Distribution system resilience assessment method based on dynamic Bayesian network

Abstract

The present invention provides a method for evaluating the resilience of a distribution system based on a dynamic Bayesian network, which belongs to the technical field of disaster assessment and power system resilience analysis. The method includes: using the Chicago unimodal rainfall model to simulate rainstorm disasters, combining a digital elevation model with a two-dimensional hydrodynamic model to simulate urban waterlogging; establishing a distribution equipment failure model based on water depth data to obtain node failure probability; using the Monte Carlo sampling method to simulate the state of the distribution system; constructing a dynamic Bayesian network to calculate power accessibility; considering load withdrawal and line topology changes to establish a distribution network flow model, calculate load loss and voltage offset, and evaluate system risk. The present invention comprehensively considers the impact of rainstorm disasters on the distribution network through multi-model coupling and probability analysis, accurately evaluates the resilience of the distribution network under rainstorm disasters, provides a scientific basis for power system planning, design, and emergency management, and improves the disaster resistance and reliability of the distribution network.

Description

Technical Field

[0001] The present invention relates to the technical field of disaster assessment and power system resilience analysis, and in particular to a distribution system resilience assessment method based on a dynamic Bayesian network. Background Art

[0002] Under heavy rain disasters, the resilience assessment of the distribution network is crucial to ensuring the reliability and safety of power supply. Traditional assessment methods mostly focus on post-disaster restoration, and are insufficient in handling the dynamic evolution and uncertainty of the distribution network under extreme weather conditions. In recent years, Bayesian networks have been widely used in related fields due to their advantages in handling uncertainty problems, but static Bayesian networks are difficult to accurately represent the impact of time slices throughout the disaster process. Dynamic Bayesian networks are more suitable for systems that need to study time-varying processes, and can be combined with heavy rain disaster scenarios to complete disaster simulation work. In terms of distribution network flow models, existing studies mostly consider single factors or static conditions, and lack modeling of the dynamic processes of load decommissioning and line topology changes under extreme heavy rain disasters, making it difficult to accurately assess the resilience and risks of the system under complex disaster scenarios. Summary of the Invention

[0003] The purpose of this invention is to provide a distribution system resilience assessment method based on a dynamic Bayesian network. Through multi-model coupling and probability analysis, it comprehensively considers the impact of rainstorm disasters on the distribution network, accurately assesses the resilience of the distribution network under rainstorm disasters, provides a scientific basis for power system planning, design and emergency management, and improves the disaster resistance and reliability of the distribution network.

[0004] To achieve the above objectives, the present invention provides a distribution system resilience assessment method based on a dynamic Bayesian network, comprising the following steps:

[0005] Step S1: Use the Chicago Unimodal Rainfall Model to simulate rainstorm disasters, obtain rainstorm intensity, combine the digital elevation model with the two-dimensional hydrodynamic model, and simulate urban waterlogging with CI as the grid unit, where CI represents critical infrastructure;

[0006] Step S2: Based on the water depth data, establish a distribution equipment failure model to obtain the failure probability of each node;

[0007] Step S3: using the Monte Carlo sampling method to simulate the state of the power distribution system, and combining the node failure probability obtained in step S2 to generate the operation status of the power distribution system under different states;

[0008] Step S4: construct a dynamic Bayesian network based on the topological connections between CI elements. Based on the power grid topology, each distribution device and the nodes in the network are used as the node set in the Bayesian network. Each edge represents the connection relationship between the nodes, and a conditional probability equation is constructed between the parent and child nodes. The power accessibility rate is calculated using the water depth data and the node failure probability.

[0009] Step S5: Considering the load shutdown and line topology changes of the distribution system caused by extreme rainstorm disasters, a distribution network flow model is established, and constraints and objective functions are introduced. The distribution system status and power accessibility are input into the distribution network flow model, and the system load loss and voltage offset are calculated. Then, the expectation and variance of the load loss and voltage offset are calculated to evaluate the system risk, and finally the resilience assessment results of the distribution network under rainstorm disasters are obtained.

[0010] Preferably, in step S1, the rainstorm intensity calculation formula is as follows:

[0011] ;

[0012] in, express Intensity of rainstorm at any moment; Indicates the duration of heavy rain; Indicates the rainstorm recurrence period; 、 、 、 Represents parameters related to rainstorm characteristics, among which, It represents the 1-minute design rainfall within the unit recurrence period; represents the rainfall duration correction parameter; represents the rainfall force variation parameter; Represents the rainstorm attenuation index.

[0013] Preferably, in step S1, the rainstorm intensity is obtained, and the digital elevation model and the two-dimensional hydrodynamic model are combined to simulate urban waterlogging using CI as the grid unit. The specific operations are as follows:

[0014] Grid the map;

[0015] Using the vector calculation formula converted from the Manning formula, combined with the quality of the water flow in the grid , gravitational acceleration and the water surface elevation difference between adjacent grids , calculate the ground friction;

[0016] ;

[0017] ;

[0018] in, represents the water flow pressure of adjacent grids; represents the ground friction of the grid; Indicates water flow rate; express The depth of water accumulation in the grid where the power distribution equipment is located at any given moment; represents the Manning coefficient;

[0019] Will 、 Bring in And simplify, calculate the water flow speed in the four directions of east, west, south and north;

[0020] ;

[0021] ;

[0022] in, Indicates water density; Indicates the grid width; Indicates a time interval; Indicates the water flow speed in the four directions of east, west, south and north; Indicates the height difference in the four directions of east, west, south and north;

[0023] According to the calculated water flow velocity in the four directions of east, west, south and north, combined with the urban building coverage rate, the grid's four directions of east, west, south and north are obtained. Water flow at any moment;

[0024] ;

[0025] in, Indicates along 、 、 、 Four directions Water flow at any moment; represents the urban building coverage rate; Indicates the west direction; Indicates the east direction; Indicates the north direction; Indicates the south direction;

[0026] Considering the discharge of urban drainage wells, model it as negative water flow and calculate Drainage flow in the grid at any moment;

[0027] ;

[0028] in, express Drainage flow in the grid at any moment; Indicates the number of drainage wells in the grid; Represents the drainage coefficient, which is a number between [0, 1]; Indicates the cross-sectional area of ​​the drainage well;

[0029] Combine the drainage flow in the grid with the water flow in the four directions of east, west, south and north, and calculate the grid according to the water flow conversion coefficient and time interval. In time interval The water depth at the last moment is calculated, and the iterative grid depth is updated to obtain the water accumulation situation of each grid;

[0030] ;

[0031] in, represents the water flow conversion coefficient; Representation Grid West direction grid flow direction grid water flow; Representation Grid East direction grid flow direction grid water flow; Representation Grid North direction grid and flow direction grid water flow; Representation Grid South direction grid flow direction grid of water flow.

[0032] Preferably, in step S2, based on the water depth data, a distribution equipment failure model is established to obtain the failure probability of each node. The specific operations are as follows:

[0033] ;

[0034] in, Indicates the The power distribution equipment on each node is at The probability of failure; Indicates the designed flood-proof height of the distribution station / room or box-type substation; Indicates the ground elevation of the cable joints of the high-voltage switchgear in the station.

[0035] Preferably, in step S3, the Monte Carlo sampling method is used to simulate the state of the power distribution system, and the operation status of the system under different states is generated in combination with the node failure probability obtained in step S2. The specific operations are as follows:

[0036] ;

[0037] in, Indicates the Nodes at time The working status of the node, 0 means the node is working normally, and 1 means the node is failed; Represents a random number.

[0038] Preferably, in step S4, the Bayesian network after the rainstorm disaster occurs is constructed as a set :

[0039] ;

[0040] in, Represents a collection of nodes; represents a set of directed edges; Represents the prior probability of each node, which is composed of the failure probability of each node.

[0041] Preferably, in step S4, when the node is in the running state, When , the power availability rate is the joint probability; when the node is in a fault state, When , the power availability is the inverse of the joint probability;

[0042] ;

[0043] in, Indicates the Node time Node working status; Representation node The parent node time Node working status; express Node in The probability used to calculate the joint probability at this moment is related to the state of the node. When the state of the node is normal, , when the node status is abnormal, ; express The parent node of the node is The probability of the moment used to calculate the joint probability; Indicates the power availability rate; A value indicating the working status.

[0044] Preferably, in step S5, the distribution network flow model is as follows:

[0045] ;

[0046] in, Represents simulation Minimize load loss costs after the second; Indicates the number of simulations; Indicates the The load loss cost caused by the simulation cycle, Indicates starting from the first simulation.

[0047] Preferably, in step S5, the objective function is as follows:

[0048] ;

[0049] in, Indicates the The loss cost caused by the loss of unit power load of each node; Indicates the nodes Power lost at any moment; 、 Indicates the operation and maintenance loss costs caused by charging and discharging unit power energy of energy storage resources; 、 Representation node Energy storage equipment Power lost at any moment; Represents the set of nodes where energy storage resources are located in the power distribution system.

[0050] Preferably, in step S5, the constraints include:

[0051] Power distribution system nodes At the moment Active and reactive power balance constraints of nodes At the moment The difference between the load power and its load, load loss and the power constraints of the connected power supply; At the moment The power supply power and the constraints of distributed power supply and energy storage output; At the moment The load reactive power and the connected distributed generation reactive power constraints; the upper and lower limit constraints of line transmission power; the load loss amount and load loss constraints; node voltage balance constraints; node voltage upper and lower limit constraints; node Energy storage equipment Power balance constraint at time; node Energy storage equipment Constraints on the unique charging and discharging state at all times; constraints on the energy capacity of energy storage equipment; and constraints on the upper and lower limits of the charging and discharging power of energy storage equipment.

[0052] Therefore, the present invention adopts the above-mentioned distribution system resilience assessment method based on dynamic Bayesian network, and the beneficial technical effects are as follows:

[0053] (1) Accurately simulate the impact of disasters: By simulating the impact of rainstorm disasters on urban waterlogging, a probability model for power distribution equipment outage is established to effectively reflect the specific impact of rainstorm disasters on the power distribution system and provide basic data support for subsequent evaluations.

[0054] (2) Improve the accuracy of assessment: By using dynamic Bayesian networks, we can fully consider the spatiotemporal correlation of nodes and analyze the impact of node load loss in combination with the importance of node load, thereby significantly improving the accuracy of system resilience assessment and making the assessment results closer to reality.

[0055] (3) Providing targeted improvement suggestions: The proposed resilience assessment method innovatively combines an outage probability model with a dynamic Bayesian network to accurately locate vulnerable nodes in the system. This provides more targeted guidance and suggestions for improving system resilience, helping decision makers develop scientific and precise measures to enhance the distribution system's ability to cope with rainstorm disasters. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 is the rainstorm intensity map;

[0057] Figure 2 This is a grid processing diagram of the power distribution system;

[0058] Figure 3 is the water flow direction diagram;

[0059] Figure 4 This is the flooding analysis diagram of the high-voltage switchgear of the power distribution system;

[0060] Figure 5 Simulate a flow chart for the Monte Carlo sampling method;

[0061] Figure 6 To transform the Bayesian graph;

[0062] Figure 7 This is a simple Bayesian network diagram;

[0063] Figure 8 It is a Bayesian computation graph;

[0064] Figure 9 It is the topology diagram of the power distribution system;

[0065] Figure 10 is the statistical and fitting analysis diagram of the rain peak coefficient, where: Figure 10 (a) is the interval and frequency diagram of the rain peak coefficient. Figure 10 (b) is the probability of the rain peak coefficient interval and the fitting curve;

[0066] Figure 11 This is the system risk assessment indicator analysis chart, where: Figure 11 (a) is the expected value of load loss, Figure 11 (b) is the expected system voltage offset;

[0067] Figure 12 Comparison of load loss before and after using dynamic Bayesian analysis;

[0068] Figure 13 This is the time series diagram of extreme rainstorm;

[0069] Figure 14 This is the grid water depth change map;

[0070] Figure 15 is the failure probability change diagram of distribution network nodes;

[0071] Figure 16 Divide the change process diagram for system islands;

[0072] Figure 17 It is a dynamic change diagram of the system's distributed power supply and energy storage resources, where: Figure 17 (a) is the system distributed power output diagram, Figure 17 (b) is the energy change diagram of the system energy storage resources;

[0073] Figure 18 It is a dynamic analysis diagram for system performance evaluation, where: Figure 18 (a) is the diagram of the system node voltage change process. Figure 18 (b) is a comparison diagram of load losses in different systems;

[0074] Figure 19 This is the system resilience diagram. DETAILED DESCRIPTION

[0075] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0076] Unless otherwise defined, technical or scientific terms used in the present invention shall have the same meaning as commonly understood by one of ordinary skill in the art to which the present invention belongs.

[0077] Example 1

[0078] Step S1: Use the Chicago unimodal rainfall model to simulate rainstorm disasters, obtain rainstorm intensity, combine the digital elevation model with the two-dimensional hydrodynamic model, and simulate urban flooding with CI as the grid unit, where CI represents critical infrastructure.

[0079] The intensity of rainstorms in different regions is expressed as follows:

[0080] (1);

[0081] in, Indicates the duration of heavy rain; express Intensity of rainstorm at any moment; Indicates the rainstorm recurrence period; 、 、 、 Represents parameters related to rainstorm characteristics, among which, It represents the design rainfall of 1 minute within the unit recurrence period. represents the rainfall duration correction parameter, represents the rainfall variation parameter, Represents the rainstorm attenuation index.

[0082] This embodiment considers a single-peak rain type. The rainstorm intensity is represented as two parts, the pre-peak part and the post-peak part, as shown in Figure 1 , formula (2) represents the calculation formula of the rain peak coefficient, formula (3) represents the rainstorm intensity before the peak, and formula (4) represents the rainstorm intensity after the peak:

[0083] (2);

[0084] (3);

[0085] (4);

[0086] in, represents the rain peak coefficient; represents the period before the peak; Indicates the duration of heavy rain; represents the period after the peak; Indicates pre-peak time Rainfall intensity (mm / min); Post-peak time rainfall intensity. , which indicates the location of the peak precipitation during this rainfall process. According to the time of the peak precipitation, the rainfall process is considered to be two stages: pre-peak and post-peak.

[0087] Grid the map, such as Figure 2 shown.

[0088] Using the vector calculation formula converted from the Manning formula, combined with the quality of the water flow in the grid , gravitational acceleration and the water surface elevation difference between adjacent grids , calculate the ground friction:

[0089] (5);

[0090] (6);

[0091] in, represents the water flow pressure of adjacent grids; represents the ground friction of the grid; Indicates water flow rate; express The depth of water accumulation in the grid where the power distribution equipment is located at any given moment; represents the Manning coefficient.

[0092] (7);

[0093] Formula (7) is the momentum theorem.

[0094] Substitute equations (5) and (6) into equation (7) to simplify:

[0095] (8);

[0096] (9);

[0097] in, is the water density; is the grid width; Indicates a time interval; Indicates the water flow speed in the four directions of east, west, south and north; Indicates the height difference in the four directions of east, west, south and north.

[0098] Formula (9) is a quadratic equation about velocity. Using the discriminant of whether the equation has roots, we can know that it has two roots, positive and negative, because , so we discard the negative root and take the positive root. When calculating the water depth of each grid, we only consider the flow in the four directions of east, west, south and north. Figure 3 , for the grid , only considering 、 、 、 Four directions; northwest is not considered ,northeast ,southwest ,southeast With Grid This is because the water flow between the computational grid The depth of water next to the grid can be taken into account. 、 、 、 , combined with the urban building coverage, we get the four directions of the grid Water flow at the moment:

[0099] (10);

[0100] in, express 、 、 、 Four directions Time flow to the grid water flow; Indicates the urban building coverage rate.

[0101] When calculating water flow, the discharge of urban drainage wells is also taken into account and modeled as negative water flow:

[0102] (11);

[0103] Where: express Drainage flow in the grid at any moment; Indicates the number of drainage wells in the grid; is the drainage coefficient, which is a number between [0, 1]; Indicates the cross-sectional area of ​​the drainage well.

[0104] According to equations (9), (10), and (11), the grid can be calculated In time interval back The water depth at the moment is calculated, and the grid depth after iteration is updated in sequence through formula (12). The simulation of urban rainstorm is completed.

[0105] (12);

[0106] Where: represents the water flow conversion coefficient; Representation Grid West direction grid flow direction grid water flow; Representation Grid East direction grid flow direction grid water flow; Representation Grid North direction grid and flow direction grid water flow; Representation Grid South direction grid flow direction grid of water flow.

[0107] At this point, the simulation of urban waterlogging caused by rainfall is completed.

[0108] Step S2: power distribution equipment failure model.

[0109] The probability of equipment failure caused by rainstorm disasters is dynamic and changes with the depth of water accumulation caused by rainstorms, such as Figure 4 In the early stages of rainfall, the impact of rain on power distribution equipment is minimal. In the middle stages of rainfall, rainwater can cause surface water accumulation in cities. When surface water exceeds the flood control height of power distribution equipment, the probability of power distribution equipment failure increases rapidly. This embodiment uses the grid as the basic unit to establish the relationship between the time-varying water depth and the probability of power distribution equipment failure:

[0110] (13);

[0111] Where: Indicates the The power distribution equipment on each node is at The probability of failure; express The degree of water accumulation in the grid where the device is located at all times; Indicates the designed flood-proof height of the distribution station (room) or box-type substation; represents the ground elevation of the cable joint of the high-voltage switchgear in the station; the rainfall depth is converted into the failure rate of the distribution equipment through formula (13).

[0112] Step S3: A method for evaluating the resilience of an urban power distribution system based on a dynamic Bayesian network.

[0113] Power distribution equipment is generally installed on corresponding nodes, so this embodiment uses the failure probability of the power distribution equipment as the node failure probability for analysis. First, the state of the power distribution system is simulated.

[0114] The distribution system state is simulated using the Monte Carlo method. Assuming that changes in the distribution system's operating state due to rainstorms are unrelated between each node and the corresponding time, the state sampling method is used to sample the node state and simulate the distribution system state.

[0115] Based on the probability of node failure, Time Node The working status can be expressed as:

[0116] (14);

[0117] Where: Indicates the Nodes at time The working status of the node, 0 means the node is working normally, and 1 means the node is failed; Represents a random number [0, 1]. When the node Exit operation; when When the node Normal operation. After being shut down, the extreme rainstorm disaster does not allow maintenance personnel to arrive for on-site inspection, so the failure probability of the node is 1 at the following time. After the rain stops and maintenance personnel repair the equipment to return to normal working state, the failure probability of the node becomes related to the depth.

[0118] Based on this, the Monte Carlo sampling method is used for simulation, such as Figure 5 .

[0119] Combined with the status of the nodes, the system is divided into three different islands using the depth-first search method: a single node, multiple nodes without power, and multiple nodes with power. This is used to calculate the load loss in the subsequent calculation. The first category is determined by whether there is power. If there is no power, it is calculated as a load loss. ; The second type is directly calculated as load loss ; The third type is to calculate the system load loss after calculating the current in the island , total load loss It can be expressed as:

[0120] (15);

[0121] Step S4: construct a dynamic Bayesian network based on the topological connection between CI elements. Based on the power grid topology diagram, each distribution device and the nodes in the network are used as the node set in the Bayesian network. Each edge represents the connection relationship between the nodes, and a conditional probability equation is constructed between the parent and child nodes. The power accessibility rate is calculated using the water depth data and the node failure probability.

[0122] Rainstorm disasters are uncertain. This embodiment uses a Bayesian network that can handle uncertainty to model the disaster. The Bayesian network after the rainstorm disaster occurs is constructed as a set :

[0123] (16);

[0124] in, Represents a collection of nodes; represents a set of directed edges; represents the prior probability of each node, which is composed of the failure probability of each node;

[0125] Based on the power grid topology diagram, the topology structure is converted into a Bayesian network diagram, such as Figure 6 , each device and node in the network is the node set in the Bayesian network , Represents the Nth node in the Bayesian network; assuming that each node has only two states, 0 and 1, the connection relationship between nodes is constructed as an edge set according to the example , each edge has its own unique direction, such as It means Node pointing Node, representing The node is The parent node of the node, the parent node of each node constitutes a set, expressed as ,like Figure 7 As shown, the parent nodes of node E in the figure are B and C, which can be expressed as In addition, the state variables of each node At a certain moment, there are only two states: normal operation and abnormality. The possible values ​​are , =1, 2; representing normal working state and abnormal working state respectively, normal is recorded as 1, abnormal is recorded as 0. Based on this, the conditional probability equation between the parent and child nodes is constructed.

[0126] When calculating the probability of each node, the Bayesian network only considers the influence of the parent node on it. Figure 8 The method shown, where A represents the parent node of node B, and B represents the child node of node A, 、 、 、 Respectively represent the working status of the parent and child nodes at time 0 and time 1, 1 is the fault state, 0 is the normal state, 、 Represents the prior probability of the node. Considering the mutual influence of parent and child nodes in time and space, the joint probability considering the temporal and spatial correlation is calculated. Among them, all conditional probability matrices The various conditional probability values ​​​​compose the joint probability table, using the joint probability, combined with different node operating states , the power accessibility of the corresponding node is obtained, that is, when the node is in operation, When , the power availability rate is the joint probability; when the node is in a fault state, When , the power availability is the inverse of the joint probability.

[0127] (17);

[0128] Where: Indicates the Node time The working status of the node, Representation node The parent node time The working status of the node, express Node in The probability used to calculate the joint probability at this moment is related to the state of the node. When the state of the node is normal, , when the node status is abnormal, ; express The parent node of the node is The probability used to calculate the joint probability at each moment is known. The power reachability of any variable can be calculated using the dynamic Bayesian network.

[0129] The total load loss after taking into account the Bayesian network can be expressed as:

[0130] (18).

[0131] Step S5: Considering the load shutdown and line topology changes of the distribution system caused by extreme rainstorm disasters, a distribution network flow model is established, and constraints and objective functions are introduced. The distribution system status and power accessibility are input into the distribution network flow model, and the system load loss and voltage offset are calculated. Then, the expectation and variance of the load loss and voltage offset are calculated to evaluate the system risk, and finally the resilience assessment results of the distribution network under rainstorm disasters are obtained.

[0132] 5.1. System power flow model.

[0133] Since extreme rainstorms can cause the distribution system load to shut down, line topology to change, and power flow to change, it is necessary to model the power flow of the distribution system when conducting resilience assessment. This embodiment models the distribution system as follows:

[0134] (19);

[0135] in, Represents simulation Minimize the load loss cost after the second Indicates the number of simulations, Indicates the The load loss cost caused by the simulation cycle.

[0136] (20);

[0137] Where: Indicates the The loss cost caused by the loss of unit power load of each node (yuan / kW); Indicates the nodes Power lost at any moment (kW); 、 Indicates the operation and maintenance loss cost caused by charging and discharging unit power energy of energy storage resources (yuan / kW); 、 express Energy storage devices on nodes Power lost at any moment (kW); Represents a set of nodes of the power distribution system; Represents the set of nodes where energy storage resources are located in the power distribution system.

[0138] The constraints considered are:

[0139] (twenty one);

[0140] (twenty two);

[0141] (twenty three);

[0142] (twenty four);

[0143] (25);

[0144] (26);

[0145] (27);

[0146] (28);

[0147] (29);

[0148] (30);

[0149] Where: Indicates line Child nodes on ; Indicates line The parent node on ; Indicates line At the moment the active current flowing through; Representation node At the moment Active power demand; Indicates line exist The current of merit flowing through every moment; Indicates line At the moment Reactive power flowing through; Representation node At the moment Reactive power demand; Indicates line exist The reactive current that flows through all the time; Representation node At the moment Active power of the connected load; Representation node At the moment Lost load active power; Representation node At the moment Active output of the connected power supply; Indicates the A distributed power source at time The meritorious contribution; express The energy release power of the energy storage device on the node; express Energy storage power of the energy storage device on the node; Indicates the Distributed power generation in Reactive output power at all times; Represents the set of nodes where distributed power sources are located in the power distribution system; Represents the set of lines connecting all nodes; 、 Indicates the transmission line Upper and lower limits of transmitted active power; 、 Indicates the transmission line Upper and lower limits of transmitted reactive power; Representation node At the moment The square of the voltage; 、 Indicates the transmission line resistance and reactance on the Representation node Lower upper limit of the square of the voltage.

[0150] Equations (21) and (22) represent the distribution system nodes At the moment The active and reactive power balance constraints of the node At the moment The load power of the node is the difference between its load and load loss and the power constraint of the connected power supply; Equation (24) represents the node At the moment The constraints of power supply power, distributed power supply and energy storage output; Equation (25) represents the node At the moment The load reactive power and the connected distributed generation reactive power constraints; Equations (26) and (27) represent the upper and lower limit constraints of the line transmission power. When the node At the moment Exit the run, then the line it is connected to Disconnect, that is, limit the power flowing through it to 0; Equation (28) represents the load loss amount and load loss constraint; Equation (29) represents the node voltage balance constraint; Equation (30) represents the node voltage upper and lower limit constraints.

[0151] (31);

[0152] (32);

[0153] (33);

[0154] (34);

[0155] (35);

[0156] Where: Representation node Energy storage equipment Energy storage capacity status at the moment; Indicates the energy conversion efficiency of energy storage equipment; Representation node Energy storage equipment Always in charging state; Representation node Energy storage equipment Always in energy-releasing state; 、 Indicates the minimum and maximum capacity of the energy storage device; 、 Indicates the minimum active power for charging and discharging energy storage equipment; 、 Indicates the maximum active power of the energy storage device charging and discharging.

[0157] Formula (31) represents the node Energy storage equipment The power balance constraint at time t, Equation (32) represents the node Energy storage equipment The unique state constraint of charging and discharging at each moment, Equation (33) represents the energy capacity constraint of the energy storage device; Equations (34) and (35) represent the upper and lower limit constraints of the charging and discharging power of the energy storage device. When it is in the working state, it is constrained; otherwise, its charging and discharging power is 0.

[0158] (36);

[0159] (37);

[0160] Where: For the Distributed power generation in Active output power at all times; For the Distributed power generation in Reactive output power at all times; 、 Indicates the upper and lower limits of the active output of distributed power sources; 、 Indicates the upper and lower limits of the reactive output of distributed generation.

[0161] Formulas (36) and (37) represent the The upper and lower power limits of distributed power generation units are set.

[0162] 5.2. System indicators.

[0163] The system load loss is selected as the system risk indicator. By calculating the load loss, the damage caused by extreme rainstorm disasters to the system can be intuitively reflected.

[0164] (38);

[0165] (39);

[0166] (40);

[0167] (41);

[0168] in, represents the load risk index of the system when the Bayesian network is not considered; Indicates the load risk index of the system; Indicates the number of sampling times of the system during the simulation; Indicates the working status of the system load; Representation node exist Power availability at the moment; Indicates the voltage risk index of the system; Indicates the Sub-sampling system voltage offset; Indicates the reference value of the square of the system voltage.

[0169] Equation (39) represents the system's load loss risk index, which is obtained by the expected load loss considering the power availability after each simulation; Equation (40) represents the system's voltage excursion risk index, which is obtained by the expected voltage excursion after each simulation process.

[0170] The present invention is further described below through specific examples.

[0171] Case information.

[0172] This example uses the IEEE 33-node example for analysis. The topology is as follows: Figure 9 Using DEM data for gridding, each node is numbered, from left to right and from top to bottom, and considered a 90×90 square for rainfall simulation. According to the legend, colors closer to brown indicate higher terrain, while colors closer to blue indicate lower terrain. Consequently, changes in precipitation depth vary after extreme rainstorms.

[0173] In the IEEE-33 node system, node 0 is the source node, and the remaining nodes are load nodes. Nodes 1, 3, 5, 8, 11, 13, 16, 19, 24, 27, and 30 are critical load nodes, while the remaining nodes are general load nodes. Load loss charges are 100 and 5 yuan / kW, respectively, based on load level. The system includes three energy storage devices and distributed power generation (DGs). Each energy storage device has an energy capacity of 500 kW·h, and its charge and discharge power is half of its energy capacity. The output limit of each DG is 500 kW. The unit power charges for charging and discharging the energy storage resources are 3 yuan / kW and 4 yuan / kW, respectively.

[0174] The optimization model was built using the Yalmip optimization toolkit and solved using the Gurobi solver. The computer CPU model was Intel Core I7 with a main frequency of 2.10 GHz and a memory capacity of 16 GB.

[0175] Disaster scenario information.

[0176] This example mainly considers extreme rainstorm disasters. When a disaster occurs, the water depth of the grid where each node is located changes, which causes the failure probability of the high-voltage switchgear at the distribution system node to change. When a node failure occurs, the connected line is disconnected, the system exits operation, and the system is split into different islands. It is assumed that after the island division, the system cannot obtain energy from the upper power grid. The entire simulation process takes 4 hours. During this period, the grids where all nodes are located are affected by the rainfall in the same way, that is, the cumulative rainfall in each grid at the same time is the same. The failure rate of the node will vary with the precipitation depth of the corresponding grid. The node failure rate is calculated by using a random number between [0, 1]. By comparing, we can determine the operating status of the nodes at the corresponding time. Using the islands divided at different times, we can calculate the system power flow distribution at the corresponding time and calculate the system load loss.

[0177] In order to achieve statistically significant load loss and voltage deviation, 100 extreme rainstorm disaster simulations were carried out. In each simulation, the rainfall peak coefficient and rainstorm recurrence period were different to characterize the impact of different rainfall intensities on the system.

[0178] The selection of the rain peak coefficient is to truly simulate the system's response under different rainstorm conditions. The national rainfall data is selected, and the classification standard is heavy rainstorm: the total precipitation within 24 hours is more than 250mm. By selecting the days of heavy rainstorm, the time of daily rainfall peak can be obtained. By counting the location of the peak time, the rain peak coefficient and its occurrence frequency in a day can be obtained. According to the location of the rain peak coefficient, it is divided into 10 equal intervals between 0 and 1. The number of occurrences of the rain peak coefficient in the data from 2012 to 2023 is counted, such as Figure 10 As shown in (a) in .

[0179] Normalize the statistical data, calculate the probability of occurrence of each interval, and fit it using a second-order polynomial, such as Figure 10 As shown in (b) in the figure, the probability curve of the interval value of the rain peak coefficient can be obtained:

[0180] (42);

[0181] in, is the range of rain peak coefficient values, is the probability corresponding to the value interval.

[0182] The rain peak coefficient is randomly selected using the curve, and the rainstorm recurrence period is randomly selected from the set [50, 60, 70, 80, 90, 100] to complete the simulation of different rainstorm intensities.

[0183] During the simulation of 100 extreme rainstorm disasters, the expectation and variance of load loss and voltage deviation during each simulation were calculated to make the evaluation process closer to the actual situation. Figure 11 From (a) in the figure, we can see that the system’s load loss is about 4.9kW. Figure 11 As shown in (b), the system voltage offset is approximately 135, which verifies the accuracy of the risk assessment.

[0184] The above is the situation after 100 simulations. In order to analyze the performance of the system, one of the rainstorm disaster situations was selected for specific analysis. Figure 12Regarding load loss, using a dynamic Bayesian approach, taking into account the impact of time and space on load loss, we found that using a Bayesian network resulted in nearly identical load losses for nodes 2, 11, 20, 21, 22, 24, 25, and 27, which had previously experienced significant load loss, compared to the approach without the Bayesian network. While the assessment of these nodes was accurate, it did not reduce their vulnerability. These nodes are susceptible to heavy rainstorms due to their low geographical location, resulting in significant load losses after a heavy rainstorm. For nodes 12 and 14, load supply efficiency decreased after accounting for power availability. Furthermore, nodes 12 and 14 are non-critical loads. To improve system security and disaster response capabilities in extreme heavy rainstorms, reducing these loads can help ensure critical loads are supplied. For nodes 4, 7, 28, 32, and 33, even after accounting for power availability, power supply efficiency decreased after the failure, due to the influence of their connected parent nodes. This reduced power supply efficiency after completing power supply to critical loads within the islands, resulting in partial load loss. Compared with the situation before the Bayesian network was used, the impact of extreme rainstorm disasters on the system was underestimated, which would lead to misjudgment by dispatchers in actual operations, which could cause huge economic losses.

[0185] At the same time, after evaluation using the proposed method, the load loss increases significantly at nodes 12, 14, 7, and 4, accounting for 70.89% of the total increase. Compared with the prior load loss calculated by the original method, the original method can only find nodes 24 and 25 with larger load losses, and pays less attention to the load loss caused by the connection relationship of the nodes. The evaluation method proposed in this invention can deeply explore the hidden vulnerable nodes in the system. The identification of these nodes can provide decision makers with more accurate risk assessment results under heavy rain disasters, helping them to formulate more scientific and accurate measures to enhance the system's ability to respond to heavy rain disasters.

[0186] The measurement time interval Set it to 5 minutes, and obtain the rainfall time series data according to formula (1), as follows: Figure 13 As shown. Among them, =9.898, =1.333, =7.1, =0.656, =100.

[0187] Figure 13 It can be seen that the rainfall intensity reaches its maximum around the 60th minute, at approximately 10 mm / min. The rainfall amount also increases most rapidly around the 60th minute, reaching 0.587 m at the 240th minute.

[0188] Each node in the calculation example is equipped with a high-voltage switchgear. Depending on the installation of the high-voltage switchgear, each node will have different flood control heights, generally between 0.2 and 0.5 meters. The flood control heights for important loads in the node are shown in the following table. The flood control heights of the remaining nodes are all set at 0.2 meters. At the same time, the cable connectors in the cabinet are grounded at an elevation of 0.3 meters.

[0189] Table 1 Designed flood prevention heights for some nodes

[0190] ;

[0191] Using rainfall data, Figure 2 The grid shown simulates the change process of rainfall and water accumulation, as shown in Figure 14 shown.

[0192] Depend on Figure 14 As can be seen, throughout the rainfall process, the grid water depth shows a trend of first increasing and then decreasing over time. Initially, the grid water depth is essentially zero. This is because each grid contains the city's drainage system. Initially, the water is drained through the drainage system due to insufficient precipitation, preventing accumulation. In the middle phase, the grid water depth begins to rise. This is because the rainfall intensity exceeds the drainage system's drainage threshold, preventing the water from draining, leading to urban flooding. Furthermore, the grid depth varies between grids due to differences in water surface elevation. When water cannot drain, it flows from higher to lower grids, resulting in varying water depths. In the second half of the rainfall, the rainfall intensity gradually decreases, allowing the city's drainage system to drain the water, and the grid water depth gradually decreases to zero. The grids containing nodes 3, 11, 19, 27, and 29 were severely affected.

[0193] Substitute the water depth into formula (13) to calculate the failure probability of each node, as follows: Figure 15 As shown in Figure 1, the node failure probability changes over time. When rainfall intensity and water volume increase, the failure probability increases. Conversely, the failure rate decreases. Different nodes and different times have different failure probabilities.

[0194] According to the failure rate, we introduce formula (14) to simulate the failure state of each node. When a node fails, it will fail during the subsequent rainstorm. The system topology changes continuously during the whole process. The specific changes in the system island division are as follows: Figure 16 In the first 75 minutes, the system operated normally; at 75 minutes, nodes 23, 27 and their connected lines stopped working, and the system was divided into 3 islands; at 80 minutes, node 29 and its connected lines stopped working, and the system had 4 islands, but the number of nodes in one of the islands decreased; at 90 minutes, node 3 and its connected lines stopped working, and the system was divided into 5 islands; at 130 minutes, node 11 and its connected lines stopped working, and the system was divided into 6 islands.

[0195] Based on the different island divisions and system models, the Gurobi solver is called to solve the system power flow of a single island. The output of the power supply within the island, the state changes of the energy storage, and the voltage stability are viewed throughout the entire process. Finally, the system load loss is calculated and the system risk index is calculated.

[0196] The system's distributed power output power is as follows: Figure 17 As shown in (a), before islanding, the system is connected to the upper-level grid, receiving energy from the upper-level grid, and the power source is not contributing. When an extreme rainstorm causes the distribution system to be divided into different islands, all three power sources in the system reach full output simultaneously. This is because the full output of the distributed generation can minimize system load losses. At this time, the load within the system islands is now supplied by the power source and energy storage resources. Subsequently, due to system load fluctuations within the islands, power sources 2 and 3 can meet the island load requirements even at a partial output, resulting in power source output drops at different times.

[0197] The energy changes of the system energy storage resources are as follows: Figure 17 As shown in (b) above, before islanding, the energy storage resources are not contributing, for the same reason as above. The island where energy storage device 1 is located initially has a high load and is fully operational. As the number of islands increases, the load on the island where energy storage device 1 is located decreases, and the load power is also low. The energy storage resources begin charging, and then, due to load fluctuations within the island, the energy storage resources choose to charge and discharge energy based on power balance. Energy storage device 2 is located on an island with a high load. After islanding, the initial load on the island is low. After a short period of energy storage resource production, the power supply is sufficient to cover the load within the island. At this point, the excess energy from the fully operational power supply converges with the energy storage resources, preparing for subsequent energy storage resource production to reduce load losses throughout the rainstorm. Later, as the load on the entire island increases, the energy storage resources are fully operational, minimizing load losses. The load on the island where energy storage device 3 is located is low, and the energy storage resources choose to charge and discharge energy based on load fluctuations and power balance.

[0198] The node voltage changes in the corresponding island are as follows: Figure 18 In (a), the node voltages within the island are all within the normal fluctuation range. At the 26th time interval, the voltages of some nodes change. This is because the system topology changes again at this time, and the number of islands increases from 4 to 5. At the same time, the load fluctuations of these nodes are relatively large. To meet the energy demand of the load during this period, the voltage of the source node of the corresponding island (the node where the distributed power source is located) increases to ensure energy supply within the island and reduce load losses. Subsequently, the load fluctuation is small, and the voltage returns to normal.

[0199] In order to verify the accuracy of the model, the present invention compares the load loss of the system under the same fault and the same islanding conditions in the IEEE33 node system, including distributed power supply and energy storage resources, power supply resources, and no resources. Figure 18 In (b), the load loss increases in each of the three cases. This is because the first system is powered by a combination of power and energy storage, the second system is powered only by energy storage resources, and the third system has no energy supply. This is consistent with the actual situation. The more energy resources there are, the less load loss there is, which is consistent with the actual situation and proves the effectiveness of the model. Finally, the load loss during the rainstorm under different conditions was counted, as shown in Table 2:

[0200] Table 2 Load loss during heavy rain (without using Bayesian network)

[0201] ;

[0202] System resilience can be measured by load loss. Combined with the intensity of a rainstorm, it can be seen that during the entire duration of a rainstorm, rainfall is initially low. Because the water flows freely and is promptly channeled through drainage wells, it does not accumulate and does not cause economic losses. In the middle phase, rainfall increases, and drainage wells are unable to promptly channel this water. Accumulation leads to load loss, which gradually increases. In the later phase, rainfall decreases, and load loss disappears. The Bayesian network method shows similar trends to the method without the Bayesian network. Furthermore, the method using the Bayesian network more closely matches the changing intensity of the rainstorm, better reflecting the impact of the rainstorm on the distribution system. The original method without the Bayesian network, however, underestimates the impact of extreme rainstorms on the distribution system during the assessment process, leading to incorrect instructions for dispatchers and potentially misallocation of resources, resulting in significant economic losses.

[0203] Figure 19 A comparison chart of system resilience before and after using Bayesian analysis is presented. The posterior load loss represents the load loss obtained after using Bayesian analysis, while the prior load loss represents the load loss obtained without Bayesian analysis. Compared to the load loss calculated using the original method, the proposed evaluation method improves load loss calculation by 14.69%. This demonstrates that the proposed method significantly improves the accuracy of load loss prediction and system assessment, fully validating its effectiveness and reliability in complex environments.

[0204] It is worth noting that the contents not elaborated in detail in the present invention are all prior art and are well known to those skilled in the art.

[0205] Therefore, the present invention adopts the above-mentioned distribution system resilience assessment method based on dynamic Bayesian network. Through multi-model coupling and probability analysis, it comprehensively considers the impact of rainstorm disasters on the distribution network, accurately assesses the resilience of the distribution network under rainstorm disasters, provides a scientific basis for power system planning, design and emergency management, and improves the disaster resistance and reliability of the distribution network.

[0206] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A distribution system resilience assessment method based on dynamic Bayesian network, characterized in that: The following steps are involved: Step S1: Use the Chicago Unimodal Rainfall Model to simulate rainstorm disasters, obtain rainstorm intensity, combine the digital elevation model with the two-dimensional hydrodynamic model, and simulate urban waterlogging with CI as the grid unit, where CI represents critical infrastructure; Step S2: Based on the water depth data, establish a distribution equipment failure model to obtain the failure probability of each node; Step S3: using the Monte Carlo sampling method to simulate the state of the power distribution system, and combining the node failure probability obtained in step S2 to generate the operation status of the power distribution system under different states; Step S4: construct a dynamic Bayesian network based on the topological connections between CI elements. Based on the power grid topology, each distribution device and the nodes in the network are used as the node set in the Bayesian network. Each edge represents the connection relationship between the nodes, and a conditional probability equation is constructed between the parent and child nodes. The power accessibility rate is calculated using the water depth data and the node failure probability. Step S5: Considering the load shutdown and line topology changes of the distribution system caused by extreme rainstorm disasters, a distribution network flow model is established, and constraints and objective functions are introduced. The distribution system status and power accessibility are input into the distribution network flow model, and the system load loss and voltage offset are calculated. Then, the expectation and variance of the load loss and voltage offset are calculated to evaluate the system risk, and finally the resilience assessment results of the distribution network under rainstorm disasters are obtained.

2. A method for evaluating the resilience of a power distribution system based on a dynamic Bayesian network according to claim 1, characterized in that: In step S1, the rainstorm intensity calculation formula is as follows: ； in, express Intensity of rainstorm at any moment; Indicates the duration of heavy rain; Indicates the rainstorm recurrence period; 、 、 、 Represents parameters related to rainstorm characteristics, among which, It represents the 1-minute design rainfall within the unit recurrence period; represents the rainfall duration correction parameter; represents the rainfall force variation parameter; Represents the rainstorm attenuation index.

3. A method for evaluating the resilience of a power distribution system based on a dynamic Bayesian network according to claim 2, characterized in that: In step S1, the rainstorm intensity is obtained, and the digital elevation model and the two-dimensional hydrodynamic model are combined to simulate urban flooding using CI as the grid unit. The specific operations are as follows: Grid the map; Using the vector calculation formula converted from the Manning formula, combined with the quality of the water flow in the grid , gravitational acceleration and the water surface elevation difference between adjacent grids , calculate the ground friction; ； ； in, represents the water flow pressure of adjacent grids; represents the ground friction of the grid; Indicates water flow rate; express The depth of water accumulation in the grid where the power distribution equipment is located at any given moment; represents the Manning coefficient; Will 、 Bring in And simplify, calculate the water flow speed in the four directions of east, west, south and north; ； ； in, Indicates water density; Indicates the grid width; Indicates a time interval; Indicates the water flow speed in the four directions of east, west, south and north; Indicates the height difference in the four directions of east, west, south and north; According to the calculated water flow velocity in the four directions of east, west, south and north, combined with the urban building coverage rate, the grid's four directions of east, west, south and north are obtained. Water flow at any moment; ； in, Indicates along 、 、 、 Four directions Water flow at any moment; represents the urban building coverage rate; Indicates the west direction; Indicates the east direction; Indicates the north direction; Indicates the south direction; Considering the discharge of urban drainage wells, model it as negative water flow and calculate Drainage flow in the grid at any moment; ； in, express Drainage flow in the grid at any moment; Indicates the number of drainage wells in the grid; Represents the drainage coefficient, which is a number between [0, 1]; Indicates the cross-sectional area of ​​the drainage well; Combine the drainage flow in the grid with the water flow in the four directions of east, west, south and north, and calculate the grid according to the water flow conversion coefficient and time interval. In time interval The water depth at the last moment is calculated, and the iterative grid depth is updated to obtain the water accumulation situation of each grid; ； in, represents the water flow conversion coefficient; Representation Grid West direction grid flow direction grid water flow; Representation Grid East direction grid flow direction grid water flow; Representation Grid North direction grid and flow direction grid water flow; Representation Grid South direction grid flow direction grid of water flow.

4. A method for evaluating the resilience of a power distribution system based on a dynamic Bayesian network according to claim 3, characterized in that: In step S2, based on the water depth data, a distribution equipment failure model is established to obtain the failure probability of each node. The specific operations are as follows: ； in, Indicates the The power distribution equipment on each node is at The probability of failure; Indicates the designed flood-proof height of the distribution station / room or box-type substation; Indicates the ground elevation of the cable joints of the high-voltage switchgear in the station.

5. A method for evaluating the resilience of a power distribution system based on a dynamic Bayesian network according to claim 4, characterized in that: In step S3, the Monte Carlo sampling method is used to simulate the state of the distribution system. Combined with the node failure probability obtained in step S2, the operation status of the system under different states is generated. The specific operations are as follows: ； in, Indicates the Nodes at time The working status of the node, 0 means the node is working normally, and 1 means the node is failed; Represents a random number.

6. A method for evaluating the resilience of a power distribution system based on a dynamic Bayesian network according to claim 5, characterized in that: In step S4, the Bayesian network after the rainstorm disaster is constructed as a set : ； in, Represents a collection of nodes; represents a set of directed edges; Represents the prior probability of each node, which is composed of the failure probability of each node.

7. A method for evaluating the resilience of a power distribution system based on a dynamic Bayesian network according to claim 6, characterized in that: In step S4, when the node is in the running state, When , the power availability rate is the joint probability; when the node is in a fault state, When , the power availability is the inverse of the joint probability; ； in, Indicates the Node time Node working status; Representation node The parent node time Node working status; express Node in The probability used to calculate the joint probability at this moment is related to the state of the node. When the state of the node is normal, , when the node status is abnormal, ; express The parent node of the node is The probability of the moment used to calculate the joint probability; Indicates the power availability rate; A value indicating the working status.

8. The method for evaluating the resilience of a power distribution system based on a dynamic Bayesian network according to claim 7, characterized in that: In step S5, the distribution network flow model is as follows: ； in, Represents simulation Minimize load loss costs after the second; Indicates the number of simulations; Indicates the The load loss cost caused by the simulation cycle, Indicates starting from the first simulation.

9. A method for evaluating the resilience of a power distribution system based on a dynamic Bayesian network according to claim 8, characterized in that: In step S5, the objective function is as follows: ； in, Indicates the The loss cost caused by the loss of unit power load of each node; Indicates the nodes Power lost at any moment; 、 Indicates the operation and maintenance loss costs caused by charging and discharging unit power energy of energy storage resources; 、 Representation node Energy storage equipment Power lost at any moment; Represents the set of nodes where energy storage resources are located in the power distribution system.

10. A method for evaluating the resilience of a power distribution system based on a dynamic Bayesian network according to claim 9, characterized in that: In step S5, the constraints include: ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； in, Indicates line Child nodes on ; Indicates line The parent node on ; Indicates line At the moment the active current flowing through; Representation node At the moment Active power demand; Indicates line At the moment the active current flowing through; Indicates line At the moment Reactive power flowing through; Representation node At the moment Reactive power demand; Indicates line At the moment Reactive power flowing through; Representation node At the moment Active power of the connected load; Representation node At the moment Lost load active power; Representation node At the moment Active output of the connected power supply; Indicates the Distributed power generation at the moment The meritorious contribution; express The energy release power of the energy storage device on the node; express Energy storage power of the energy storage device on the node; Indicates the Distributed power generation at the moment Reactive output power; Represents the set of nodes where distributed power sources are located in the power distribution system; Represents the set of lines connecting all nodes; 、 Represents transmission lines Upper and lower limits of transmitted active power; 、 Represents transmission lines Upper and lower limits of transmitted reactive power; Representation node At the moment The square of the voltage; 、 Represents transmission lines resistance and reactance on the Represents nodes respectively Lower and upper limits of the square of voltage; Representation node Energy storage equipment on the moment Energy storage capacity status; Indicates the energy conversion efficiency of energy storage equipment; Representation node Energy storage equipment on the moment Charging status; Representation node Energy storage equipment on the moment energy release state; 、 Respectively represent the minimum and maximum capacity of the energy storage device; 、 Respectively represent the minimum active power of energy storage equipment charging and discharging; 、 Respectively represent the maximum active power of energy storage equipment charging and discharging; Indicates the Distributed power generation at the moment Active output power; Indicates the Distributed power generation at the moment Reactive output power; 、 Respectively represent the upper and lower limits of the active output of distributed generation; 、 They represent the upper and lower limits of the reactive output of distributed generation respectively.

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