Power distribution system toughness evaluation method based on dynamic Bayesian network

Abstract

The invention provides a power distribution system toughness evaluation method based on a dynamic Bayesian network, and belongs to the technical field of disaster evaluation and power system toughness analysis. The method comprises the following steps: simulating a rainstorm disaster by utilizing a Chicago unimodal rainfall model, and simulating urban waterlogging in combination with a digital elevation model and a two-dimensional hydrodynamic model; establishing a power distribution equipment failure model based on the ponding depth data to obtain a node failure probability; simulating the state of the power distribution system by adopting a Monte Carlo sampling method; constructing a dynamic Bayesian network to calculate a power reachable rate; and considering load exit and line topology change to establish a power flow model of the power distribution network, calculating load loss and voltage offset, and evaluating system risk. Through multi-model coupling and probability analysis, the influence of the rainstorm disaster on the power distribution network is comprehensively considered, the toughness of the power distribution network under the rainstorm disaster is accurately evaluated, a scientific basis is provided for planning, design and emergency management of a power system, and the disaster resistance and reliability of the power distribution network are improved.

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 method for evaluating the resilience of a distribution system based on a dynamic Bayesian network. Background Art

[0002] Under rainstorm disasters, the resilience assessment of the distribution network is crucial for ensuring the reliability and safety of power supply. Traditional assessment methods mainly focus on post-disaster repair and are insufficient in dealing with the dynamic evolution and uncertainty of the distribution network under extreme weather. In recent years, Bayesian networks have been widely used in related fields due to their advantages in dealing with uncertainty problems. However, static Bayesian networks are difficult to accurately represent the influence between time slices in the whole process of disasters. Dynamic Bayesian networks are more suitable for systems that need to study time-varying processes and can combine rainstorm disaster scenarios to complete disaster deduction work. In terms of the distribution network power flow model, existing studies mostly consider single factors or static conditions and are insufficient in modeling the dynamic processes of load withdrawal and line topology change under extreme rainstorm disasters, making it difficult to accurately evaluate the resilience and risk of the system in complex disaster scenarios. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for evaluating the resilience of a distribution system 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 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 ability and reliability of the distribution network.

[0004] To achieve the above object, the present invention provides a method for evaluating the resilience of a distribution system based on a dynamic Bayesian network, including the following steps: Step S1: Use the Chicago single-peak rainfall model to simulate rainstorm disasters, obtain the rainstorm intensity, and combine the digital elevation model and two-dimensional hydrodynamic model to simulate urban waterlogging with CI as the grid unit, where CI represents critical infrastructure; Step S2: Based on the waterlogging depth data, establish a failure model for distribution equipment to obtain the failure probability of each node; Step S3: Use the Monte Carlo sampling method to simulate the state of the distribution system, and combine the node failure probability obtained in Step S2 to generate the operating conditions of the distribution system in different states; Step S4: Construct a dynamic Bayesian network based on the topological connection between CI elements. Based on the power grid topological diagram, use each distribution equipment and the nodes in the network as the node set in the Bayesian network, where each edge represents the connection relationship between nodes, and construct a conditional probability equation between parent and child nodes. Calculate the power reach rate using the waterlogging depth data and node failure probability; Step S5: Considering the load disconnection from operation and the change in line topology of the distribution system caused by extreme rainstorm disasters, establish a power flow model for the distribution network, introduce constraint conditions and objective functions, input the distribution system state and power reach rate into the power flow model of the distribution network, calculate the load loss and voltage offset of the system, and then calculate the expectations and variances of the load shedding amount and voltage offset to evaluate the risk of the system, and finally obtain the resilience evaluation result of the distribution network under rainstorm disasters.

[0005] Preferably, in step S1, the rainstorm intensity calculation formula is as follows: ; where represents the rainstorm intensity at time represents the rainstorm duration; represents the rainstorm recurrence period; , , , represent parameters related to the characteristics of the rainstorm, where represents the 1-minute design rainfall within the unit recurrence period; represents the rainfall duration correction parameter; represents the rainfall intensity variation parameter; represents the rainstorm attenuation index.

[0006] Preferably, in step S1, to obtain the rainstorm intensity and simulate urban waterlogging with CI as the grid unit by combining the digital elevation model and the two-dimensional hydrodynamic model, the specific operations are as follows: Perform grid processing on the map; Use the vector calculation formula transformed from the Manning formula, combined with the mass of the water flow within the grid , gravitational acceleration and the water surface elevation difference between adjacent grids , to calculate the ground friction; ; ; where represents the water flow pressure between adjacent grids; represents the ground friction of the grid; represents the water flow velocity; represents the water accumulation depth of the grid where the power distribution equipment is located at time represents the Manning coefficient; Substitute , into and simplify to calculate the water flow velocities in the east, west, south, and north directions; ; ; Wherein, represents the water density; represents the grid width; represents the time interval; represents the water flow velocities in the four directions of east, west, south, and north; represents the height differences in the four directions of east, west, south, and north; According to the calculated water flow velocities in the four directions of east, west, south, and north, combined with the urban building coverage rate, the water flow rates in the four directions of east, west, south, and north of the grid are obtained at the moment; ; Wherein, represents along , , , the four directions at the moment; represents the urban building coverage rate; represents the west direction; represents the east direction; represents the north direction; represents the south direction; Considering the drainage volume of urban drainage wells, it is modeled as negative water flow rate, and the drainage flow rate within the grid at the moment is calculated; ; Wherein, represents the drainage flow rate within the grid at the moment; represents the drainage coefficient, which is a number between [0, 1]; represents the cross-sectional area of the drainage well; Combining the drainage flow rate within the grid with the water flow rates in the four directions of east, west, south, and north, according to the water flow rate conversion coefficient and the time interval, the waterlogging depth of the grid after the time interval is calculated, and the grid depth is updated iteratively to obtain the waterlogging situation of each grid; ; Wherein, represents the water flow rate conversion coefficient; represents the water flow rate from the west-direction grid of the grid to the grid ; represents the water flow rate from the east-direction grid of the grid to the grid ; Indicates the grid The northward grid flow of flows into the grid The water flow rate; Indicates the grid The southward grid flow of flows into the grid The water flow rate.

[0007] Preferably, in step S2, based on the accumulated water depth data, a failure model of the power distribution equipment is established to obtain the failure probability of each node. The specific operation is as follows: ; Wherein, Indicates the th The failure probability of the power distribution equipment on the th node at time ; Indicates the designed flood prevention height of the substation / room or box-type substation; Indicates the ground elevation of the cable joint of the high-voltage switchgear in the station.

[0008] Preferably, in step S3, the Monte Carlo sampling method is used to simulate the state of the power distribution system. Combining with the node failure probability obtained in step S2, the operation conditions of the system under different states are generated. The specific operation is as follows: ; Wherein, Indicates the th The working state of the th node at time , 0 indicates that the node is working normally, and 1 indicates that the node has failed; Indicates a random number.

[0009] Preferably, in step S4, the Bayesian network after the occurrence of the rainstorm disaster is constructed as a set : ; Wherein, Indicates the node set; Indicates the set of directed edges; Indicates the prior probability of each node, which is composed of the failure probability of each node.

[0010] Preferably, in step S4, when the node is in the operating state, When , the power reachability rate is the joint probability; when the node is in the fault state, When , the power reachability rate is the reciprocal of the joint probability; ; Wherein, Indicates the th The node working state at time ; Indicates the node The parent node time The node working state; Indicates The node at The probability used to calculate the joint probability at time, which is related to the state of the node. When the state of the node is normal, , when the node state is abnormal, ; Indicates The probability of the parent node of the node at time used to calculate the joint probability; Indicates the power reach rate; Indicates the value of the working state.

[0011] Preferably, in step S5, the distribution network power flow model is as follows: ; Among them, Indicates the simulation times to minimize the load loss cost; Indicates the number of simulations; Indicates the th simulation cycle causes the load loss cost, Indicates starting from the first simulation.

[0012] Preferably, in step S5, the objective function is as follows: ; Among them, Indicates the th node loses the loss cost caused by unit power load; Indicates the th node time loses the power; , Indicates the operation and maintenance loss cost caused by charging and discharging unit power energy of energy storage resources; , Indicates the node The energy storage device on time loses the power; Indicates the set of nodes where the energy storage resources are located in the distribution system.

[0013] Preferably, in step S5, the constraint conditions include: The active and reactive power balance constraints of the distribution network node at time ; The node at time The constraint of the load power and the difference between its load, load loss and the power of the connected power supply; The node At time constraints on the power of the power supply, the output of distributed power sources, and the energy storage; node At time constraints on the reactive power of the load and the reactive power of the connected distributed power sources; upper and lower limits of the line transmission power; load loss and load loss constraints; node voltage balance constraints; upper and lower limits of node voltage; node energy storage device on power balance constraint at time energy storage device on unique charge and discharge state constraint at time; energy capacity constraint of the energy storage device; upper and lower limits of the charge and discharge power of the energy storage device.

[0014] Therefore, the present invention adopts the above-mentioned method for evaluating the resilience of a distribution system based on a dynamic Bayesian network, and the beneficial technical effects are as follows: (1) Precise simulation of disaster impact: By simulating the impact of rainstorm disasters on urban waterlogging, a probability model for the outage of distribution equipment is established, which effectively reflects the specific impact of rainstorm disasters on the distribution system and provides basic data support for subsequent evaluations.

[0015] (2) Improvement of evaluation accuracy: By using a dynamic Bayesian network, the spatio-temporal correlation of nodes is fully considered, and the importance of node loads is combined to analyze their impact on load loss, thus significantly improving the accuracy of system resilience evaluation and making the evaluation results closer to reality.

[0016] (3) Provide targeted improvement suggestions: The proposed resilience evaluation method innovatively combines the 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, helps decision-makers formulate scientific and accurate measures, and enhances the ability of the distribution system to cope with rainstorm disasters. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 is a rainstorm intensity map; Figure 2 is a grid processing map of the distribution system; Figure 3 is a water flow direction map; Figure 4 is an analysis map of the flooding of high-voltage switch cabinets in the distribution system; Figure 5 is a simulation flow chart of the Monte Carlo sampling method; Figure 6 is a transformed Bayesian graph; Figure 7 is a schematic diagram of a simple Bayesian network; Figure 8 is a Bayesian calculation graph; Figure 9 It is a topology diagram of the power distribution system; Figure 10 It is a statistical and fitting analysis diagram of the rain peak coefficient. Among them, Figure 10 In (a), it is a diagram of the interval and frequency of the rain peak coefficient appearance; Figure 10 In (b), it is the interval probability and fitting curve of the rain peak coefficient; Figure 11 It is an analysis diagram of the system risk assessment index. Among them, Figure 11 In (a), it is the expected value of load loss; Figure 11 In (b), it is the expected value of system voltage deviation; Figure 12 It is a comparison diagram of load loss before and after using dynamic Bayesian; Figure 13 It is a time series diagram of extreme rainstorms; Figure 14 It is a diagram of the change in grid waterlogging depth; Figure 15 It is a diagram of the change in the failure probability of distribution network nodes; Figure 16 It is a diagram of the change process of system island division; Figure 17 It is a dynamic change diagram of the system's distributed power sources and energy storage resources. Among them, Figure 17 In (a), it is a diagram of the output power of the system's distributed power sources; Figure 17 In (b), it is a diagram of the energy change of the system's energy storage resources; Figure 18 It is a dynamic analysis diagram of system performance evaluation. Among them, Figure 18 In (a), it is a diagram of the change process of system node voltage; Figure 18 In (b), it is a comparison diagram of different system load losses; Figure 19 It is a system resilience diagram. Specific implementation manners

[0018] The technical solutions of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0019] Unless otherwise defined, the technical terms or scientific terms used in the present invention shall have the ordinary meanings understood by those of ordinary skill in the field to which the present invention pertains.

[0020] Embodiment 1 Step S1: Use the Chicago single-peak rainfall model to simulate rainstorm disasters, obtain the rainstorm intensity, and combine the digital elevation model and the two-dimensional hydrodynamic model to simulate urban waterlogging with CI as the grid unit, where CI represents critical infrastructure.

[0021] The rainstorm intensity in different regions is expressed by the following formula: (1); Among them, represents the heavy rain duration; represents the heavy rain intensity at the moment; represents the heavy rain recurrence period; , , , represent parameters related to the characteristics of heavy rain. Among them, represents the 1-minute design rainfall within the unit recurrence period, represents the rainfall duration correction parameter, represents the rainfall intensity variation parameter, represents the heavy rain attenuation index.

[0022] This embodiment considers a single-peak rainfall pattern. The heavy rain intensity is respectively expressed as two parts before and after the peak, such as Figure 1 . Equation (2) represents the calculation formula for the rain peak coefficient, Equation (3) represents the heavy rain intensity before the peak, and Equation (4) represents the heavy rain intensity after the peak: (2); (3); (4); Among them, represents the rain peak coefficient; represents the time period before the peak; represents the heavy rain duration; represents the time period after the peak; represents the moment before the peak rainfall intensity (mm / min); represents the moment after the peak rainfall intensity. , represents the position of the peak precipitation during this rainfall process. By the time of the peak precipitation, the rainfall process is considered as two stages before and after the peak.

[0023] The map is gridded, as shown in Figure 2 .

[0024] Using the vector calculation formula transformed by the Manning formula, combined with the mass of the water flow in the grid , gravitational acceleration and the water surface elevation difference between adjacent grids , calculate the ground friction: (5); (6); Among them, represents the water flow pressure between adjacent grids; Represents the ground friction of the grid; Represents the water flow velocity; Represents The accumulated water depth of the grid where the power distribution equipment is located at a certain moment; Represents the Manning coefficient.

[0025] (7); Equation (7) is the momentum theorem.

[0026] Substitute Equation (5) and Equation (6) into Equation (7) for simplification: (8); (9); Among them, Is the water density; Is the grid width; Represents the time interval; Represents the water flow velocities in the four directions of east, west, south, and north; Represents the height differences in the four directions of east, west, south, and north.

[0027] Equation (9) is a quadratic equation of one variable about velocity. Using the discriminant of whether the equation has roots, it can be known that there are two roots, positive and negative. Because , so the negative root is discarded and the positive root is taken. When calculating the accumulated water depth of each grid, only consider the flow in the four directions of east, west, south, and north of the grid. For example Figure 3 , for the grid , only consider , , , Four directions; do not consider the water flow between the northwest , northeast , southwest , southeast And the grid This is because when calculating the accumulated water depth of the grid Next to it, it can be considered. Through the calculated velocities , , , , combined with the urban building coverage rate, obtain the water flow in the four directions of the grid At a certain moment: (10); Among them, Represents , , , Four directions At a certain moment, the water flow towards the grid The water flow rate; Represents the urban building coverage rate.

[0028] When calculating the water flow rate, the drainage volume of urban drainage wells is also considered and modeled as negative water flow: (11); In the formula: Represents The drainage flow rate in the grid at time Represents the number of drainage wells in the grid; Is the drainage coefficient, a number between [0, 1]; Represents the cross-sectional area of the drainage well.

[0029] According to equations (9), (10), and (11), the water depth in the grid At the time interval After The water depth at time can be calculated, and the grid depth after successive updates and iterations is obtained through equation (12). The simulation of urban rainstorms is completed.

[0030] (12); In the formula: Represents the water flow conversion coefficient; Represents the grid The water flow rate from the west-direction grid of the grid to the grid ; Represents the grid The water flow rate from the east-direction grid of the grid to the grid ; Represents the grid The water flow rate from the north-direction grid of the grid to the grid ; Represents the grid The water flow rate from the south-direction grid of the grid to the grid ;

[0031] Thus, the simulation of rainfall in urban waterlogging is completed.

[0032] Step S2, power distribution equipment failure model.

[0033] The probability of equipment failure caused by rainstorm disasters is dynamically changing and will change with the change of the water depth caused by rainstorms, as Figure 4 Shown. In the initial stage of rainfall, the impact of rainwater on power distribution equipment is small. In the middle stage of rainfall, rainfall will cause surface water accumulation in the city. When the surface water accumulation exceeds the flood prevention height of the power distribution equipment, the probability of power distribution equipment failure will increase rapidly. In this embodiment, the grid is used as the basic unit to establish the relationship between the time-varying water depth and the probability of power distribution equipment failure: (13); Wherein: represents the failure probability of the power distribution equipment at the th node at time ; represents the water accumulation degree of the grid where the equipment is located at time represents the designed flood prevention height of the substation (room) or box-type substation; represents the ground elevation of the cable joint of the high-voltage switchgear in the station; Through formula (13), the rainfall depth is converted into the failure rate of the power distribution equipment.

[0034] Step S3, Urban power distribution system resilience assessment method based on dynamic Bayesian network in extreme conditions.

[0035] The power distribution equipment is generally installed on the corresponding nodes. Therefore, in this embodiment, the failure probability of the power distribution equipment is used as the node failure probability for analysis. First, the state of the power distribution system is simulated.

[0036] The state of the power distribution system is simulated by the Monte Carlo method. It is assumed that there is no correlation between the working states of the power distribution system caused by rainstorm disasters among the nodes and corresponding times. The state sampling method is used to complete the sampling of the node states, and the simulation of the power distribution system state is realized.

[0037] Based on the node failure probability as the judgment basis, the working state of node at time (14); Wherein: represents the th node at time ; 0 indicates that the node is working normally, and 1 indicates that the node fails; represents a random number in [0, 1]. When , node exits the operation; when , node works normally. When node exits the operation, due to the extreme rainstorm disaster, there are no conditions for maintenance personnel to arrive for repair. Therefore, the failure probability of the node at subsequent times is 1. Until after the rain stops and the maintenance personnel repair and make the equipment return to the normal working state, the failure probability of the node becomes depth-related.

[0038] Based on this, the Monte Carlo sampling method is used for simulation, as shown in Figure 5 .

[0039] Combined with the status of the nodes, using the depth-first search method, the system is divided into three different islands: single node, multiple nodes without power supply, and multiple nodes with power supply, which are used for subsequent calculation of load loss. For the first type, by judging whether there is a power supply, if there is no power supply, it is calculated as load loss. ; For the second type, it is directly calculated as load loss. ; For the third type, after calculating the power flow in the island, the system load loss is calculated. The total load loss can be expressed as: (15); Step S4: Construct a dynamic Bayesian network based on the topological connection between CI elements. Based on the power grid topological graph, each distribution device and the nodes in the network are used as the node set in the Bayesian network, and each edge represents the connection relationship between nodes, and a conditional probability equation between parent and child nodes is constructed. The power reachability is calculated using the ponding depth data and the node failure probability.

[0040] Rainstorm disasters are uncertain. In this embodiment, a Bayesian network that can handle uncertainty is used for modeling, and the Bayesian network after the occurrence of a rainstorm disaster is constructed as a set : (16); Among them, represents the node set; represents the set of directed edges; represents the prior probability of each node, which is composed of the failure probability of each node; Based on the power grid topological graph, the topological structure is transformed into a Bayesian network graph, such as Figure 6 , and each device and the nodes in the network are 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 , and each edge has its own direction, such as represents the node pointing to the node, representing the node is the parent node of the node, and the parent nodes of each node form a set, which is expressed as , such as Figure 7 shown in the figure, the parent nodes of node E in the figure are B and C, expressed as . In addition, the state variable of each node has only two states, normal operation and abnormality, at a certain moment, and the possible values are , = 1, 2; respectively represent the normal working state and the abnormal working state, with normal recorded as 1 and abnormal recorded as 0. Based on this, the conditional probability equation between the parent and child nodes is constructed.

[0041] When calculating the probability of each node in the Bayesian network, only the influence of the parent node on it is considered. Then, the method shown as Figure 8 is used between the parent and child nodes, where A represents the parent node of node B, and B represents the child node of node A. 、 、 、 respectively represent the working states of the parent and child nodes at time 0 and time 1, with 1 being the fault state and 0 being the normal state. 、 represent the prior probability of the node. Considering the mutual influence of the parent and child nodes in time and space, the joint probability considering spatio-temporal correlation is calculated. Among them, all the conditional probability values of the conditional probability matrix form the joint probability table. Using the joint probability and combining different node operating states , the power reach rate of the corresponding node is obtained. That is, when the node is in the operating state, , the power reach rate is the joint probability; when the node is in the fault state, , the power reach rate is the reciprocal of the joint probability.

[0042] (17); In the formula: represents the node working state at the th node time , represents the node working state at the parent node time of node , represents the probability of the node used to calculate the joint probability at time , which is related to the state of the node. When the state of the node is normal, , when the state of the node is abnormal, ; represents the probability of the parent node of the node used to calculate the joint probability at time . Under the known probability, the power reach rate of any variable can be calculated using the dynamic Bayesian network.

[0043] The total load loss considering the Bayesian network can be expressed as: (18).

[0044] ​​Step S5: Considering the load disconnection from operation and the change in line topology caused by extreme rainstorm disasters, establish a power flow model for the distribution network, introduce constraint conditions and objective functions, input the distribution system state and power reachability rate into the power flow model of the distribution network, calculate the load loss and voltage offset of the system, and then calculate the expectations and variances of the load loss and voltage offset to evaluate the risk of the system, and finally obtain the resilience evaluation result of the distribution network under rainstorm disasters.

[0045] 5.1. System power flow model.

[0046] Since extreme rainstorm disasters will cause the load of the distribution system to disconnect from operation and the line topology to change, resulting in a change in the power flow of the distribution system, it is necessary to model the power flow of the distribution system when conducting resilience evaluation. The following modeling is carried out for the distribution system in this embodiment: (19); Wherein, represents the minimum load loss cost after simulations, represents the number of simulations, represents the -th simulation period's load loss cost.

[0047] (20); In the formula: represents the loss cost (yuan / kW) caused by the loss of unit power load at the -th node; represents the power loss (kW) at the -th node at time; , represent the operation and maintenance loss costs (yuan / kW) caused by the charging and discharging of unit power energy of energy storage resources; , represent the power loss (kW) of the energy storage device at the node at represents the set composed of the nodes of the distribution system; represents the set composed of the nodes where the energy storage resources are located in the distribution system.

[0048] Considered constraint conditions: (21); (22); (23); (24); (25); (26); (27); (28); (29); (30); where: represents the sub-node on the line ; represents the parent node on the line ; represents the active power flow flowing through the line at time represents the active power demand of the node at time represents the active power flow flowing through the line at time represents the reactive power flow flowing through the line at time represents the reactive power demand of the node at time represents the reactive power flow flowing through the line at time represents the active power of the load connected to the node at time represents the active power loss of the load of the node represents the active power output of the power source connected to the node represents the active power output of the nth distributed power source represents the discharging power of the energy storage device on the node represents the energy storage power of the energy storage device on the node represents the set of nodes where distributed power sources are located in the distribution system; Denote the set formed by the lines connecting all nodes; , Denote the transmission line The upper and lower limits of the active power transmitted; , Denote the transmission line The upper and lower limits of the reactive power transmitted; Denote the node At time The square of the voltage; , Denote the transmission line The resistance and reactance on it; Denote the node The lower and upper limits of the square of the voltage.

[0049] Equations (21) and (22) represent the active and reactive power balance constraints of the distribution system node At time ; Equation (23) represents the constraint of the difference between the load power of node at time and its load, load loss, and the power of the connected power source; Equation (24) represents the constraint of the power of node at time and the power of the distributed power source and the energy storage output; Equation (25) represents the constraint of the reactive power of node at time and the reactive power of the connected distributed power source; Equations (26) and (27) represent the upper and lower limits of the line transmission power. When node is taken out of operation at time , then the line it is connected to is disconnected, that is, the power flowing through it is restricted to 0; Equation (28) represents the load loss and load loss constraint; Equation (29) represents the node voltage balance constraint; Equation (30) represents the node voltage upper and lower limits constraint.

[0050] (31); (32); (33); (34); (35); In the formula: Denote the energy storage capacity state of the energy storage device on node at time ; Denote the energy conversion efficiency of the energy storage device; Denote the node Energy storage devices Always in charging state; Representation Node Energy storage devices Always in energy-releasing state; , Indicates the minimum and maximum capacity of the energy storage device; , Indicates the minimum active power of energy storage equipment for charging and discharging; , Indicates the maximum active power of charging and discharging energy storage equipment.

[0051] Formula (31) represents the node Energy storage devices The power balance constraint at time t, Equation (32) represents the node Energy storage devices The unique state constraint of charging and discharging at all times, formula (33) represents the energy capacity constraint of the energy storage device; formulas (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.

[0052] (36); (37); Where: For the Distributed power generation Active output power at any time; For the Distributed power generation 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.

[0053] Formulas (36) and (37) represent The upper and lower power limits of distributed power sources are defined.

[0054] 5.2. System indicators.

[0055] 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.

[0056] (38); (39); (40); (41); Among them, represents the load risk index of the system without considering the Bayesian network; represents the load risk index of the system; represents the number of sampling times of the system during the simulation process; represents the working state of the system load; represents the node at the power reach rate at the moment; represents the voltage risk index of the system; represents the voltage deviation situation of the system during the represents the reference value of the square of the system voltage.

[0057] Equation (39) represents the load loss risk index of the system, which is obtained from the load loss expectation considering the power reach rate after each simulation; Equation (40) represents the voltage deviation risk index of the system, which is obtained from the voltage deviation expectation after each simulation process.

[0058] The following further illustrates the present invention through specific examples.

[0059] Example information.

[0060] This example uses the IEEE 33-node example for analysis, and the topology is as Figure 9 , the DEM data is processed into a grid, and each node is considered as a 90×90 square in sequence according to the serial number, from left to right and from top to bottom for rainfall simulation. According to the legend, the color approaching brown indicates a higher terrain; approaching blue indicates a lower terrain. After being affected by extreme rainstorm disasters accordingly, the change in precipitation depth is also different.

[0061] In the IEEE-33 node system, node 0 is the source node, and the rest are load nodes; among them, nodes 1, 3, 5, 8, 11, 13, 16, 19, 24, 27, 30 are important load nodes, and the rest are general loads. The load loss cost is divided into 100 and 5 yuan / kW according to the load level. The system contains three energy storage devices and distributed power sources. The energy capacity of each energy storage device is 500 kW·h, and the charging and discharging power is half of the energy capacity; the output upper limit of each distributed power source is 500 kW. The unit power costs of the energy storage resources for charging and discharging are 3 yuan / kW and 4 yuan / kW respectively.

[0062] The Yalmip optimization toolbox is used to model the optimization model, and the Gurobi solver is called for solution. The computer CPU model is Intel Core I7, the main frequency is 2.10 GHz, and the memory capacity is 16 GB.

[0063] Disaster scenario information.

[0064] This example mainly considers extreme rainstorm disasters. When a disaster occurs, the water depth in the grid where each node is located changes, resulting in a change in the failure probability of the high-voltage switchgear at the nodes of the power distribution system. Node failures occur, causing the connected lines to break and withdraw from the system operation, splitting the system into different islands. It is assumed that after the island division, the system cannot obtain energy from the superior power grid. The entire simulation process is 4 hours. During this period, all grids where the nodes are located are affected by rainfall equally, that is, the cumulative rainfall in each grid is the same at the same moment. The failure rate of the node will change differently with the precipitation depth of the corresponding grid. Use the random number between the failure rate of the node and [0, 1] Compare to determine the operating state of the node at the corresponding moment. Use the islands divided at different times to calculate the power flow distribution of the system at the corresponding moment and count the load loss of the system.

[0065] To achieve a statistically significant load loss and voltage deviation, 100 simulations of extreme rainstorm disasters were carried out. In each simulation, the rain peak coefficient and the rainstorm recurrence period of the rainfall were different to represent the impact of different rainfall intensities on the system.

[0066] For the selection of the rain peak coefficient, in order to truly simulate the response of the system under different rainstorm conditions. The rainfall data of the whole country was selected. Taking the extreme rainstorm situation: the total precipitation within 24 hours of a day exceeds 250 mm as the division standard. The number of days of extreme rainstorms can be selected to obtain the time when the daily rainfall peak occurs. By counting the position of the peak time, the rain peak coefficient and its occurrence times within a day can be obtained. Divide the position where the rain peak coefficient appears into 10 equal intervals between 0 and 1. The number of times the rain peak coefficient appears in the data from 2012 to 2023 was counted, as shown in Figure 10 shown in (a) of

[0067] Normalize the statistical data, calculate the probability of each interval, and use a second-order polynomial for fitting, as shown in Figure 10 shown in (b) of (42); Among them, is the value range of the rain peak coefficient, is the probability corresponding to the value range.

[0068] 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.

[0069] During the simulation of 100 extreme rainstorm disasters, the expectations and variances of load shedding and voltage deviation were calculated for each entire simulation process, so as to make the evaluation process closer to the actual situation. As can be seen from (a) in Figure 11 , the load shedding of the system is about 4.9 kW. As can be seen from (b) in Figure 11 , the voltage deviation of the system is about 135, verifying the accuracy of the risk assessment.

[0070] The above is the situation after 100 simulation runs. To analyze the performance of the system, one of the rainstorm disaster situations was selected for specific analysis. For example, Figure 12 load loss. After using the dynamic Bayesian method and considering the influence of time and space on load loss, it can be seen that after using the Bayesian network, for the nodes with relatively large original load losses: 2, 11, 20, 21, 22, 24, 25, 27, etc., compared with the method without using the Bayesian network, the load losses are almost the same, and the assessment of these nodes is accurate without reducing the disaster situation of these nodes. These nodes are vulnerable to rainstorm disasters because of their relatively low geographical locations, and huge load losses will be caused after the rainstorm disaster occurs. For nodes 12 and 14, after considering the power availability rate, the load supply efficiency decreases. At the same time, nodes 12 and 14 are non-important loads. In the case of extreme rainstorm disasters, to improve the system security and disaster response capabilities, reducing these loads is beneficial to ensuring the power supply of important loads. For nodes 4, 7, 28, 32, 33, etc., after considering the power availability rate, due to the influence of the connected parent nodes, after the fault occurs and an island is formed, the power supply efficiency of the power source decreases, and after the power supply of the important loads in the island is completed, some load losses are caused. Compared with before using the Bayesian network, the impact on the system after extreme rainstorm disasters is underestimated, which may cause misjudgment by dispatchers in actual operation and may result in huge economic losses.

[0071] At the same time, after evaluating using the proposed method, for nodes 12, 14, 7, and 4 with relatively large increases in load loss, their increments account for 70.89% of the total increment. Compared with the prior load losses calculated by the original method, the original method can only find nodes with relatively large load losses such as 24 and 25, and pays less attention to the load losses caused by the connection relationship of nodes. Through the evaluation method proposed by the present invention, the hidden vulnerable nodes in the system can be deeply mined. The identification of these nodes can provide more accurate risk assessment results for decision-makers under rainstorm disasters, helping them formulate more scientific and accurate measures to improve the system's ability to respond to rainstorm disasters.

[0072] Set the measurement time interval to 5 min, and obtain the rainfall time series data according to Equation (1), as shown in Figure 13 . Among them, =9.898, = 1.333, = 7.1, = 0.656, = 100.

[0073] Figure 13 It can be seen that during the entire rainfall process, the rainfall intensity reaches the maximum value at about 60 min, and the rainfall intensity is about 10 mm / min. The rainfall also increases most rapidly at about 60 min and reaches 0.587 m at 240 min.

[0074] A high-voltage switchgear device is installed on each node in the example. Depending on the different installations of the high-voltage switchgear, each node will have a different flood prevention height, generally between 0.2 - 0.5. The flood prevention heights of important loads in the nodes are as shown in the following table, and the flood prevention heights of the remaining nodes are all set at 0.2 m. At the same time, the ground elevation of the cable joints in the cabinet is 0.3 m.

[0075] Table 1 Design flood prevention heights of some nodes ; Using the rainfall data, simulate the change process of rainfall ponding in the Figure 2 shown grid, as Figure 14 shown.

[0076] From Figure 14 it can be seen that during the entire rainfall process, the ponding depth in the grid shows a trend of first rising and then falling with time. In the initial stage, the ponding depth in the grid is basically 0 because each grid contains an urban drainage system, the initial precipitation is too little, and the ponding is drained through the drainage system without accumulation. In the middle stage, the ponding depth in the grid begins to rise because the rainfall intensity exceeds the drainage threshold of the drainage system, and the ponding cannot be drained, causing urban waterlogging. At the same time, the grid depths between different grids are different, and there is a water surface elevation difference between the grids. When the ponding cannot be drained, it will flow from the grid with relatively higher terrain to the lower grid, resulting in different ponding depths between the grids. In the second half of the rainfall, the rainfall intensity gradually decreases, and the urban drainage system drains the ponding in the grid, and the ponding in the grid gradually decreases to 0. Among them, the grids where nodes 3, 11, 19, 27, and 29 are located are severely affected.

[0077] Substitute the ponding depth into formula (13) to calculate the failure probability of each node. As Figure 15 shown, the failure probability of the node changes with time. When the rainfall intensity increases and the ponding volume increases, the failure probability increases. Conversely, the failure rate decreases. Different nodes have different failure probabilities at different times.

[0078] Simulate the fault states of each node according to the failure rate and substitute it into formula (14). When a node fails, during the subsequent rainstorm process, this node remains faulty. The system topology continuously changes throughout the process. The specific changes in system island division are as follows Figure 16 , in the first 75 minutes, the system operates normally; at 75 minutes, nodes 23, 27 and their connected lines are taken out of operation, and the system is divided into 3 islands; at 80 minutes, node 29 and its connected lines are taken out of operation, and the islands in the system are divided into 4 parts, but the number of nodes in one of the islands decreases; at 90 minutes, node 3 and its connected lines are taken out of operation, and the system is divided into 5 islands; at 130 minutes, node 11 and its connected lines are taken out of operation, and the system is divided into 6 islands.

[0079] According to different island divisions, call the Gurobi solver according to the system model to solve the system power flow of a single island, check the output of the power sources within the island, the state changes of the energy storage, and the voltage stability throughout the process. Finally, count the load loss of the system and calculate the system risk index.

[0080] The output power of the distributed power sources in the system is as shown in Figure 17 (a). Before the island division, the system is connected to the superior power grid, and the energy is provided by the superior power grid, and the power sources do not output power; when extreme rainstorm disasters cause the distribution system to be divided into different islands, the three power sources in the system reach full output at the same time. This is because the full output of the distributed power sources can reduce the load loss of the system. At this time, the load within the system island is powered by the power sources and energy storage resources. After that, due to the load fluctuations within the island in the system, the power sources can ensure the load demand within the island even when not at full output. Therefore, the output of the power sources decreases at different times.

[0081] The energy change of the system energy storage resources is as shown in Figure 17 (b). Before the island division, the energy storage resources do not output power for the same reason as above. The initial load of the island where energy storage device 1 is located is relatively large, and it outputs full power. After that, the number of islands increases, the load of the island where energy storage device 1 is located becomes smaller, and at the same time the load power is relatively small, and the energy storage resources start to charge. After that, due to the load fluctuations within the island, the energy storage resources will choose to charge or discharge according to the power balance; energy storage device 2 is located in an island with a relatively large load. After the island division, the initial island has a relatively small load. After the energy storage resources output power for a short period of time, the power sources are sufficient to cover the load within the island. At this time, the excess energy after the power sources output full power will converge to the energy storage resources to prepare for the subsequent reduction of the load loss by the energy storage resources during the entire rainstorm process. After that, the load of the entire island increases, and the energy storage resources output full power to reduce the load loss. The island where energy storage device 3 is located has a relatively small load, and the energy storage resources choose to charge or discharge according to the load fluctuations and the power balance.

[0082] The voltage change of the corresponding nodes within the island is as followsFigure 18 In (a) of , the node voltages within the isolated island are all within the normal fluctuation range. At the 26th time interval, the voltages of some nodes changed because the system topology changed again at this time, and the isolated island changed from 4 to 5. At the same time, the load fluctuations of these nodes were relatively large. To meet the energy demand of the load during this period, the voltage of the source node (the node where the distributed power source is located) of the corresponding isolated island increased to ensure the energy supply within the isolated island and reduce the load loss. Subsequently, the load fluctuations were small, and the voltage returned to normal.

[0083] To verify the accuracy of the model, the present invention compared the load loss situations of the IEEE 33-node system under the conditions of including distributed power sources and energy storage resources, power sources, and without any resources when the same faults occurred and the same isolated islands were generated, as Figure 18 shown in (b) of . The load loss amounts in the three cases increased in sequence. This is because the first system is powered by power sources and energy storage, the second system is only powered by energy storage resources, and the third system has no resources for power supply, which is in line with the actual situation. The more energy supply resources, the less the load loss, which is in line with the actual situation and proves the effectiveness of the model. Finally, the load loss amounts during the rainstorm process under different conditions were counted, as shown in Table 2: Table 2 Load Loss Amounts during the Rainstorm Process (without Using Bayesian Network) ; The system resilience can be reflected by the load loss of the system. Combining with the rainstorm intensity, it can be seen that during the entire process of the rainstorm, in the initial state, the rainfall is small. Since the precipitation flows everywhere and can be drained in time through drainage wells, etc., the precipitation cannot accumulate and will not cause economic losses; in the middle period, the precipitation increases, and the drainage wells cannot drain these precipitations in time, so the precipitation accumulates, causing load loss, and the loss gradually increases; in the later period, the precipitation decreases and the load loss disappears. Compared with the method without using the Bayesian network, the trend is basically the same. At the same time, the method using the Bayesian network is more similar to the change process of the rainstorm intensity and can better reflect the impact of the rainstorm process on the distribution system. However, the original method without using the Bayesian network results in a lower calculated load loss, underestimates the impact of extreme rainstorm disasters on the distribution system during the evaluation process, may give wrong instructions to the dispatcher, and may cause incorrect allocation of resources, thus resulting in huge economic losses.

[0084] Figure 19It shows a comparison chart of the system resilience before and after using Bayesian. The posterior load loss represents the load loss obtained after using Bayesian, and the prior load loss represents the load loss obtained without using Bayesian. Compared with the load loss calculated by the original method, the evaluation method of the present invention has improved by 14.69% in load loss calculation. It shows that the proposed research method has significant advantages in improving the prediction accuracy of load loss and the accuracy of system evaluation, and fully verifies its effectiveness and reliability in complex environments.

[0085] It should be noted that the content not elaborated in detail in the present invention is all prior art and is well known to those skilled in the art.

[0086] Therefore, the present invention adopts the above-mentioned method for evaluating the resilience of a distribution system 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 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 ability and reliability of the distribution network.

[0087] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A resilience assessment method for a distribution system based on a dynamic Bayesian network, characterized in that It includes the following steps: Step S1: Simulate rainstorm disasters using the Chicago single-peak rainfall model to obtain the rainstorm intensity. Combine the digital elevation model and the two-dimensional hydrodynamic model to simulate urban waterlogging with CI as the grid unit, where CI represents critical infrastructure; Step S2: Based on the waterlogging depth data, establish a failure model for power distribution equipment to obtain the failure probability of each node; Step S3: Use the Monte Carlo sampling method to simulate the state of the power distribution system. Combine the node failure probabilities obtained in Step S2 to generate the operating conditions 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 topological map, use each power distribution equipment and the nodes in the network as the node set in the Bayesian network. Each edge represents the connection relationship between nodes, and construct the conditional probability equation between parent and child nodes. Calculate the power reachability rate using the waterlogging depth data and the node failure probability; Step S5: Consider the load disconnection from operation and the line topology change of the power distribution system caused by extreme rainstorm disasters. Establish a power flow model for the distribution network, and introduce constraint conditions and objective functions. Input the power distribution system state and the power reachability rate into the power flow model of the distribution network to calculate the load loss and voltage offset of the system. Then calculate the expectations and variances of the load loss and voltage offset to evaluate the risk of the system, and finally obtain the resilience evaluation result of the distribution network under rainstorm disasters.

2. The method for evaluating the resilience of a distribution system based on a dynamic Bayesian network according to claim 1, wherein In Step S1, the rainstorm intensity calculation formula is as follows: ； Among them, represents the intensity of rainstorm at a certain moment; represents the duration of rainstorm; represents the recurrence interval of rainstorm; 、 、 、 represent parameters related to the characteristics of rainstorm. Among them, represents the 1-minute design rainfall within the unit recurrence interval; represents the rainfall duration correction parameter; represents the rain force variation parameter; represents the rainstorm attenuation index.

3. The method for evaluating the resilience of a distribution system based on a dynamic Bayesian network according to claim 2, wherein In Step S1, to obtain the rainstorm intensity, combine the digital elevation model and the two-dimensional hydrodynamic model to simulate urban waterlogging with CI as the grid unit. The specific operations are as follows: Perform grid processing on the map; The vector calculation formula after transformation using the Manning formula, combined with the mass of the water flow within the grid , the acceleration due to gravity and the water surface elevation difference between adjacent grids , to calculate the ground friction force; ； ； Among them, represents the water flow pressure of adjacent grids; represents the ground friction of the grid; represents the water flow velocity; represents the water accumulation depth of the grid where the power distribution equipment is located at the moment; represents the Manning coefficient; Bring , into and simplify to calculate the water flow velocities in the east, west, south, and north directions; ； ； Among them, represents the water density; represents the grid width; represents the time interval; represents the water flow velocities in the four directions of east, west, south, and north; represents the height differences in the four directions of east, west, south, and north; Based on the calculated water flow velocities in the four directions of east, west, north, and south, combined with the urban building coverage rate, the water flow in the four directions of east, west, north, and south of the grid is obtained at each moment; ； Among them, represents the water flow rate at the , , , four directions time; represents the urban building coverage rate; represents the west direction; represents the east direction; represents the north direction; represents the south direction; Considering the drainage volume of urban drainage wells, modeling it as negative water flow, and calculating the drainage flow within the grid at a given moment; ； Among them, represents the drainage flow rate within the time grid; represents the number of drainage wells within the grid; represents the drainage coefficient, which is a number between [0, 1]; represents the cross-sectional area of the drainage well; Combined with the drainage flow within the grid and the water flows in the four directions of east, west, north, and south, calculate the grid at the time interval the accumulated water depth at the subsequent moment, and update and iterate the grid depth to obtain the accumulated water conditions of each grid; ； Among them, represents the water flow conversion coefficient; represents the grid water flow from the west-direction grid of the grid to the grid represents the grid water flow from the east-direction grid of the grid to the grid represents the grid water flow from the north-direction grid of the grid to the grid represents the grid water flow from the south-direction grid of the grid to the grid.

4. A resilience evaluation method for a distribution system based on a dynamic Bayesian network according to claim 3, characterized in that In Step S2, based on the waterlogging depth data, establish a failure model for power distribution equipment to obtain the failure probability of each node. The specific operations are as follows: ； Among them, represents the failure probability of the power distribution equipment at the th node at time ; represents the designed flood prevention height of the substation / room or box-type substation; represents the ground elevation of the cable joint of the high-voltage switchgear in the station.

5. The resilience assessment method of a distribution system based on a dynamic Bayesian network according to claim 4, characterized in that In Step S3, use the Monte Carlo sampling method to simulate the state of the power distribution system. Combine the node failure probabilities obtained in Step S2 to generate the operating conditions of the system under different states. The specific operations are as follows: ； Among them, represents the th node's working state at time ; 0 indicates that the node is working properly, and 1 indicates that the node has failed; represents a random number.

6. The method for evaluating the resilience of a distribution system based on a dynamic Bayesian network according to claim 5, wherein In step S4, the Bayesian network after the occurrence of rainstorm disasters is constructed as a set : ； Among them, represents a set 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 resilience evaluation method for a 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, the power reachability rate is the joint probability; when the node is in the fault state, the power reachability rate is the reciprocal of the joint probability. ； Among them, represents the working state of the node at the th node moment; represents the working state of the node at the parent node moment of the node; represents the probability used by the node to calculate the joint probability at the moment, which is related to the state of the node. When the state of the node is normal, , when the state of the node is abnormal, ; represents the probability used by the parent node of the node to calculate the joint probability at the moment; represents the power reach rate; represents the value of the working state.

8. A resilience evaluation method for a distribution system based on a dynamic Bayesian network according to claim 7, characterized in that, In Step S5, the power flow model of the distribution network is as follows: ； Among them, represents minimizing the load loss cost after simulations; represents the number of simulations; represents the th load loss cost caused by the simulation cycle, indicating starting from the first simulation.

9. The method for evaluating the resilience of a distribution system based on a dynamic Bayesian network according to claim 8, characterized in that, In Step S5, the objective function is as follows: ； Among them, represents the loss cost caused by the loss of unit power load of the th node; represents the th node time loss of power; , represent the operation and maintenance loss costs caused by the charging and discharging of unit power energy of energy storage resources; , represent the energy storage device on node time loss of power; represents the set composed of the nodes where the energy storage resources are located in the distribution system.

10. A resilience evaluation method for a distribution system based on a dynamic Bayesian network according to claim 9, characterized in that In Step S5, the constraint conditions include: ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； ； Among them, represents the child node on the line ; represents the parent node on the line ; represents the active power flow flowing through the line at time represents the active power demand of the node at time represents the active power flow flowing through the line at time represents the reactive power flow flowing through the line at time represents the reactive power demand of the node at time represents the reactive power flow flowing through the line at time represents the active power of the load connected to the node at time represents the active power of the lost load of the node at time represents the active power output of the power source connected to the node represents the active power output of the th distributed power source at time represents the discharging power of the energy storage device on the node; represents the energy storage power of the energy storage device on the node; represents the reactive power output of the th distributed power source at time represents the set of nodes where distributed power sources are located in the distribution system; represents the set of lines connecting all nodes; and respectively represent the upper and lower limits of the active power transmitted by the transmission line and respectively represent the upper and lower limits of the reactive power transmitted by the transmission line; represents the node At the moment The square of the voltage; and respectively represent the resistance and reactance on the transmission line ; respectively represent the lower and upper limits of the square of the node voltage; represents the energy storage capacity state of the energy storage device on the node at the moment ; represents the energy conversion efficiency of the energy storage device; represents the charging state of the energy storage device on the node at the moment ; represents the discharging state of the energy storage device on the node at the moment ; and respectively represent the minimum and maximum capacities of the energy storage device; and respectively represent the minimum active power for charging and discharging of the energy storage device; and respectively represent the maximum active power for charging and discharging of the energy storage device; represents the active power output of the th distributed power source at the moment ; represents the reactive power output of the th distributed power source at the moment ; and respectively represent the upper and lower limits of the active power output of the distributed power source; and respectively represent the upper and lower limits of the reactive power output of the distributed power source.

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