it is to the maximum value, the higher the node importance score. To eliminate the influence of different dimensions and numerical ranges, ensure the fairness and comparability of each index in decision-making, and improve the accuracy of calculation and the robustness of the model, the scores are normalized: .

[0263] Step 5: To effectively guide the restoration of the cyber-physical power distribution system, the mobile emergency power supply and the mobile communication vehicle are respectively used as the controllable emergency power supply of the power grid and the local area emergency wireless communication of the information network to carry out post-disaster maintenance on the cyber-physical power distribution system, and the resilience improvement effect is quantified by the resilience index.

[0264] The mobile emergency power supply is a reliable controllable power supply for the power distribution network. After the system is affected by extreme disasters, it can be used as a backup power supply to reduce load shedding. The output constraints and configuration state constraints to be satisfied are as follows:

[0265]

[0266]

[0267]

[0268] Among them, and are respectively the active power output and reactive power output of the mobile emergency power supply at node at time and are the upper limits of the output of the mobile emergency power supply at node ; the binary variable represents the configuration state of the mobile emergency power supply at node at time is the number of mobile emergency power supplies in the power distribution network.

[0269] The mobile emergency communication vehicle can help restore communication, enabling adjacent nodes to communicate wirelessly, thereby helping the power network to mobilize distributed units and energy storage devices earlier to accelerate the restoration of load demand and reduce overall losses. The information constraints and configuration state constraints to be satisfied are as follows:

[0270]

[0271]

[0272] Among them, is the total number of communication nodes in the information network; represents whether a mobile emergency communication vehicle is configured at node , if It indicates that there is a configuration, and vice versa if there is no configuration; It represents the information flow of wireless communication; It is the number of emergency communication vehicles equipped in the information network.

[0273] From the perspective of the overall system, by integrating the load curve in Figure 2 the system resilience index is defined as the ratio of the area between the actual load curve and the time axis to the area between the expected load curve and the time axis, reflecting the level of overall load loss of the system:

[0274]

[0275] Among them, is the mathematical expectation; is the research period; is the system operation curve under normal conditions; is the system operation curve under extreme disasters.

[0276] Set the same scenario set, and solve and calculate the load shedding loss of the distribution network in the cyber-physical system with different configurations, that is, whether it contains mobile emergency power sources and mobile emergency communication vehicles, so as to measure the effectiveness of the resilience improvement method.

[0277] Example:

[0278] Based on the IEEE33-node network, by investigating historical data, assuming that the line fault probability under extreme disasters is , the fault line is likely to cause insufficient load supply to its adjacent nodes. Due to the close connection within the system, cascading faults are likely to spread in the network and expand the fault range. Therefore, the abnormality of the front-end nodes will also threaten the normal operation of the back-end nodes. Set the number of sampling times to 1000 times, and use the Monte Carlo simulation method based on random sampling to generate a series of scenarios to simulate the damage situation of the distribution network under extreme disasters. Taking the minimization of the sum of weighted load shedding of the system as the goal, solve the optimal load shedding model, and conduct a resilience assessment of the distribution network according to the statistical data results. The assessment results are shown in Table 1. Note that for the distribution network nodes 6 and 12 equipped with gas turbines, their load shedding probabilities are lower than those of other nodes.

[0279] Table 1. Resilience assessment results under the original load weight coefficient

[0280]

[0281] The results of the resilience assessment reflect the vulnerability of the nodes. It is considered that when different load nodes are affected under the same external conditions, the nodes with a greater possibility and degree of being affected have a higher vulnerability, and vice versa. Combining the results of the vulnerability analysis, the originally set load weight coefficients are corrected to obtain a new comprehensive load index. The index matrix is processed by TOPSIS analysis based on the entropy weight method to solve and determine the weights of each index, as shown in Table 2. To eliminate the influence of different dimensions and value ranges, ensure the fairness and comparability of each index in the decision-making, and improve the calculation accuracy and the robustness of the model, the scores are normalized, and the scores of each node are shown in Table 3. Before and after the correction of the weighting coefficient, that is, the comparison of the unit load shedding penalty coefficient and the comprehensive coefficient that only reflects the importance is as Figure 4 shown. To visually display the differences between the two coefficients, they have been processed into [ 0 . 1 , 1 ] values within the range. For the load nodes with a higher comprehensive index, such as nodes 24, 25, and 32, it shows that these nodes play a greater role in ensuring the stability of social life and reducing the system load shedding. Corresponding reinforcement and operation and maintenance measures need to be taken when necessary.

[0282] Table 2. Weights of evaluation indicators

[0283]

[0284] Table 3. TOPSIS evaluation results

[0285]

[0286] After the weighting coefficient of the load importance is corrected, the failure scenario set generated by the Monte Carlo simulation is used as the initial scenario again to solve the optimal load shedding model. The original weight coefficient of the load classification is multiplied by the load shedding of the corresponding node to obtain the system weighted load shedding that can reflect the level of ensuring important loads. The comparison of the total system load shedding before and after the correction is shown in Table 4. Without using any emergency resources, the average system load shedding is reduced by , and the load shedding amount of important loads is reduced. It shows that taking proactive preventive measures such as reinforcement for the nodes with high scores before extreme events can improve the overall resilience of the system.

[0287] Table 4. Comparison of the average system load shedding and the total load shedding weighted by the important coefficient before and after the coefficient correction

[0288]

[0289] Using the improved IEEE33-node distribution network model, the parameters and locations of various power sources and the coupling relationships between the distribution network and the information network corresponding to the equipment are shown in Table 5. The coupling with the 21-node information network is as Figure 5 shown. The dotted lines in the figure represent the coupling relationships between the power system and the communication system.

[0290] Table 5. Power supply parameters of various types and their corresponding coupling relationships between the distribution network and the information network

[0291]

[0292] Extreme disasters attack both the distribution network and the information network. Assume that the faulty lines of the distribution network are 、 、 、 、 and at the lines, and the faulty lines of the information network are 、 、 、 、 and at the lines. The specific distribution is as shown in Figure 5 and the active and reactive load demand curves of the system are as shown in Figure 6 .

[0293] To study the damage situation and resilience level of the cyber-physical system of the distribution network under extreme disasters and verify the feasibility of the resilience improvement scheme, 4 case scenarios are established as shown in Table 6. The elements considered in the cases are indicated by √, and vice versa by ×. Specifically, Case 1 is the basic scenario without taking any measures; Case 2 considers the vulnerability degree of nodes combined with the importance degree of loads as a comprehensive index to provide a reference for taking active preventive measures such as strengthening the grid construction before the disaster; Case 3 uses a mobile communication vehicle as a local emergency wireless communication; Case 4 adds a mobile power vehicle as an emergency power source. Both Case 3 and Case 4 are emergency recoveries after the failure occurs. Cases 2-4 divide the resilience improvement into two situations: pre-disaster prevention and post-disaster recovery from the time perspective, and the elements considered in the post-disaster recovery increase from less to more in order to study the effects of various emergency resources on improving the system operation state.

[0294] Table 6. Elements considered in each case scenario

[0295]

[0296] Considering different emergency resource elements, in the disaster scenario where both the above-mentioned power lines and information lines are damaged, the optimal load shedding scheme is solved. Table 7 shows the comparison of the total load shedding of the system, the average value of the total load shedding weighted by the importance coefficient, and the system resilience for Cases 1-4.

[0297] Table 7. Comparison of the load loss situation and resilience of the system for Cases 1-4

[0298]

[0299] Analysis of Example 1 shows that if nodes with high vulnerability are not concerned about before the disaster and no measures are taken after the fault, the damaged communication nodes will not be able to regulate the corresponding distributed units and energy storage devices in the distribution network. The degree of system restoration is limited and it is difficult to support the operation requirements of the system after extreme disasters. The average load shedding of the system within the scheduling period reaches . If nodes with relatively high comprehensive indicators can be evaluated before the disaster and corresponding measures are taken, the load shedding of the system will be reduced and the resilience level will be improved.

[0300] On the basis of Example 1, Example 3 considers the use of mobile communication vehicles. The closer the information network node is to the control center, the wider its affected communication range and the more important it is for the restoration of the faulty system. Two mobile communication vehicles are configured at information network nodes 3 and 14. After the fault occurs, the mobile communication vehicle located at communication node 3 helps to restore local communication, and wireless communication can be realized between nodes 2, 3, 4 and 19; the wireless communication vehicle located at communication node 14 helps to restore the communication between nodes 1 and 14. Since the communication network is a ring network structure, all nodes in the network quickly restore communication requirements, enabling the distributed units and energy storage devices in the power network to be in a controllable state and able to adjust their working states according to the actual situation to respond to load demands, reducing load losses.

[0301] The mobile emergency power supply is a flexible emergency power supply and is often used as a stable and reliable backup power supply during extreme disasters to reduce the operation losses of the system. Considering that the load nodes at the end of the line are the farthest from the power source, the line between them is the longest, and the probability of failure is the highest. At the same time, it can also be seen from the resilience evaluation results that the load shedding probability of nodes 30 - 33 is the highest. Therefore, in Example 4, mobile power vehicles are added at distribution network nodes 22 and 33, which can be flexibly regulated according to the actual load demand. The active power output change curve within the scheduling period is as Figure 7 shown, and the system resilience is significantly improved, further improving the system operation.

[0302] Aiming at problems such as the challenge of the distribution network resisting disaster disturbances under extreme weather, the present invention is based on the cyber - physical system of the distribution network. By establishing a coordinated optimization scheduling model containing multiple power sources, minimizing the system load shedding considering the coupling of the information network, and meeting the power consumption needs of important loads in combination with the load priority, the reduction of the removal of important loads in the system is promoted. Through case analysis using the relevant data of the power network and the communication network, it is found that considering the coupling of the information network and using resources such as mobile emergency power supplies and communication vehicles can effectively improve the system resilience in the scenario where line damage is caused by extreme disasters, reduce the huge losses brought by disasters, ensure social stability and residents' lives, and verify the feasibility of the present invention.

[0303] The above are only the preferred embodiments of the present invention. It should be understood that the present invention is not limited to the form disclosed herein, and should not be regarded as excluding other embodiments, but can be used in various other combinations, modifications and environments, and can be changed within the scope of the concept described herein through the above teachings or the technology or knowledge in the relevant field. Any changes and modifications made by those skilled in the art without departing from the spirit and scope of the present invention shall fall within the protection scope of the appended claims of the present invention.

Claims

1. A method for evaluating and enhancing the resilience of a power distribution cyber-physical system under disasters, characterized in that, It includes the following steps: Step 1: Establish a bidirectional dynamic model of the distribution network cyber-physical system based on complex network theory, including: a distribution network model, an information network model, and a bidirectional connection model. In the distribution network model, substation distribution equipment is abstracted as nodes, and branch connection lines are abstracted as edges; in the information network model, sensor communication equipment is abstracted as nodes, and optical fibers are abstracted as edges; based on the distribution network model and the information network model, the bidirectional connection model is a bidirectional network architecture and model in which power nodes provide energy flow to information nodes and information nodes provide information flow to power nodes; Step 2: Generate a set of distribution network damage scenarios under large-scale extreme disasters through the Monte Carlo simulation method, and establish a scenario basis for the evolution of the distribution network state in the current period to obtain the data set required for statistical analysis; Step 3: Establish an optimal load shedding model considering distributed units and energy storage equipment system resources. The model aims to minimize the system load shedding, takes into account the importance of loads, and considers distribution network constraints, information network constraints, and the coupling constraints between the two networks; Step 4: Use the Gurobi solver to solve the bidirectional dynamic model of the distribution network cyber-physical system and the optimal load shedding model, calculate the resilience evaluation index to quantitatively analyze the grid resilience, according to the node vulnerability reflected by the evaluation results, combined with the node importance, use TOPSIS analysis based on the entropy weight method to obtain the comprehensive coefficient, and solve the optimal load shedding model to compare and analyze the system resilience before and after the weighted coefficient correction; Step 5: Use mobile emergency power supplies and mobile communication vehicles as controllable emergency power supplies for the power grid and local area emergency wireless communication for the information network respectively to maintain the distribution network cyber-physical system after the disaster, and quantitatively evaluate the resilience improvement effect with resilience indicators.

2. A method for evaluating and enhancing the resilience of a power distribution cyber-physical system under disasters according to claim 1, characterized in that In Step 1, the bidirectional dynamic model of the distribution network cyber-physical system is established based on complex network theory, including a distribution network model, an information network model, and a bidirectional connection model, specifically as follows: The distribution network model abstracts substations, generator sets, and power distribution equipment as nodes, and branch connection lines and circuit breakers as connecting edges to characterize the distribution network. The node set , the connecting edge set , and the node adjacency matrix are as follows: ； ； ； wherein, is the number of nodes in the distribution network; if there is a connection edge between node and node , then , otherwise it is 0; if and there is a connection edge between node and node , then , otherwise it is 0; The information network model abstracts sensors, data storage devices, and communication devices as nodes, and cables and optical fibers as edges to characterize the information network. The set of information network nodes , the set of edges , and the node adjacency matrix are as follows: ； ； ； Among them, is the number of nodes in the information network; if there is an edge between node and node , then , otherwise it is 0; if and there is an edge between node and node , then , otherwise it is 0; The support matrix for power nodes to provide energy flow to information nodes is as follows: ； Among them, if the distribution network node can provide an energy flow to the information network node , then , otherwise it is 0; The support matrix for information nodes to provide information flow to power nodes is as follows: ； Among them, if the information network node can provide information flow to the distribution network node , then , otherwise it is 0; If the power distribution network and the information network are coupled bidirectionally, then , if the two networks are not coupled bidirectionally, then and are determined separately according to the actual situation; further, this bidirectional connection model is: the topological matrix of the power distribution network cyber-physical system: 。 3. A method for evaluating and enhancing the resilience of a power distribution cyber-physical system under disasters according to claim 1, characterized in that, In Step 2, a scenario basis for the evolution of the distribution network state in the current period is established, and the Monte Carlo simulation method generates a set of distribution network damage scenarios as follows: Based on the known failure probability, random number sampling is performed on the probability of component states to determine the system component states, and then the states of all components are combined to obtain the system state; without considering the mutual influence between component states, there is: ； in, Indicates The status of each component; For the The failure probability of each component; To obey A uniformly distributed random number; The state vector of a system composed of elements is: 。 4. A method for evaluating and enhancing the resilience of a power distribution cyber-physical system under disasters according to claim 1, characterized in that, In Step 3, an optimal load shedding model considering the importance of loads is established. The model objective is to minimize the system load shedding, and the objective function is as follows: ； Among them, is the time index; is the total operating cost of the system; is the load shedding cost; Loss of load cost As shown below: ； Among them, is the distribution network node index; is the set of devices connecting nodes; is the unit loss-of-load penalty factor reflecting the importance of the load; is the loss-of-load power.

5. A method for evaluating and enhancing the resilience of a power distribution cyber-physical system under disasters according to claim 1, characterized in that In Step 3, an optimal load shedding model considering the importance of loads is established. The system contains distributed units and energy storage equipment resources. The model considers distribution network constraints, information network constraints, and the coupling constraints between the two networks. The distribution network constraints are specifically as follows: Node power balance constraint: ； ； ； ； Among them, is the set of all child nodes with node as the starting node; is the set of lines of the distribution network; and are respectively the active power and reactive power of the line with node as the starting node at time and are respectively the active power and reactive power of the power line at time and are respectively the active power and reactive power transmitted from the superior power grid to the distribution network at time and are respectively the predicted values of the active load and reactive load at the position of node at time is the magnitude of the active power of the load cut off by the load connected to the system node at time and are respectively the active power output and reactive power output of the gas turbine unit at node at time and are respectively the active power output and reactive power output of the wind turbine unit at node at time and are respectively the charge and discharge power of the energy storage device at node at time and are respectively the active power output and reactive power output of the mobile emergency power supply at node at time and respectively represent the minimum and maximum values of the variable; the binary variable represents the state of the power line at time ; if , it means that the line is not damaged and is in the closed state, otherwise it means that the line is damaged or in the open state.

6. A method for evaluating and enhancing the resilience of a power distribution cyber-physical system under disasters according to claim 1, characterized in that In Step 3, an optimal load shedding model considering the importance of loads is established. The system contains distributed units and energy storage equipment resources. The model considers distribution network constraints, information network constraints, and the coupling constraints between the two networks. The information network constraints are specifically as follows: Node flow balance constraint: ； Among them, is the node set of the information network; is the communication node index; is the communication source node index; is the optical fiber communication link index; and respectively represent the sending end and the receiving end of the information link ; is the node index for configuring the wireless communication vehicle; and respectively represent the sending end and the receiving end of the wireless communication link ; is the information flow on the source node; is the information flow on the information link; indicates whether the communication node is connected to the control master station. If , it means that at the moment, the communication node is connected to the control master station, otherwise it is not; represents the information flow of wireless communication; the number 1 represents the requirements of each node; Communication link availability constraint: ； ； ； Among them, is the total number of communication nodes in the information network; indicates whether the communication link is available. If , it means the communication link fails; otherwise, it means the communication link is normal.

7. A method for evaluating and enhancing the resilience of a power distribution cyber-physical system under disasters according to claim 1, characterized in that, In step 3, an optimal load shedding model considering the importance of load is established. The system contains distributed units and energy storage device resources. The model considers the constraints of the distribution network, the information network, and the coupling constraints between the two networks. The coupling constraints between the two networks are specifically as follows: Distributed unit coupling constraint: ； ； ； ； Among them, and are the control states of the corresponding communication nodes for the gas units and wind turbine units in the distribution network, respectively; represents the communication node information requirements for controlling the gas units or wind turbine units. If , it means that at the moment, the communication node is connected to the control master station, and the corresponding unit control state variable value is 1, that is, the unit is in a controllable state, otherwise it is uncontrollable.

8. A method for evaluating and improving the resilience of a power distribution cyber-physical system under disasters according to claim 1, characterized in that, The resilience evaluation index established in step 4 is as follows: Load shedding probability : ； Among them, is the number of Monte Carlo simulation sampling times; is the node and is the number of samples of load shedding occurring at the node during the research period.

9. A method for evaluating and enhancing the resilience of a power distribution cyber-physical system under disasters according to claim 1, characterized in that In step 4, according to the node vulnerability reflected by the evaluation results, the TOPSIS analysis based on the entropy weight method is used to correct the weighted coefficient. The specific steps of the TOPSIS analysis based on the entropy weight method are as follows: Step 4.1: The TOPSIS model generally operates based on all indicators being of the extremely large type. Therefore, first determine the type of each indicator and perform data normalization according to the indicator type; the load shedding probability and the average load shedding level are both extremely large type indicators. The larger their values, the higher the vulnerability of the load node. Prioritizing the protection of nodes with high vulnerability is beneficial for reducing the degree of system damage; while the load shedding penalty coefficient based on load classification , which reflects whether the impact on social life is significant when the node is abnormal, is also an extremely large type indicator. Vulnerability and load shedding penalty coefficient comprehensively characterize the importance of the node in the system. The matrix obtained after data normalization is denoted as the normalized matrix : ； Step 4.2: Since the dimensions of the indicators are different, standardization is carried out to eliminate the influence of dimensions, so that different indicators can be compared and analyzed on the same scale; establish a standardization matrix , Each element in is: ； Step 4.3: Calculate the proportion of the th indicator for the th sample, and regard it as the probability used in the relative entropy calculation. The matrix formed by the above probabilities is denoted as the probability matrix , ; Step 4.4: Assume represents a certain situation that may occur, and represents the probability of this situation occurring. Define , because , so ; If the possible situations of event are respectively , define the information entropy of event as , and its calculation formula is . The essence of information entropy is the expected value of the amount of information; when , takes the maximum value. At this time . In order to make the information entropy lie in the interval, divide by ; Then for the th item of the index, the calculation formula of the information entropy is . Since there may be a value of 0 in the probability matrix, set to 0; Step 4.5: Calculate the information utility value ; The information utility value reflects the discrimination ability of the index, that is, the larger the information utility value, the stronger the discrimination ability of the index, the more information it carries, and the greater the contribution to the comprehensive evaluation. Therefore, its weight is also larger; It can also be known from the formula that the information entropy is larger, indicating that the information of the th index is less; Step 4.6: Normalize the information utility value and calculate the entropy weight of each index ; Step 4.7: Define the maximum value corresponding to each index and the minimum value i.e., , , , define the distance of the th node from the maximum value , and the distance from the minimum value , where is an element of the standardized matrix; Step 4.8: Calculate the scores before and after normalization; when not normalized, the score of the th node and , the larger the smaller, that is, the closer to the maximum value, the higher the node importance score; to eliminate the influence of different dimensions and value ranges, ensure the fairness and comparability of each index in decision-making, and improve the accuracy of calculation and the robustness of the model, normalize the scores .

10. A method for evaluating and enhancing the resilience of a power distribution cyber-physical system under disasters according to claim 1, characterized in that In step 5, the mobile emergency power supply and the mobile communication vehicle are used as the adjustable emergency power supply for the power grid and the local area emergency wireless communication for the information network respectively. The constraints satisfied by the two emergency resources are specifically as follows: Mobile emergency power supply constraint: ； ； ； Among them, and are respectively the active power output and reactive power output of the mobile emergency power supply at the time node; and are the upper limits of the output of the mobile emergency power supply at node ; the binary variable indicates the configuration status of the mobile emergency power supply at the time node; is the number of mobile emergency power supplies in the distribution network; Mobile emergency communication vehicle constraint: ； ； Among them, is the total number of communication nodes in the information network; indicates the node where a mobile emergency communication vehicle is configured. If it means there is a configuration, otherwise there is no configuration; represents the information flow of wireless communication; is the number of emergency communication vehicles equipped in the information network.

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