Power distribution network pre-disaster toughness improvement method considering typhoon time sequence and information physics cooperative regulation and control

Abstract

A power distribution network pre-disaster toughness improvement method considering typhoon time sequence and information physics cooperative regulation comprises the following steps: by analyzing the time sequence and uncertainty of a typhoon disaster, constructing a DCPS element vulnerability model under the influence of a strong wind-rainstorm dual disaster-inducing factor; generating a typical DPCS disaster scene set based on a DCPS element vulnerability model in combination with historical typhoon disaster data; the dynamic response of the power distribution network in the typhoon disaster process is incorporated into a pre-disaster toughness improvement framework by considering information physical cooperative regulation; and establishing a pre-disaster toughness improvement model, and performing solution in the generated typical DPCS disaster scene set to obtain an optimal pre-disaster toughness improvement scheme. According to the method, by considering the typhoon disaster time sequence and the system dynamic response, the static hypothesis limitation that the typhoon disaster is simplified into an instantaneous uniform impact event in the traditional research is broken through, and a toughness improvement scheme better meeting the actual requirements of the system is formulated.

Description

Technical Field

[0001] The present invention relates to the field of improving the resilience of power systems, and specifically to a method for improving the pre-disaster resilience of distribution networks by considering typhoon timing and information-physical coordinated regulation. Background Art

[0002] In recent years, extreme disasters such as typhoons and floods have occurred frequently, causing huge economic losses to the power grid. Coastal areas in particular must not only cope with the strong winds of typhoons, but also consider the accompanying rainstorms, which has seriously impacted the safe and stable operation of the power grid. Compared with transmission networks, the operating environment of distribution networks is more complex and more vulnerable to typhoon disasters. At the same time, with the rapid development of modern information and communication technologies, the degree of informatization of power systems is also continuously deepening. Traditional distribution networks are gradually transforming into distribution cyber-physical systems (DCPS). While improving the monitoring and control capabilities of distribution networks, they also increase the operational risks of the system in the face of extreme disasters. Therefore, how to build a more resilient distribution network in the face of typhoon disasters from the perspective of deep cyber-physical coupling has become an important issue that needs to be addressed urgently.

[0003] Existing research frameworks for improving pre-disaster resilience are mostly limited to the single dimension of the physical system, failing to consider the deep coupling between the information and physical layers and overlooking the crucial role of information systems in pre-disaster resilience. Furthermore, they simplify disaster impacts into instantaneous uniform events by assuming synchronous failures and use the total static load shedding at the end of the disaster as an evaluation metric, ignoring the temporal evolution of the disaster and the real-time operational status of the system.

[0004] Traditional static resilience planning methods fail to take into account the temporal nature of typhoon disasters and the deep coupling of information physics, resulting in the difficulty of formulating pre-disaster prevention and reinforcement plans to improve the system's ability to resist disasters, and the effects of improving the system's resilience and economy are significantly limited. Summary of the Invention

[0005] In order to solve the above technical problems, the present invention provides a method for improving the pre-disaster resilience of distribution networks by considering the temporal nature of typhoons and the coordinated regulation of information and physics. By considering the temporal nature of typhoon disasters and the dynamic response of the system, this method breaks through the static assumption limitation of traditional research that simplifies typhoon disasters into instantaneous uniform impact events, and formulates a resilience improvement plan that is more in line with the actual needs of the system.

[0006] The technical solution adopted by the present invention is:

[0007] The method for improving the pre-disaster resilience of distribution networks by considering typhoon timing and cyber-physical coordinated control includes the following steps:

[0008] Step 1: By analyzing the temporal nature and uncertainty of typhoon disasters, a DCPS component vulnerability model under the influence of strong wind and heavy rain dual disaster factors is constructed;

[0009] Step 2: Generate a set of typical DPCS disaster scenarios based on the DCPS component vulnerability model and historical typhoon disaster data;

[0010] Step 3: Consider cyber-physical coordinated control and incorporate the dynamic response of the distribution network during typhoon disasters into the pre-disaster resilience improvement framework;

[0011] Step 4: Based on step 3, a pre-disaster resilience improvement model is established. The typical DPCS disaster scenarios generated in step 2 are centrally solved to obtain the optimal pre-disaster resilience improvement plan.

[0012] In step 1, in order to improve the resilience of the distribution system, the focus is on the dual disaster-causing factors of strong winds and heavy rains. The DCPS component vulnerability model specifically includes:

[0013] 1) DCPS component vulnerability model under strong winds:

[0014] During typhoon disasters, strong winds primarily impact DCPS components such as power lines and communication links. Assuming that communication links utilize fiber-optic communication and are installed via poles and towers, they are laid out in parallel or intersecting patterns with the power lines. The core components of both power lines and communication links are conductors and towers. Therefore, this paper analyzes the vulnerability characteristics of conductor and tower structures under typhoon conditions:

[0015] The tower bears both the wind load of the pole body and the wind load of the conductor traction. The wind loads acting on the conductor and the pole body are:

[0016]

[0017] In the above formula, W c,t and W p,t are the wind loads acting on the conductor and tower at time t; v t is the typhoon wind speed at time t; μ u 、μ H 、μ sc and μ sp are wind pressure unevenness coefficient, wind pressure height variation coefficient, conductor shape coefficient and tower shape coefficient respectively; δ t is the moving direction angle of the typhoon at time t; D is the outer diameter of the conductor; l s is the span of the conductor; l and l2 are the height and burial depth of the tower respectively; d r and d p are the diameters of the bottom and top of the tower respectively;

[0018] Based on the wind load acting on the conductor and the pole, the bending moment at the base of the tower and the stress on the conductor can be calculated:

[0019] M line,t =2W c,t l1+W c,t (l-l2) (3);

[0020] M pole,t =W p,t (l-l2) / 2 (4);

[0021]

[0022] σ′ c,t =W c,t / S c (6);

[0023] In the above formula, M line,t and M pole,t are the bending moments at the base of the tower caused by the wind load acting on the conductor and tower at time t; l1 is the height of the tower above the ground; M′ c,t is the composite root bending moment of the tower; σ′ c,t is the cross-sectional stress of the conductor; S c is the cross-sectional area of ​​the wire.

[0024] During a typhoon disaster, the line is under continuous stress. The damage state of the line depends not only on the typhoon intensity during the current period, but also on the historical damage state. Therefore, the fatigue damage coefficient α is introduced to quantify the dynamic cumulative damage of strong winds to the line:

[0025] M c,t =M′ c,t +αM c,t-1 (7);

[0026] σ c,t =σ′ c,t +ασ c,t-1 (8);

[0027] In the above formula, M c,t M is the composite root bending moment of the tower at time t considering the fatigue damage of the tower; c,t-1 is the composite root bending moment of the tower at time t-1 considering the fatigue damage of the tower; c,t is the cross-sectional stress of the conductor at time t when considering the fatigue damage of the conductor; σ c,t-1 is the cross-sectional stress of the conductor at time t-1 considering the fatigue damage of the conductor.

[0028] Assume that the tensile strength of the conductor and the bending strength of the tower obey the normal distribution:

[0029]

[0030] In the above formula, p pole and p line are the failure probabilities of towers and conductors respectively; M p and σ l are the bending strength of the tower and the tensile strength of the conductor respectively; μ p and δ p are the mean and standard deviation of the tower bending strength respectively; μ l and δ l are the mean and standard deviation of the tensile strength of the wire; M c is the composite root bending moment of the tower considering the fatigue damage of the tower; c is the cross-sectional stress of the conductor considering the fatigue damage of the conductor; exp[·] is in exponential form.

[0031] From this we can get the failure probability of the power line for:

[0032]

[0033] In formula (11): K pole is the number of towers of the line; p pole,a and p line,b are the failure probabilities of the ath tower and the bth conductor respectively; Indicates from a=1 to K pole , (1-p pole,a ) Indicates from b=1 to K pole -1, (1-p line,b ) is the cumulative product of .

[0034] 2) DCPS component vulnerability model under heavy rain:

[0035] Heavy rainstorms can cause insulator flashover and water ingress to transformers, leading to line failures. The following section analyzes the vulnerability of insulators and transformers.

[0036] 2.1) Insulator vulnerability analysis:

[0037] When the rainfall intensity exceeds a certain threshold, the insulator will flash over. Assume that the rainfall intensity Ri satisfies the normal distribution:

[0038]

[0039] In the above formula: P ins is the failure probability of a single insulator; Ri ins is the critical value of rainfall intensity for insulator flashover; is the failure probability of the i-th insulator; nins is the number of insulators on the line; P l,ins is the probability of line outage due to insulator flashover. The line will be out of service only when more than s% of the insulators on the line fail. ins >0} indicates that the rainfall intensity Ri exceeds the critical value Ri of the insulator flashover ins The probability of rainfall intensity Ri; f(Ri) is the probability density function of rainfall intensity Ri, which shows that the rainfall intensity Ri satisfies the normal distribution; Indicates the number of combinations from n ins The number of combinations of i elements without repetition in ; s% represents the critical value of the number of insulator failures; i represents the i-th insulator.

[0040] 2.2) Transformer vulnerability analysis:

[0041] The main effects of heavy rain on transformers are spark discharge of insulating oil and breakdown of oil-impregnated paper;

[0042]

[0043] In the above formula: Ri1 and Ri2 are the critical rainfall intensity of insulating oil spark discharge and oil-impregnated paper breakdown respectively; P tran1 and P tran2 are the probability of insulating oil spark discharge and the probability of oil-impregnated paper breakdown, respectively; P{Ri-Ri1>0} represents the probability that the rainfall intensity Ri exceeds the critical value Ri1 of the rainfall intensity for insulator flashover; P{Ri-Ri2>0} represents the probability that the rainfall intensity Ri exceeds the critical value Ri2 of the rainfall intensity for insulator flashover.

[0044] From this we can get the probability P that the power line will be shut down due to transformer failure l,tran for:

[0045] P l,tran =P tran1 +P tran2 -P tran1 P tran2 (16);

[0046] Transformer water ingress and insulator flashover can both cause power line outages. Assuming the two fault events are independent of each other, the probability of power line failure due to heavy rain is for:

[0047]

[0048] In step 2, the disaster scenario generation process is as follows:

[0049] Based on the wind speed data and rainfall data of historical typhoon disasters, the Monte Carlo method was used to generate multiple typhoon disaster scenarios. Then, the scenarios were reduced using the improved K-means method. The wind speed data and rainfall data of each fault period were clustered in the same period, and finally a typical scenario that took into account the correlation between strong wind and heavy rain disasters was obtained.

[0050] The above is the application of Monte Carlo method.

[0051] The above is the specific content of the Monte Carlo method and improved K-means method used:

[0052] 1. Optimal number of clusters:

[0053] The number of clusters K in the K-means algorithm is usually selected through experience or experiments, which can easily affect the clustering results. Therefore, this paper determines the optimal number of clusters based on the clustering effect. The clustering effect is determined by the CH index, which is defined as follows:

[0054] CH(k)=[t B (Nk)] / [t W (k-1)];

[0055] In the above formula: CH(k) is the CH index, which is used to evaluate the quality of clustering effect; k is the number of clusters; t B is the sum of squares of the differences between categories; W is the sum of squares of deviations within each class; N is the number of samples; when CH(k) is the largest, the corresponding k value is the optimal number of clusters.

[0056] 2. Optimal cluster center:

[0057] For the same cluster set, different selections of initial cluster centers may produce different clustering results. If different initial cluster centers are selected, the clustering results may be unstable or fall into a local optimum. Therefore, the cohesion function is introduced to select samples with high compactness as cluster centers, which is defined as follows:

[0058]

[0059] Where: A(S n ,d mean ) is the aggregation function, which can reflect the sample data S n As the center, with the sample average distance d mean The data within the radius and S n The degree of distance, A(S n ,d mean )∈(0,1);S n is the nth cluster center sample; d mean is the sample average clustering; Represents sample S n and Similarity measure between ; represents the n1th domain sample; N is the total number of samples; Represents sample S n and The Euclidean distance between n,1 Represents sample S n The first eigenvalue of ; For samples The previous sample of S n,T Represents sample S n Eigenvalue at time T; Representation sample The eigenvalue before time T.

[0060] The steps for generating the initial cluster center candidate set are as follows:

[0061] Step 1: Calculate the density parameter of each data and find the data S corresponding to the maximum value n ;

[0062] Step 2: If S n Only, then S n Add to the initial cluster center candidate set. If it corresponds to multiple sample data, the data with the smallest cohesion is selected according to the cohesion function and added to the initial cluster center candidate set;

[0063] Step 3: S n Centered, d mean The data within the radius are deleted from the sample set;

[0064] Step 4: Repeat Step 1 to Step 3 until you find Initial cluster centers.

[0065] 3. Typical scenario generation process:

[0066] The clustering process is as follows Figure 7 As shown in Figure 3, the number of clusters corresponding to the maximum value of the CH(k) index is the optimal number of clusters, and its clustering result is the optimal classification. Each classification center is the selected typical scenario.

[0067] For each typical scenario, the impact of strong winds and heavy rain on power lines and communication links is comprehensively considered. Assuming that the impacts of the two types of events on DCPS are independent of each other, we can obtain:

[0068]

[0069] In the above formula: P line is the probability of the line being affected by the typhoon; is the probability of line failure due to strong wind; is the probability of line failure due to heavy rain.

[0070] According to the above formula, the probability P of the line being affected by the typhoon is calculated line ,Then the Monte Carlo simulation sampling method is used to deal with the uncertainty of the line disaster status, as follows:

[0071] P line The line status is determined based on the comparison result with a random number uniformly distributed between [0,1]. The mathematical expression is as follows:

[0072]

[0073] In the above formula: q ij,t is a 0-1 variable, indicating whether line ij is affected by the typhoon at time t, q ij,t =1 indicates normal operation, otherwise it is affected; P un is a random number, P un ~U(0,1), U(0,1) is 0-1 uniform distribution; P un ~U(0,1) represents P un Obey the uniform distribution of 0-1.

[0074] After the line is reinforced, the probability of failure is extremely low. It is assumed that the reinforced line will not fail during the disaster. In addition, since emergency repairs cannot be performed on the faulty line during the disaster, the line will remain in the faulty state until the disaster ends. This is expressed as follows:

[0075]

[0076] In the above formula: is a 0-1 variable, indicating the fault status of line ij at time t. Indicates that there is no fault in the line, otherwise it means that there is a fault in the line; x ij is the line strengthening state variable, x ij =1 means line ij has been strengthened, otherwise it has not been strengthened; It is a 0-1 variable, indicating the fault status of line ij at time t+1.

[0077] In step 3, the pre-disaster resilience enhancement framework is as follows:

[0078] In the context of typhoon disaster response, the pre-disaster resilience framework refers to a systematic methodology or decision-support system. It aims to optimize the structure and operational strategies of distribution networks before typhoons through cyber-physical coordinated control. This combines the real-time monitoring and prediction capabilities of cyber systems with the dynamic response capabilities of physical equipment. This approach enhances their resilience, rapid recovery, and adaptability to disasters. The goal is to minimize the impact of disasters on the system by incorporating real-time responses during disasters, such as fault isolation and load shifting, into pre-disaster planning.

[0079] In step 3, the dynamic response of the distribution network during a typhoon disaster is incorporated into the pre-disaster resilience improvement framework, and a pre-disaster resilience improvement plan is formulated, as follows:

[0080] Improving the resilience of the power distribution cyber-physical system (DCPS) in the pre-disaster phase mainly focuses on long-term investment decisions, such as strengthening key nodes and pre-configuring DGs, with the goal of improving preventive resilience. During the mid-disaster phase, more attention is paid to the real-time dynamic response of the system, such as network reconstruction and DG output adjustment, with the goal of improving adaptive resilience. The formulation of the resilience improvement plan proposed in this invention relies on simulating the dynamic response decisions of the system during the mid-disaster phase, combining the real-time response plans of the system in multiple scenarios, and formulating the optimal pre-disaster prevention and reinforcement plan.

[0081] 1) Pre-disaster prevention measures:

[0082] Based on historical typhoon disaster data and taking into account the temporal nature and uncertainty of typhoons, a set of typical DCPS typhoon disaster scenarios was generated. Based on this set of typical disaster scenarios, a pre-disaster resilience improvement model was constructed to formulate a pre-disaster prevention and enhancement plan.

[0083] The prevention plan primarily focuses on strengthening power lines and communication links to enhance the system's resilience to disasters. A vulnerability analysis of DCPS components reveals that the primary affected components are conductors, towers, insulators, and transformers. Therefore, improving DCPS resilience in the pre-disaster phase can be achieved by strengthening vulnerable components. Specific measures include managing vegetation near towers, reinforcing tower conductors, installing flood control measures near transformers, and installing double-hole insulators.

[0084] 2) Cyber-physical collaborative control scheme:

[0085] Power lines and communication links that have been reinforced before a disaster will not fail due to the impact of the typhoon. However, for unreinforced lines, after encountering a typhoon disaster, it is difficult to dispatch mobile energy storage resources or dispatch emergency personnel to carry out on-site repairs due to geographical barriers and traffic interruptions. Considering the remote monitoring and control functions of the information system, the information system can be used for dynamic response during the disaster. During each typhoon disaster period, the operating status of the corresponding physical nodes is monitored in real time through the communication nodes of the information system (sensors deployed in the distribution network, such as PMUs). The operating status of the corresponding physical nodes is uploaded to the control center of the information system. If the physical node is operating normally, the information system does not make any decisions. If a physical node fails, the information system adjusts the DG output or controls the RCS to disconnect to reconfigure the network and formulate corresponding response measures to reduce the losses caused by physical node failures.

[0086] For DG nodes, the power supply needs of adjacent nodes are guaranteed by adjusting the DG output. For nodes where remote-controlled switches (RCSs) are located, the RCSs are switched on and off to achieve dynamic network reconfiguration. Specifically, the information system control constraint part of the DCPS coupling constraint includes the contents of Equations (54) and (55).

[0087] In step 4, the pre-disaster resilience improvement model is as follows:

[0088] 1) Objective function:

[0089] During the pre-disaster prevention phase, the system’s dynamic response under each typical disaster scenario is simulated, and a pre-disaster prevention plan is formulated with the goal of minimizing the system strengthening cost and the simulated load shedding penalty cost.

[0090] min{f1+E p [f2(x,K)]}(22);

[0091] In formula (22), f1 is the line enhancement cost; x is the line enhancement plan; K is the typical scenario set; E p [f2(x,K)] is the expected value of the load shedding penalty cost under all typical scenarios K; f2(x,K) is the load shedding penalty cost under all typical scenarios K.

[0092] The line reinforcement cost is related to the line reinforcement plan, which is determined by typical scenarios. The line reinforcement plan that minimizes the system load shedding penalty cost under all typical scenarios is the optimal plan.

[0093]

[0094] In formula (23): c rein is the line reinforcement cost per unit length; L ijis the length of line ij; Ω N A collection of system nodes.

[0095] For any scene k in the scene set K, we have:

[0096]

[0097]

[0098] In the above formula: c p,i is the unit load shedding penalty cost of node i; is the load shedding of node i at time t; p k is the probability of scenario k occurring; T represents the typhoon impact time.

[0099] 2) Constraints:

[0100] 2.1) Line reinforcement constraints:

[0101] Considering the economic efficiency of system operation, it is assumed that the maximum number of line reinforcement is

[0102]

[0103] 2.2) Physical system operation constraints:

[0104] a) Load shedding constraints:

[0105]

[0106] Where: is the load active power demand of node i at time t under scenario k; is the reactive load of node i at time t under scenario k; and are the upper limit of active power and reactive power of node i respectively.

[0107] b) Virtual power flow constraints:

[0108] The reconstructed power grid needs to ensure that it meets the radial topology requirements. Therefore, a virtual power flow network is introduced, and the single commodity flow method is used to ensure the connectivity and radial structure of the reconstructed network.

[0109]

[0110] In formula (29): Ω B is a set of virtual flow nodes; represents the fault status of line ij at time t in scenario k; N node and N DG are the number of physical system nodes and DG number respectively.

[0111]

[0112] In formula (30): is the virtual power flow of branch ij of the virtual power flow network; is the branch jh virtual power flow of the virtual power flow network; V j,t is the virtual power emitted by node j in the virtual power flow network; and are the inflow node set and outflow node set of virtual network node j respectively;

[0113]

[0114] In formula (31): is the connection matrix of DG; M is a sufficiently large positive number.

[0115]

[0116] c)RCS switch constraints:

[0117] Considering the safety of the equipment, frequent operation of RCS should be avoided. Assuming that the maximum number of RCS switches is ψ max .

[0118]

[0119] In formula (34): is a 0-1 variable, indicating the on / off state of the RCS at node i at time t+1 in scenario k; is a 0-1 variable, indicating the on / off state of the RCS at node i in scenario k. Indicates that the RCS is closed, otherwise it is open.

[0120] d) Energy storage constraints:

[0121]

[0122] In formula (35): and are the capacities of energy storage i at time t and time t+1 respectively; and are the charging and discharging active powers of energy storage i at time t respectively; and are the charging and discharging efficiencies of energy storage i, respectively;

[0123]

[0124] In formula (36): and Configure upper and lower limits for the energy storage i capacity respectively;

[0125]

[0126] In formula (37): and are the upper limits of charging and discharging active power of energy storage i respectively; and are 0-1 variables, representing the charging and discharging states of energy storage i at time t.

[0127]

[0128] In formula (38): represents the charging reactive power of energy storage i at time t; represents the discharge reactive power of energy storage i at time t; and are the upper limits of charging and discharging reactive power of energy storage i respectively;

[0129]

[0130] e) Power flow constraints:

[0131] The Dist-Flow model is used to describe the radial network flow of the system:

[0132]

[0133] Where: P ij,t and Q ij,t is the active power flow and reactive power flow of line ij at time t; r ij and x ij are the resistance and reactance of line ij respectively; and are the inflow node and outflow node of node j respectively; I′ ij,t is the square value of the current of line ij at time t; represents the discharge active power of node i at time t; represents the DG active power of node i at time t; represents the active load shedding amount of node i at time t; P jk,t represents the active power flow of line jk at time t; represents the charging active power of node i at time t; represents the load active power of node i at time t; represents the discharge reactive power of node i at time t; represents the DG reactive power of node i at time t; represents the reactive load shedding amount of node i at time t; Q jk,trepresents the reactive power flow of line jk at time t; represents the charging reactive power of node i at time t; Represents the reactive power of the load at node i at time t.

[0134] To ensure stable system operation, the system power, voltage, and current must also meet the following constraints:

[0135]

[0136] Where: U′ i,t is the square value of the voltage at node i; U′ j,t is the square value of the voltage at node j; auxiliary variable μ ij,t and ν ij,t The introduction of μ is to transform the nonlinear power flow constraint into a linear solvable form. ij,t Represents the voltage amplitude square difference U′ i,t -U′ j,t The upper bound of the absolute value of ν ij,t Represents the voltage amplitude square difference U′ i,t -U′ j,t The offset reference.

[0137] Perform the second-order cone relaxation on Equation (44), as shown below:

[0138]

[0139] In formula (44): I′ ij,t It represents the square of the current in line ij at time t.

[0140] 2.3) Information system operation constraints

[0141] a) Information flow balance constraints:

[0142] During a disaster, the control center of the information system collects real-time status information from each communication node, formulates corresponding response measures, and distributes them to each communication node. Information flow is transmitted in the form of communication links. The information flow balance constraint of the communication link is expressed as follows:

[0143]

[0144] In the above formula: is the information flow through the communication link ij; ω in (j) and ω out (j) are the inflow node set and outflow node set of communication node j respectively; is the information load reduction of communication node j at time t; is the information load of communication node j; is a 0-1 variable, indicating the energy supply status of communication node j, It indicates that the node is supplying energy normally, otherwise it indicates insufficient energy supply; Variable, indicating the operating status of the communication link ij, Indicates that the communication link ij is operating normally, otherwise it indicates a fault; T ij is the bandwidth of the communication link ij.

[0145] b) Information load reduction constraints:

[0146] If the information load at node i is reduced too much, the node will not be able to fully receive the command from the control center. At this time, the communication node fails. The mathematical expression is as follows:

[0147]

[0148] In formula (51): is the control state variable of communication node i; a i is the control capability of communication node i; is the information load of communication node i.

[0149] 2.2) DCPS Coupling Constraints

[0150] a) Physical system energy constraints:

[0151] Information systems require energy from physical systems to ensure the normal operation of nodes. When the physical node corresponding to a communication node cannot meet its energy supply requirements, the communication node will be unable to execute control commands. The mathematical expression is as follows:

[0152]

[0153] Where: is a 0-1 variable, indicating the energy supply status of communication node j; is the lower limit of energy demand of communication node i; is the energy supply of communication node i at time t; Ω T is the set of communication nodes; Ω Y The source node where the control center is located is generally equipped with an independent power supply to ensure its power supply; is the lower limit of energy demand of communication node i.

[0154] b) Information system control constraints:

[0155] For a DG node, if the corresponding communication node fails, the control center cannot adjust the power output. To ensure the safe operation of the system, when the communication node fails, the corresponding DG node stops running. The mathematical expression is as follows:

[0156]

[0157] In formula (54): and are the active power and reactive power of DG at node i at time t respectively; and are the upper limit of active power and reactive power of DG at node i respectively.

[0158] For the node where the RCS is located, if the corresponding communication node fails, the control center cannot control the RCS switching. Therefore, the RCS controlled by the failed communication node remains disconnected, and the mathematical expression is as follows:

[0159]

[0160] In formula (55): Ω C The node set where RCS is located; is a 0-1 variable, indicating the RCS switching command issued by the control center at time t. It means that the control RCS is closed and the corresponding interconnection line is put into operation. Otherwise, it means that the control RCS is disconnected and the corresponding interconnection line is out of operation.

[0161] The DCPS resilience improvement model constructed according to the above steps has decision variables including 0-1 variables (line strengthening variables) and continuous variables (load shedding). It is a multi-scenario mixed integer linear programming (MILP) problem and can be solved by calling Gurobi12.0.1 using MATLAB.

[0162] In step 3, the optimal pre-disaster resilience enhancement plan is obtained, that is, the system's pre-disaster line reinforcement plan while minimizing system load shedding losses and line reinforcement costs. The line reinforcement plan includes vegetation management near towers, tower conductor reinforcement, flood control measures near transformers, and installation of double-hole insulators.

[0163] The present invention provides a method for improving the pre-disaster resilience of distribution networks by considering typhoon timing and cyber-physical coordinated control. The technical effects are as follows:

[0164] 1) Step 1 of the present invention analyzes the temporal sequence and uncertainty of typhoon disasters and constructs a DCPS component vulnerability model under the influence of the dual disaster factors of strong winds and heavy rains. This breaks through the static assumption limitation of traditional research that simplifies typhoon disasters into instantaneous uniform impact events.

[0165] 2) In step 2 of the present invention, based on the DCPS component vulnerability model and combined with historical typhoon disaster data, a set of typical DPCS disaster scenarios is generated to more realistically simulate various scenarios that may occur in DCPS during typhoon disasters.

[0166] 3) Step 3 of the present invention takes into account cyber-physical coordinated control and incorporates the dynamic response of the distribution network during a typhoon disaster into the pre-disaster resilience enhancement framework to obtain a pre-disaster resilience enhancement solution that better meets the actual operation needs of the system.

[0167] 4) Step 4 of the present invention utilizes the monitoring and control functions of the information system to establish a pre-disaster resilience enhancement model that considers information-physical collaboration, effectively improving the system's ability to resist typhoon disasters and reducing the system's operating costs during typhoon disasters. BRIEF DESCRIPTION OF THE DRAWINGS

[0168] The present invention will be further described below with reference to the accompanying drawings and examples:

[0169] Figure 1 This is the improved PG&E69 active distribution system network topology diagram.

[0170] Figure 2 Schematic diagram of the typhoon's path.

[0171] Figure 3 Schematic diagram of time-varying fault probability of power lines.

[0172] Figure 4 Schematic diagram of time-varying failure probability of communication link.

[0173] Figure 5 This is the system load shedding diagram under different line reinforcement numbers.

[0174] Figure 6 This is the system load supply diagram during the disaster process.

[0175] Figure 7 Clustering flow chart. DETAILED DESCRIPTION

[0176] A method for improving the pre-disaster resilience of distribution networks by considering typhoon timing and cyber-physical coordinated control includes the following steps: Step 1: By analyzing the timing and uncertainty of typhoon disasters, a DCPS component vulnerability model under the influence of the dual disaster factors of strong winds and heavy rain is constructed; Step 2: Based on the DCPS component vulnerability model and combined with historical typhoon disaster data, a set of typical DCPS disaster scenarios is generated; Step 3: Considering cyber-physical coordinated control, the dynamic response of the distribution network during typhoon disasters is incorporated into the pre-disaster resilience improvement framework and a pre-disaster resilience improvement plan is formulated; Step 4: Based on Step 3, a pre-disaster resilience improvement model is established and solved on the typical DCPS disaster scenarios generated in Step 2 to obtain the optimal pre-disaster resilience improvement plan. By considering the timing of typhoon disasters and the dynamic response of the system, this method develops a pre-disaster resilience improvement plan that better meets the actual operational needs of the system, significantly improving the resilience and economic efficiency of the system during typhoon disasters.

[0177] Example:

[0178] This paper takes the improved PG&E69 active distribution network in a coastal city of China as an example to verify the effectiveness of the proposed pre-disaster resilience improvement method. Communication routing is installed at the DG nodes and RCS adjacent nodes of the corresponding physical system, and 13 routing nodes are set, such as Figure 1 Nodes are divided into three levels based on load importance. When formulating resilience improvement plans, priority is given to ensuring the energy supply needs of important nodes. The node levels are shown in Table 1. DG and energy storage parameters are shown in Tables 2 and 3.

[0179] Table 1 Load level information

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[0181] Table 2DG operating parameters

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[0183] Table 3 Energy storage operation parameters

[0184]

[0185] Typhoon disaster simulation for "SANBA" in October 2023. Typhoon data and rainfall data are all from the China Meteorological Administration. The maximum wind force near the typhoon center is level 7, with a wind speed of 54km / h, and it moves southeast at a speed of 10-15km / h. It is assumed that the typhoon disaster lands at 8:00 and begins to affect the system. The duration is 6 hours. The typhoon transit route is shown in Figure 2 shown.

[0186] According to step 1, based on the typhoon disaster data, the time-varying failure probability of power lines and communication links is calculated as follows: Figure 3 and Figure 4 shown.

[0187] Depend on Figure 3 and Figure 4 The line failure probability shows that the relationship between line failure probability and typhoon wind speed during a disaster is not linear. For example, from 8:00 to 9:00, Line 6 was within the typhoon's maximum wind speed radius, significantly increasing the line failure probability. From 9:00 to 1:00, the typhoon left Line 6's area, but due to the accumulated damage caused by the typhoon, Line 6 still had a high failure probability. Furthermore, the line failure probability is also related to the impact of heavy rain on the line. For example, Line 29 remained outside the typhoon's maximum wind speed radius and was less affected by the typhoon. However, at 1:00, due to the heavy rain, the failure probability of Line 29 increased dramatically.

[0188] According to step 2, five typical DCPS typhoon disaster scenarios are generated, as shown in Table 4:

[0189] Table 4 Typical disaster scenario information

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[0191] According to step 4, in order to determine the optimal line reinforcement number, different line reinforcement numbers are set for simulation. The results are shown in Figure 5 and Table 5:

[0192] Table 5 Simulation results under different line reinforcement numbers

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[0194] From the perspective of system resilience, as the number of line reinforcements increases, Figure 5 It can be seen that the load shedding of the system gradually decreases. Therefore, it can be concluded that the pre-disaster line reinforcement plan can effectively reduce the load shedding loss of the system and improve the resilience of the system.

[0195] From the perspective of system economics, the total cost of the system shown in Table 5 gradually decreases as the number of line reinforcements increases from 2 to 5. However, when the number of line reinforcements exceeds 6, the total cost of the system increases because the increase in line reinforcement costs exceeds the reduction in load shedding losses. Therefore, considering both system resilience and economics, the optimal pre-disaster line reinforcement number is set to 5, and the optimal line reinforcement plan is to strengthen lines 6, 49, 51, 54, and 57.

[0196] Based on the optimal line reinforcement plan, the resilience improvement effect of the plan is analyzed by taking typical scenario 1 as an example. The operating status and load supply of the system during the disaster period are shown in Table 6 and Figure 6 As shown, the total operating cost of the system is 314637.3238 yuan.

[0197] Table 6 System operation status during disaster

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[0199]

[0200] As shown in Table 6, due to economic considerations, the optimal line reinforcement scheme cannot completely cover all lines affected by typhoon disasters. However, combined with cyber-physical coordinated control, it can still effectively reduce the system's load shedding and maintain stable system operation.

[0201] Depend on Figure 6As can be seen, by leveraging the pre-disaster prevention and reinforcement plan and utilizing the information system to dynamically respond during each disaster-affected period, the system was able to consistently maintain its load supply capacity, effectively improving power supply reliability. Zero load shedding was achieved during the first three disaster-affected periods, effectively ensuring the system's load supply capacity during the disaster, significantly enhancing its resilience and economic efficiency.

Claims

1. A method for improving the resilience of distribution networks before disasters by considering typhoon timing and cyber-physical coordinated control, characterized by The following steps are involved: Step 1: By analyzing the temporal nature and uncertainty of typhoon disasters, a DCPS component vulnerability model under the influence of strong wind and heavy rain dual disaster factors is constructed; Step 2: Generate a set of typical DPCS disaster scenarios based on the DCPS component vulnerability model and historical typhoon disaster data; Step 3: Consider cyber-physical coordinated control and incorporate the dynamic response of the distribution network during typhoon disasters into the pre-disaster resilience improvement framework; Step 4: Based on step 3, a pre-disaster resilience improvement model is established. The typical DPCS disaster scenarios generated in step 2 are centrally solved to obtain the optimal pre-disaster resilience improvement plan.

2. The method for improving the pre-disaster resilience of distribution networks by considering typhoon temporality and cyber-physical coordinated control according to claim 1 is characterized by: In step 1, the DCPS component vulnerability model includes a DCPS component vulnerability model under the influence of strong winds, which is specifically as follows: Analyze the vulnerability characteristics of the conductor and tower structure under typhoon conditions: the tower bears both the wind load of the pole body and the wind load of the conductor traction; the wind loads acting on the conductor and the pole body are: In the above formula, W c,t and W p,t are the wind loads acting on the conductor and tower at time t; v t is the typhoon wind speed at time t; μ u 、μ H 、μ sc and μ sp are wind pressure unevenness coefficient, wind pressure height variation coefficient, conductor shape coefficient and tower shape coefficient respectively; δ t is the moving direction angle of the typhoon at time t; D is the outer diameter of the conductor; l s is the span of the conductor; l and l2 are the height and burial depth of the tower respectively; d r and d p are the diameters of the bottom and top of the tower respectively; Based on the wind load acting on the conductor and the pole, the bending moment at the tower base and the stress on the conductor are calculated: M line,t =2W c,t l1+W c,t (l-l2) (3); M pole,t =W p,t (l-l2) / 2 (4); in c,t =W c,t / S c (6); In the above formula, M line,t and M pole,t are the bending moments at the base of the tower caused by the wind load acting on the conductor and tower at time t; l1 is the height of the tower above the ground; M′ c,t is the composite root bending moment of the tower; σ′ c,t is the cross-sectional stress of the conductor; S c is the cross-sectional area of ​​the wire.

3. The method for improving the pre-disaster resilience of distribution networks by considering typhoon temporality and cyber-physical coordinated control according to claim 2 is characterized by: The fatigue damage coefficient α is introduced to quantify the dynamic cumulative damage of strong winds to the line: M c,t =M′ c,t +αM c,t-1 (7); s c,t =σ′ c,t +as c,t-1 (8); In the above formula, M c,t M is the composite root bending moment of the tower at time t considering the fatigue damage of the tower; c,t-1 is the composite root bending moment of the tower at time t-1 considering the fatigue damage of the tower; c,t is the cross-sectional stress of the conductor at time t when considering the fatigue damage of the conductor; σ c,t-1 is the cross-sectional stress of the conductor at time t-1 considering the fatigue damage of the conductor; Assume that the tensile strength of the conductor and the bending strength of the tower obey the normal distribution: In the above formula, p pole and p line are the failure probabilities of towers and conductors respectively; M p and σ l are the bending strength of the tower and the tensile strength of the conductor respectively; μ p and δ p are the mean and standard deviation of the tower bending strength respectively; μ l and δ l are the mean and standard deviation of the tensile strength of the wire; M c is the composite root bending moment of the tower considering the fatigue damage of the tower; c The cross-sectional stress of the conductor considering the fatigue damage of the conductor; exp[·] is the exponential form; From this we can get the failure probability of the power line for: In formula (11): K pole is the number of towers of the line; p pole,a and p line,b are the failure probabilities of the ath tower and the bth conductor respectively; Indicates from a=1 to K pole , (1-p pole,a ) Indicates from b=1 to K pole -1, (1-p line,b ) is the cumulative product of .

4. The method for improving the pre-disaster resilience of distribution networks by considering typhoon temporality and cyber-physical coordinated control according to claim 2 is characterized by: In step 1, the DCPS component vulnerability model also includes a DCPS component vulnerability model under the influence of heavy rain, and performs vulnerability analysis on insulators and transformers: 2.1) Insulator vulnerability analysis: When the rainfall intensity exceeds a certain threshold, the insulator will flash over. Assuming that the rainfall intensity Ri satisfies the normal distribution: In the above formula: P ins is the failure probability of a single insulator; Ri ins is the critical value of rainfall intensity for insulator flashover; is the failure probability of the i-th insulator; n ins is the number of insulators on the line; P l,ins is the probability of line outage due to insulator flashover. The line will be out of service only when more than s% of the insulators on the line fail. ins >0} indicates that the rainfall intensity Ri exceeds the critical value Ri of the insulator flashover ins f(Ri) is the probability density function of rainfall intensity Ri, which shows that rainfall intensity Ri satisfies normal distribution; Indicates the number of combinations from n ins The number of combinations of i elements without repetition in ; s% represents the critical value of the number of insulator failures; i represents the i-th insulator; 2.2) Transformer vulnerability analysis: The main effects of heavy rain on transformers are spark discharge of insulating oil and breakdown of oil-impregnated paper; In the above formula: Ri1 and Ri2 are the critical rainfall intensity of insulating oil spark discharge and oil-impregnated paper breakdown respectively; P tran1 and P tran2 are the probability of insulating oil spark discharge and the probability of oil-impregnated paper breakdown, respectively; P{Ri-Ri1>0} represents the probability that the rainfall intensity Ri exceeds the critical value Ri1 of the rainfall intensity for insulator flashover; P{Ri-Ri2>0} represents the probability that the rainfall intensity Ri exceeds the critical value Ri2 of the rainfall intensity for insulator flashover; From this we can get the probability P that the power line will be shut down due to transformer failure l,tran for: P l,tran =P tran1 +P tran2 -P tran1 P tran2 (16); Transformer water ingress and insulator flashover can both cause power line outages. Assuming the two fault events are independent of each other, the probability of power line failure due to heavy rain is for:

5. The method for improving the pre-disaster resilience of distribution networks by considering typhoon temporality and cyber-physical coordinated control according to claim 1 is characterized by: In step 2, the disaster scenario generation process is as follows: Based on the wind speed data and rainfall data of historical typhoon disasters, the Monte Carlo method was used to generate multiple typhoon disaster scenarios. Then, the scenarios were reduced using the improved K-means method. The wind speed data and rainfall data of each fault period were clustered in the same period, and finally a typical scenario that took into account the correlation between strong wind and heavy rain disasters was obtained.

6. The method for improving the pre-disaster resilience of distribution networks by considering typhoon temporality and cyber-physical coordinated control according to claim 1 is characterized by: Apply the Monte Carlo method and the improved K-means method, specifically including:

1. Optimal number of clusters: The optimal number of clusters is determined based on the clustering effect. The clustering effect is determined by the CH indicator, which is defined as follows: CH(k)=[t B (N-k)] / [t W (k-1)]; In the above formula: CH(k) is the CH index, which is used to evaluate the quality of clustering effect; k is the number of clusters; t B is the sum of squares of the differences between categories; W is the sum of squares of deviations within each class; N is the number of samples; when CH(k) is the largest, the corresponding k value is the optimal number of clusters; 2. Optimal cluster center: Introduce the cohesion function and select samples with high compactness as cluster centers, which is defined as follows: Where: A(S n ,d mean ) is the aggregation function, which can reflect the sample data S n As the center, with the sample average distance d mean The data within the radius and S n The degree of distance, A(S n ,d mean )∈(0,1);S n is the nth cluster center sample; d mean is the sample average clustering; Represents sample S n and Similarity measure between ; represents the n1th domain sample; N is the total number of samples; Represents sample S n and The Euclidean distance between n,1 Represents sample S n The first eigenvalue of ; For samples The previous sample of S n,T Represents sample S n Eigenvalue at time T; Representation sample The eigenvalue before time T; The steps for generating the initial cluster center candidate set are as follows: Step 1: Calculate the density parameter of each data and find the data S corresponding to the maximum value n ; Step 2: If S n Only, then S n Add to the initial cluster center candidate set. If it corresponds to multiple sample data, the data with the smallest cohesion is selected according to the cohesion function and added to the initial cluster center candidate set; Step 3: S n Centered, d mean The data within the radius are deleted from the sample set; Step 4: Repeat Step 1 to Step 3 until you find Initial cluster centers; 3. Typical scenario generation process: The number of clusters corresponding to the maximum value of the CH(k) index is the optimal number of clusters, and its clustering result is the optimal classification. Each classification center is the selected typical scene; For each typical scenario, the impact of strong winds and heavy rain on power lines and communication links is comprehensively considered. Assuming that the impacts of the two types of events on DCPS are independent of each other, we can obtain: In the above formula: P line is the probability of the line being affected by the typhoon; is the probability of line failure due to strong wind; is the probability of line failure due to heavy rain; According to the above formula, the probability P of the line being affected by the typhoon is calculated line ,Then the uncertainty of the line disaster status is handled by Monte Carlo simulation sampling method.

7. The method for improving the pre-disaster resilience of distribution networks by considering typhoon temporality and cyber-physical coordinated control according to claim 6 is characterized by: P line The line status is determined based on the comparison result with a random number uniformly distributed between [0,1]. The mathematical expression is as follows: In the above formula: q ij,t is a 0-1 variable, indicating whether line ij is affected by the typhoon at time t, q ij,t =1 indicates normal operation, otherwise it is affected; P un is a random number, P un ~U(0,1), U(0,1) is 0-1 uniform distribution; P un ~U(0,1) represents P un Obey the uniform distribution of 0-1; After the line is strengthened, the probability of failure is extremely low, assuming that the strengthened line will not fail during the disaster; In addition, since it is impossible to perform emergency repairs on the faulty line during the disaster, the line will remain in the faulty state until the disaster ends, as described below: In the above formula: is a 0-1 variable, indicating the fault status of line ij at time t. Indicates that there is no fault in the line, otherwise it means that there is a fault in the line; x ij is the line strengthening state variable, x ij =1 means line ij has been strengthened, otherwise it has not been strengthened; It is a 0-1 variable, indicating the fault status of line ij at time t+1.

8. The method for improving the pre-disaster resilience of distribution networks by considering typhoon temporality and cyber-physical coordinated control according to claim 1 is characterized by: In step 3, the dynamic response of the distribution network during a typhoon disaster is incorporated into the pre-disaster resilience improvement framework, and a pre-disaster resilience improvement plan is formulated, as follows: The development of resilience enhancement plans relies on simulating the dynamic response decisions of the system during the disaster phase, combining the real-time response plans of the system under multiple scenarios to develop the optimal pre-disaster prevention and reinforcement plan; 1) Pre-disaster prevention measures: Improvements to DCPS resilience in the pre-disaster phase are achieved by strengthening vulnerable components, including vegetation management near towers, strengthening tower conductors, installing flood control measures near transformers, and installing double-hole insulators. 2) Cyber-physical collaborative control solution: During each typhoon disaster-affected period, the operating status of the corresponding physical nodes is monitored in real time through the communication nodes of the information system. The operating status of the corresponding physical nodes is uploaded to the control center of the information system. If the physical node is operating normally, the information system does not make any decisions. If a physical node fails, the information system adjusts the DG output or controls the RCS to disconnect to reconfigure the network and formulates corresponding response measures to reduce the losses caused by physical node failures. For DG nodes, the DG output is adjusted to ensure the power supply needs of its adjacent nodes. For the nodes where the remote switch RCS is located, the RCS is controlled to be switched on and off to achieve dynamic network reconstruction.

9. The method for improving the pre-disaster resilience of distribution networks by considering typhoon temporality and cyber-physical coordinated control according to claim 1 is characterized by: In step 4, the pre-disaster resilience enhancement model includes an objective function, which is specifically as follows: During the pre-disaster prevention phase, the system's dynamic response to each typical disaster scenario is simulated, and a pre-disaster prevention plan is developed with the goal of minimizing system reinforcement costs and simulated load shedding penalty costs. min{f1+E p [f2(x,K)]} (22); In formula (22), f1 is the line enhancement cost; x is the line enhancement plan; K is the typical scenario set; E p [f2(x,K)] is the expected value of the load shedding penalty cost under all typical scenarios K; f2(x,K) is the load shedding penalty cost under all typical scenarios K; The line reinforcement cost is related to the line reinforcement plan, which is determined by typical scenarios. The line reinforcement plan that minimizes the system load shedding penalty cost under all typical scenarios is the optimal plan. In formula (23): c rein is the line reinforcement cost per unit length; L ij is the length of line ij; Ω N is the set of system nodes; For any scene k in the scene set K, we have: In the above formula: c p,i is the unit load shedding penalty cost of node i; is the load shedding of node i at time t; p k is the probability of scenario k occurring; T represents the typhoon impact time.

10. The method for improving the pre-disaster resilience of distribution networks by considering typhoon temporality and cyber-physical coordinated control according to claim 9 is characterized by: In step 4, the pre-disaster resilience enhancement model includes constraints, which include: 2.1) Line reinforcement constraints: Considering the economic efficiency of system operation, it is assumed that the maximum number of line reinforcement is 2.2) Physical system operation constraints: a) Load shedding constraints: Where: is the load active power demand of node i at time t under scenario k; is the reactive load of node i at time t under scenario k; P i L，max and are the upper limit of active power and reactive power of node i respectively; b) Virtual power flow constraints: A virtual flow network is introduced, and a single commodity flow method is used to ensure the connectivity and radial structure of the reconstructed network; In formula (29): Ω B is a set of virtual flow nodes; represents the fault status of line ij at time t in scenario k; N node and N DG are the number of physical system nodes and DGs respectively; In formula (30): is the virtual power flow of branch ij of the virtual power flow network; is the branch jh virtual power flow of the virtual power flow network; V j,t is the virtual power emitted by node j in the virtual power flow network; and are the inflow node set and outflow node set of virtual network node j respectively; In formula (31): is the connection matrix of DG; M is a sufficiently large positive number; c)RCS switch constraints: Considering the safety of the equipment, frequent operation of RCS should be avoided. Assuming that the maximum number of RCS switches is ψ max ; In formula (34): is a 0-1 variable, indicating the on / off state of the RCS at node i at time t+1 in scenario k; is a 0-1 variable, indicating the on / off state of the RCS at node i in scenario k. Indicates that the RCS is closed, otherwise it is open; d) Energy storage constraints: In formula (35): and are the capacities of energy storage i at time t and time t+1 respectively; and are the charging and discharging active powers of energy storage i at time t respectively; and are the charging and discharging efficiencies of energy storage i, respectively; In formula (36): and Configure upper and lower limits for the energy storage i capacity respectively; In formula (37): P i ch,max and are the upper limits of charging and discharging active power of energy storage i respectively; and are 0-1 variables, representing the charge and discharge states of energy storage i at time t; In formula (38): represents the charging reactive power of energy storage i at time t; represents the discharge reactive power of energy storage i at time t; and are the upper limits of charging and discharging reactive power of energy storage i respectively; e) Power flow constraints: The Dist-Flow model is used to describe the radial network flow of the system: Where: P ij,t and Q ij,t is the active power flow and reactive power flow of line ij at time t; r ij and x ij are the resistance and reactance of line ij respectively; and are the inflow node and outflow node of node j respectively; I′ ij,t is the square value of the current of line ij at time t; represents the discharge active power of node i at time t; represents the DG active power of node i at time t; represents the active load shedding amount of node i at time t; P jk,t represents the active power flow of line jk at time t; represents the charging active power of node i at time t; represents the load active power of node i at time t; represents the discharge reactive power of node i at time t; represents the DG reactive power of node i at time t; represents the reactive load shedding amount of node i at time t; Q jk,t represents the reactive power flow of line jk at time t; represents the charging reactive power of node i at time t; represents the load reactive power of node i at time t; To ensure stable system operation, the system power, voltage, and current must also meet the following constraints: -m ij,t +n ij,t ≤U′ i,t -U′ j,t ≤μ ij,t +n ij,t (45); Where: U′ i,t is the square value of the voltage at node i; U′ j,t is the square value of the voltage at node j; auxiliary variable μ ij,t and ν ij,t The introduction of μ is to transform the nonlinear power flow constraint into a linear solvable form. ij,t Represents the voltage amplitude square difference U′ i,t -U′ j,t The upper bound of the absolute value of ν ij,t Represents the voltage amplitude square difference U′ i,t -U′ j,t The offset reference; Perform the second-order cone relaxation on Equation (44), as shown below: In formula (44): I′ ij,t represents the square of the current in line ij at time t; 2.3) Information system operation constraints a) Information flow balance constraints: During a disaster, the control center of the information system collects real-time status information from each communication node, formulates corresponding response measures, and distributes them to each communication node. Information flow is transmitted in the form of communication links. The information flow balance constraint of the communication link is expressed as follows: In the above formula: is the information flow through the communication link ij; ω in (j) and ω out (j) are the inflow node set and outflow node set of communication node j respectively; is the information load reduction of communication node j at time t; is the information load of communication node j; is a 0-1 variable, indicating the energy supply status of communication node j, It indicates that the node is supplying energy normally, otherwise it indicates insufficient energy supply; is a 0-1 variable, indicating the operating status of the communication link ij, Indicates that the communication link ij is operating normally, otherwise it indicates a fault; T ij is the bandwidth of the communication link ij; b) Information load reduction constraints: If the information load at node i is reduced too much, the node will not be able to fully receive the command from the control center. At this time, the communication node fails. The mathematical expression is as follows: In formula (51): is the control state variable of communication node i; a i is the control capability of communication node i; is the information load of communication node i; 2.2) DCPS coupling constraints: a) Physical system energy constraints: Information systems require energy from physical systems to ensure the normal operation of nodes. When the physical node corresponding to a communication node cannot meet its energy supply requirements, the communication node will be unable to execute control commands. The mathematical expression is as follows: Where: is a 0-1 variable, indicating the energy supply status of communication node j; P i cyb,min is the lower limit of energy demand of communication node i; is the energy supply of communication node i at time t; Ω T is the set of communication nodes; Ω Y is the source node; P i cyb,min is the lower limit of energy demand of communication node i; b) Information system control constraints: For a DG node, if the corresponding communication node fails, the control center cannot adjust the power output. To ensure the safe operation of the system, the corresponding DG node stops running after the communication node fails. The mathematical expression is as follows: In formula (54): and are the active power and reactive power of DG at node i at time t; P i DG,max and are the upper limit of active power and reactive power of DG at node i respectively; For the node where the RCS is located, if the corresponding communication node fails, the control center cannot control the RCS switching; therefore, the RCS controlled by the failed communication node remains disconnected. The mathematical expression is as follows: In formula (55): Ω C The node set where RCS is located; is a 0-1 variable, indicating the RCS switching command issued by the control center at time t. It means that the control RCS is closed and the corresponding interconnection line is put into operation. Otherwise, it means that the control RCS is disconnected and the corresponding interconnection line is out of operation.

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