Risk assessment method of distribution network under thunderstorm rain composite disaster based on blind number theory

Abstract

The application provides a lightning storm composite disaster-based distribution network risk assessment method based on blind number theory, considers the influence of rainfall intensity on the insulation flashover voltage of the distribution line to construct a distribution line fault probability model, considers the influence of rainfall intensity on the insulation margin of the fan blade to construct a fan fault probability model, and constructs a transformer fault probability model; the information entropy method is used to select a typical fault scene of the distribution network under the lightning storm composite disaster; the loss of load rate, the heavy load proportion of the distribution line, the heavy load proportion of the transformer and the node voltage out-of-limit proportion are respectively expressed as different blind numbers, the risk measurement of each risk assessment index is calculated through the expectation operation of the blind numbers, the weight of different risk assessment indexes is comprehensively considered, the fusion value of the distribution network risk assessment index is calculated, and the risk grade of the distribution network is determined. The application can improve the accuracy and comprehensiveness of the distribution network risk assessment under the lightning storm composite disaster.

Description

Technical Field

[0001] This invention relates to the field of power emergency technology, and in particular to a risk assessment method for distribution networks under combined lightning and rainstorm disasters based on blind number theory. Background Technology

[0002] Risk assessment of distribution networks under combined lightning and rainstorm disasters can provide decision-making basis for power grid companies to conduct pre-disaster special inspections, apply for external assistance, and deploy emergency forces, ensuring the accurate implementation of defense measures. A reasonable assessment of the impact of combined lightning and rainstorm disasters on distribution networks is crucial for more accurate pre-disaster prediction of distribution network damage. The impact of lightning and rainstorms on distribution networks is mainly reflected in insulation flashover of distribution lines caused by lightning and rainstorms, failure of new energy equipment due to lightning strikes, and transformer failure due to water accumulation caused by rainstorms. Risk assessment mainly involves predicting the failure status of distribution network equipment before a disaster, calculating the risk indicators of the distribution network under the disaster, and then integrating the risk indicators to obtain a risk classification and early warning. Regarding the mechanism of disaster impact on distribution networks, current research on the impact of combined lightning and rainstorm disasters on distribution networks is still in its early stages compared to other extreme disasters. Most domestic and international studies only consider the impact of lightning or rainstorms alone on distribution networks, or simply study the impact of rainwater on insulation through experiments, without considering the combined effects of lightning and rainstorms on distribution networks. In terms of risk indicator integration, mainstream risk indicator system construction methods include fuzzy comprehensive evaluation, analytic hierarchy process, Monte Carlo simulation, and subjective and objective weighting method. However, these methods are not comprehensive in handling multi-source uncertainties, are greatly affected by subjective factors, and the consistency of results is difficult to guarantee, thus limiting their engineering applications.

[0003] Therefore, existing risk assessment methods for distribution networks under combined lightning and rainstorm disasters have the following two main shortcomings: First, they only consider the impact of a single lightning or rainstorm disaster on the distribution network, ignoring the impact mechanism of combined lightning and rainstorm scenarios on the distribution network; second, the risk indicator fusion method is too subjective, requires a large amount of historical data, is computationally complex, and does not provide a comprehensive assessment of extreme scenarios. Summary of the Invention

[0004] To improve the accuracy and comprehensiveness of risk assessment for distribution networks under combined lightning and rainstorm disasters, this invention provides a risk assessment method for distribution networks under combined lightning and rainstorm disasters based on blind number theory.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical method: a risk assessment method for distribution networks under combined lightning and rainstorm disasters based on blind number theory, comprising:

[0006] I. Constructing a probability model for power distribution network equipment failure under combined lightning and rainstorm disasters, including: considering the impact of rainfall intensity on the flashover voltage of power distribution line insulation, constructing a probability model for power distribution line failure based on the strike distance method; considering the impact of rainfall intensity on the insulation margin of wind turbine blades, constructing a probability model for wind turbine failure based on the effective interception area of ​​wind turbine blades struck by lightning; and constructing a probability model for transformer failure based on a two-dimensional hydraulic model.

[0007] II. Selecting typical fault scenarios of power distribution networks under combined lightning and rainstorm disasters using the information entropy method;

[0008] III. Integration and hierarchical early warning of risk assessment indicators under combined lightning and rainstorm disasters based on blind number theory: The four types of risk assessment indicators, namely, load shedding rate, distribution line overload ratio, transformer overload ratio, and node voltage overrun ratio, are represented by different blind numbers. The risk measure of each risk assessment indicator is calculated by the expectation operation of the blind numbers. Then, the weights of different risk assessment indicators in the risk assessment are combined to calculate the integrated value of the distribution network risk assessment indicators, and thus determine the risk level of the distribution network.

[0009] Furthermore, in the power distribution network equipment failure probability model under the combined lightning and rainstorm disaster:

[0010] 1) The expression for the power distribution line fault probability model is as follows:

[0011] (1)

[0012] In the formula, The probability of power line failure under combined lightning and rainstorm disasters; The tripping rate of the power distribution line; This represents the ratio between the probability of a power distribution line failure and the tripping rate.

[0013] (2)

[0014] (3)

[0015] (4)

[0016] (5)

[0017] In the formula, Indicates the current time; The direct lightning strike trip rate of power distribution lines; The tripping rate of induced lightning on power distribution lines; The shielding factor for lightning strikes caused by trees; Lightning strike density; For the arc-building rate; The width of the projection of the topmost conductor onto the ground; This refers to the lightning strike range on one side of an overhead power distribution line. The lightning withstand level of the power distribution line; This represents the average operating voltage gradient of the insulator string;

[0018] (6)

[0019] (7)

[0020] In the formula, Rainfall intensity; The lightning withstand voltage of the power distribution line has a negative exponential power function relationship with the rainfall intensity; , These are the characteristic coefficient and index of rainfall intensity, respectively;

[0021] 2) The expression for the wind turbine failure probability model is as follows:

[0022] (8)

[0023] (9)

[0024] In the formula, The probability of wind turbine failure under combined lightning and rainstorm disasters; This refers to the effective receiving area of ​​the wind turbine; For the fan position factor; This is a correction factor for the impact of rainfall intensity on the damage to wind turbine blades caused by lightning strikes. This represents the probability of a single lightning strike causing a wind turbine blade to fail, assuming the wind turbine is equipped with a lightning arrester. Take 0.02, when there is no lightning arrester Take 1; The value ranges from 0.5 to 1.0, and is calibrated based on historical fault statistics for the region. This represents the lower limit of rainfall intensity during heavy rain. This represents the upper limit of rainfall intensity during periods of no rain or light rain.

[0025] 3) The expression for the transformer failure probability model is as follows:

[0026] (10)

[0027] In the formula, The probability of transformer failure under combined lightning and rainstorm disasters; These are the coefficients of the transformer fault probability model; The depth of water accumulation in the area where the power distribution equipment is located; The design height for flood protection of power distribution equipment.

[0028] Furthermore, the process of sampling typical fault scenarios of the distribution network under combined lightning and rainstorm disasters using the information entropy method includes:

[0029] 1) Collect current meteorological and power grid data for the area to be evaluated;

[0030] 2) Divide the assessment period and calculate the failure probability of power distribution lines, wind turbines and transformers under the combined disaster of lightning and rainstorm according to the failure probability model of power distribution network equipment under the combined disaster of lightning and rainstorm.

[0031] 3) Based on the calculated failure probabilities of power distribution lines, wind turbines, and transformers, the entropy value corresponding to different failure scenarios is calculated using the information entropy method. Typical failure scenarios are selected by sampling from the interval with the highest probability of entropy value occurrence.

[0032] (11)

[0033] (12)

[0034] In the formula, The entropy value of the fault scenario; , These are the upper and lower limits of the interval where the entropy value has the highest probability of occurring, respectively. This indicates the time it takes for extreme weather to travel through the distribution network area; for Real-time distribution network equipment The probability of failure, the equipment includes power distribution lines, fans, transformers; for Power distribution lines Did the malfunction just happen? For the malfunction to occur, To prevent malfunctions, The value of follows the distribution of the failure probability of distribution network equipment; For distribution network line collection.

[0035] Furthermore, the process of fusing system-level risk assessment indicators for combined lightning and rainstorm disasters based on blind number theory includes:

[0036] 1) Simulate the power grid operation status under typical fault scenarios on the simulation platform, and determine whether there are isolated nodes in the power grid. If so, calculate the load loss of the isolated node first, and then perform power flow calculation. If not, perform power flow calculation directly.

[0037] 2) Determine whether all typical scenarios have been simulated. If not, continue the simulation. If so, calculate the risk assessment index values ​​of the impact of lightning and rainstorm combined disasters on the distribution network lines, including the load failure rate, the proportion of heavy load on distribution lines, the proportion of heavy load on transformers, and the proportion of voltage exceeding the limit at nodes.

[0038] 3) Modeling each risk assessment indicator using blind number theory: Assuming the risk assessment indicators have There are several types, and each type of risk assessment indicator has... The range of values ​​is defined as the nth interval. Type 1 The risk assessment indicators for each value range are: , ; ; Based on the information entropy method, typical failure scenarios are sampled, and the minimum, average, and maximum values ​​of each risk assessment indicator are denoted as follows: , , And the values ​​in typical fault scenarios fall within , , The probabilities of these three intervals are denoted as follows: Risk assessment indicators Represented as blind numbers, as shown in the following formula:

[0039] (13)

[0040] In the formula, Represents the possible values ​​of the blind number; Indicates possible values The corresponding credibility;

[0041] 4) Calculate the risk measure for each risk assessment indicator using the following formula. ;

[0042] (14)

[0043] 5) Select any pair of indicators from all risk assessment indicators. , To compare their importance, and Construct a judgment matrix based on the importance judgment values ​​between each pair of elements. Find the judgment matrix Eigenvectors under the largest eigenvalue The feature vectors were normalized to obtain the weights of different risk assessment indicators in the risk assessment of combined lightning and rainstorm disasters. ;

[0044] (15)

[0045] (16)

[0046] In the formula, To determine the matrix The Middle Line number Column elements, , For the first The importance judgment value of various risk assessment indicators For the first The importance judgment value of various risk assessment indicators;

[0047] 6) Calculate the fusion value of the risk assessment index of the distribution network under the combined disaster of lightning and rainstorm using the following formula. ;

[0048] (17).

[0049] Furthermore, based on the integrated value of distribution network risk assessment indicators... Determine the risk level of the power distribution network: A level 3 risk rating indicates that the consequences of the malfunction are extremely serious. A level 2 risk rating indicates that the failure will cause a significant reduction in production. Level 1 risk indicates that a short-term power outage will not cause significant losses; Levels 0-1 are defined as low risk, Levels 1-2 as medium risk, and Levels 2-3 as high risk.

[0050] Preferably, in the process of integrating system-level risk assessment indicators under combined lightning and rainstorm disasters based on blind number theory, Distflow is used for power flow calculation. The constraints of this power flow calculation include: power balance constraints, node voltage constraints, line current and transmission capacity constraints, load shedding constraints, and second-order cone constraints. The second-order cone constraints are obtained by converting the nonlinear constraints between voltage, current, and power in the line current and transmission capacity constraints through the second-order cone relaxation principle.

[0051] This invention provides a risk assessment method for distribution networks under combined lightning and rainstorm disasters based on blind number theory. This method covers risks at each stage of the power supply, grid, and load chain. In the fault probability modeling process, it fully considers the impact of combined lightning and rainstorm disasters on distribution network equipment, taking into account the influence of rainfall intensity on line insulation flashover voltage. It also corrects the fault probability of lightning-struck wind turbines under rainfall conditions, making the modeling of the distribution network's impact mechanism more accurate. Secondly, this invention combines blind number theory with information entropy sampling methods to conduct risk assessments based on four indicators: load shedding rate, distribution line overload ratio, transformer overload ratio, and node voltage exceedance ratio. The integration of risk assessment indicators fully considers both subjective and objective factors, improving the accuracy and comprehensiveness of the risk assessment. This provides data support for the power grid's decision-making in pre-disaster prevention, in-disaster management, and rapid post-disaster recovery. Attached Figure Description

[0052] Figure 1 This is a flowchart of the distribution network risk assessment method based on blind number theory under combined lightning and rainstorm disasters involved in this invention.

[0053] Figure 2 This is a topology diagram of a power distribution system in Guangxi Province according to an embodiment of the present invention;

[0054] Figure 3 This is a schematic diagram of the probability of power line failure under combined lightning and rainstorm disasters in the embodiments of the present invention before modification;

[0055] Figure 4 This is a schematic diagram illustrating the probability of power line faults under a modified combined lightning and rainstorm disaster in an embodiment of the present invention.

[0056] Figure 5 This is a schematic diagram showing the wind turbine failure probability before and after the modification in the embodiments of the present invention;

[0057] Figure 6 This is a schematic diagram illustrating the transformer failure probability in an embodiment of the present invention;

[0058] Figure 7 This is a comparison chart of the fusion values ​​of risk assessment indicators before and after reconstruction in an embodiment of the present invention;

[0059] Figure 8 This is a comparison chart of risk levels before and after reconstruction in an embodiment of the present invention. Detailed Implementation

[0060] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments and accompanying drawings. The content mentioned in the embodiments is not intended to limit the present invention.

[0061] like Figure 1 As shown, the risk assessment method for power distribution networks under combined lightning and rainstorm disasters based on blind number theory provided by this invention mainly includes the following steps.

[0062] Step S1: Construct a fault probability model for power distribution network equipment under combined lightning and rainstorm disasters. Model the impact mechanism of combined lightning and rainstorm disasters on power distribution lines, wind turbines, and transformers. The specific process is as follows:

[0063] 1) Construct a distribution line fault probability model based on the strike distance method

[0064] The point of impact when lightning strikes the ground is uncertain, depending on which object the discharge path first enters within its strike distance. A direct lightning strike within the strike distance of a conductor causes a tripping breaker, while a strike within the strike distance to the ground causes an induced lightning strike. The strike distance of medium-voltage overhead distribution lines is also considered. Taking into account the possibility of trees near distribution lines, which may prevent a direct strike to the conductor and create a shielding section, this model incorporates the shielding effect of trees on lightning strikes to distribution lines.

[0065] Wire distance Tree shooting distance Ground distance The calculation formulas are as follows:

[0066] (18)

[0067] (19)

[0068] (20)

[0069] In the formula, The average height of the conductor. This represents the strongest lightning current amplitude. This is the comprehensive influence coefficient of topography and geology; for open plains, this value is taken as 0.6.

[0070] The height of the intersection of the exposed earth arc and the exposed conductor arc is equal to The corresponding lightning current ;

[0071] (twenty one)

[0072] In the formula, The ground is tilted.

[0073] Lightning range on one side of overhead power distribution line The calculation formula is:

[0074] (twenty two)

[0075] (twenty three)

[0076] In the formula, The x-coordinate of the intersection of the conductor strike distance and the ground strike distance. Let be the probability density function of lightning current amplitude.

[0077] Lightning shielding factor of lines caused by trees :

[0078] (twenty four)

[0079] (25)

[0080] In the formula, The length of the shielded segment. Tree height, It is the horizontal distance between the tree and the guide wire.

[0081] At present time in general regions The tripping rates of distribution lines, direct lightning strikes, and induced lightning strikes within the network are expressed as follows:

[0082] (2)

[0083] (3)

[0084] (4)

[0085] (5)

[0086] In the formula, The direct lightning strike trip rate of power distribution lines; The tripping rate of induced lightning on power distribution lines; The shielding factor for lightning strikes caused by trees; Lightning strike density; For the arc-building rate; The width of the projection of the topmost conductor onto the ground; This refers to the lightning strike range on one side of an overhead power distribution line. The lightning withstand level of the power distribution line; This represents the average operating voltage gradient of the insulator string.

[0087] In traditional distribution network lightning protection design and risk assessment, the lightning withstand level of lines is usually considered a fixed parameter independent of environmental conditions, making it difficult to reflect the dynamic changes in insulation performance under lightning and rainstorm coupled conditions. In reality, heavy rainfall alters the electrical environment around conductor insulators; rainwater causes moisture on the insulator surface and increases the conductivity of the pollution layer, leading to a decrease in flashover voltage and weakening the line's withstand capability against lightning strikes and induced overvoltages. Therefore, this invention addresses the lightning withstand level of distribution lines... Make the correction as follows:

[0088] (6)

[0089] (7)

[0090] In the formula, Rainfall intensity; The lightning withstand voltage of a power distribution line exhibits a negative exponential power function relationship with rainfall intensity, with a maximum reduction of up to 35.7%. , These are the characteristic coefficients and indices affecting rainfall intensity, respectively. It is related to factors such as external environmental parameters, insulator type, and arrangement.

[0091] Currently, there is a lack of mature models that quantitatively establish the relationship between the probability of power line faults and the cumulative tripping rate. Therefore, a fitting approach based on historical data can be used, employing the least squares method to establish a functional relationship between the two. A proportional coefficient showing a linear relationship between the two can be obtained from historical data of a specific region. Therefore, the probability model for power distribution line faults can be obtained, and its expression is as follows:

[0092] (1)

[0093] In the formula, The probability of power line failure under combined lightning and rainstorm disasters; The tripping rate of the power distribution line; This represents the ratio between the probability of a power distribution line failure and the tripping rate.

[0094] 2) Construct a wind turbine failure probability model based on the effective cut-off area of ​​the wind turbine blades struck by lightning.

[0095] Wind turbine blades are key components that disrupt the electric field and determine the equivalent height and interception area of ​​the turbine. Their high-speed rotation significantly increases the probability of lightning leaders being captured, making them more susceptible to lightning strikes. Therefore, blade damage is a major failure mode in lightning-induced wind turbine failures. Under combined lightning and rainstorm disasters, heavy rainfall increases the surface humidity and conductivity of the blades, weakens the external insulation margin, and further amplifies the probability of lightning damage. Based on this, this invention establishes a wind turbine failure probability model based on the effective interception area of ​​the wind turbine blades, using the blade lightning damage probability as the core indicator of wind turbine failure, and adjusting the failure probability using a correction coefficient related to rainfall intensity.

[0096] Assuming the fan operates at a constant speed under stable conditions, the angle through which the blades rotate per unit time remains constant. At this point, the effect of blade rotation on the overall equivalent height of the wind turbine varies periodically and is unevenly distributed, resulting in a wind turbine nacelle height of [missing information]. The blade length is The maximum height of the blade tip above the ground is affected by The minimum height is The change in height during the rotation of the fan. for:

[0097] (26)

[0098] According to the calculation method of IEC / TH61400-24, the height is related to the cut-off area. The formula for the influence is Therefore, after considering the change in height during the rotation of the fan, for The formula was improved to obtain the improved interception area. The formula for the influence is:

[0099] (27)

[0100] when When changing from 0° to 60° The range of change is approximately This indicates that different rotation angles have different effects on the equivalent interception area; the closer the rotation angle is to 90°, the greater the range of variation in the blade tip height, and the greater the impact on... The impact is also more significant. Given that this model focuses on the probability of wind power equipment being struck by lightning per unit time, this invention takes a representative operating condition. Substituting into formula (26), we get:

[0101] (28)

[0102] At this time, the relative height of the blade tip from the ground is Therefore, the effective interception area under lightning strike wind turbine failure can be derived. The expression is as follows:

[0103] (29)

[0104] Based on the effective interception area of ​​wind turbines, the lightning strike density under lightning disasters, and the location factor of wind turbines, combined with the mechanism analysis of the decrease in blade insulation strength and the reduction in lightning arrester interception efficiency caused by moisture and precipitation, this invention corrects the probability of damage to wind turbine blades caused by lightning strikes, and obtains a wind turbine failure probability model, the expression of which is as follows:

[0105] (8)

[0106] (9)

[0107] In the formula, The probability of wind turbine failure under combined lightning and rainstorm disasters; This refers to the effective receiving area of ​​the wind turbine; For the fan position factor; This is a correction factor for the impact of rainfall intensity on the damage to wind turbine blades caused by lightning strikes. This represents the probability of a single lightning strike causing a wind turbine blade to fail, assuming the wind turbine is equipped with a lightning arrester. Take 0.02, when there is no lightning arrester Take 1; The value ranges from 0.5 to 1.0, and is calibrated based on historical fault statistics for the region. This represents the lower limit of rainfall intensity during heavy rain. This represents the upper limit of rainfall intensity during periods of no rain or light rain.

[0108] 3) Construct a transformer fault probability model based on a two-dimensional hydraulic model.

[0109] In the overall scenario of combined lightning and rainstorm disasters, due to the combined effects of rainfall, topographical factors, and urban drainage systems, the risk of power distribution cabinet equipment failure caused by rainstorms in low-lying urban areas and areas with insufficient drainage capacity is directly related to the depth of water accumulation.

[0110] In the urban flooding simulation software Mike21, a two-dimensional hydraulic model was used to simulate the water depth of each grid cell. Based on this water depth, a transformer fault probability model was constructed, the expression of which is as follows:

[0111] (10)

[0112] In the formula, The probability of transformer failure under combined lightning and rainstorm disasters; These are the coefficients of the transformer fault probability model; The depth of water accumulation in the area where the power distribution equipment is located; The design height for flood protection of power distribution equipment.

[0113] In summary, the probability model for power distribution network equipment failure under the combined disaster of lightning and rainstorm is obtained as follows:

[0114] (30).

[0115] Step S2: Select typical fault scenarios of the power distribution network under combined lightning and rainstorm disasters using the information entropy method.

[0116] 1) Collect current meteorological and power grid data for the area to be evaluated.

[0117] 2) Divide the assessment period and calculate the failure probability of power distribution lines, wind turbines and transformers under the combined disaster of lightning and rainstorm according to the failure probability model of power distribution network equipment under the combined disaster of lightning and rainstorm.

[0118] 3) Fault scenario selection based on system information entropy

[0119] First, using the information entropy method, the failure probabilities of distribution network lines, wind turbines, and transformers under the coupled disaster of lightning and rainstorms are calculated according to step 1, and failure scenarios are selected accordingly. The number of multiple failure scenarios resulting from combinations of different faulty components is enormous. Therefore, it is necessary to analyze the possible failure scenarios under the combined disaster of lightning and rainstorms based on the probability and uncertainty of scenario occurrence and the failure rate of overhead lines. The system information entropy method is a method of selecting reasonable system state scenarios based on the probability of a single event. Entropy represents the degree of uncertainty of a system. The distribution network is an uncertain system that may fail at any moment, and its entropy value is:

[0120] (11)

[0121] In the formula, The entropy value of the fault scenario; This indicates the time it takes for extreme weather to travel through the distribution network area; for Real-time distribution network equipment The probability of failure, the equipment includes power distribution lines, fans, transformers; for Power distribution lines Did the malfunction just happen? For the malfunction to occur, To prevent failures, each resilience analysis scenario corresponds to a specific scenario. A vector, corresponding to the entropy value of the system in that scenario; For distribution network line collection.

[0122] Considering the uncertainty of failure scenarios The value of should follow the distribution of the failure rate. The higher the failure rate of a line, the greater the probability of the uncertain event of a line failure occurring, and the more scenarios corresponding to it. The value is 1, for example, the line. With a failure rate of 0, the uncertainty of a component failure event is infinite, meaning there will definitely be one failure event in all scenarios. Therefore, considering the likelihood of such scenarios occurring in real-world situations, the reasonable value of the resilience analysis scenario entropy cannot be too large or too small, satisfying the following:

[0123] (12)

[0124] In the formula, , These are the upper and lower limits of the interval where the entropy value has the highest probability of occurring, respectively.

[0125] Based on the calculated fault probabilities of distribution lines, wind turbines, and transformers, the entropy value corresponding to different fault scenarios is calculated using the information entropy method. Typical fault scenarios are selected by sampling from the interval with the highest probability of entropy occurrence. The calculation of system-level risk requires time-series correlation simulation optimization of these typical fault scenarios to assess risks such as system load loss, node voltage exceedances, and line power flow exceedances. Fault scenarios that meet the selected criteria, characterized by a high probability of occurrence and severe consequences, constitute typical fault scenarios in distribution network risk assessment.

[0126] Step S3: Based on blind number theory, integrate and classify risk assessment indicators for combined lightning and rainstorm disasters for early warning.

[0127] 1) Simulate the power grid operation under typical fault scenarios on the Matlab simulation platform to determine whether isolated nodes have appeared in the power grid. If so, calculate the load loss of the isolated node first, and then perform power flow calculation. If not, perform power flow calculation directly. For radial distribution networks, the Distflow power flow equation is used. The constraints under this power flow calculation are:

[0128] ① Power balance constraints

[0129] (31)

[0130] (32)

[0131] In the formula, and They are nodes The set of child nodes and parent nodes, and For the scene Down Time Node The active and reactive power transmitted to child nodes. and For the scene Down At any time, the parent node sends data to the node. The transmitted active and reactive power, and These are the resistance and reactance of the circuit, respectively. For the scene Downline exist The square term of the current transmitted at any given time. and Indicates the upper-level power grid in the scenario Down Time to node The active and reactive power flow of transmission. and Representing a scene Down Time Node The active and reactive power generated by the wind turbine generator; Reduction factor categorized by load level; , Scenes Down Time Node The active and reactive power requirements; , Scenes Down Time Node The active and reactive power under load.

[0132] ② Node voltage constraints

[0133] For radial distribution networks, the network topology constantly changes as lines are out of service during disasters; therefore, a large-scale... The method relaxes the nodal voltage equations, and the nodal voltage constraints are as follows:

[0134] (33)

[0135] (34)

[0136] (35)

[0137] In the formula, and They are the scenes Next node and nodes exist The square of the voltage at time t, , It is a node Permissible minimum and maximum voltages Indicates the line In the scene Down The running status at any given moment; It is a maximum value.

[0138] ③ Line current and transmission capacity constraints

[0139] The current and capacity transmitted through the line must not exceed the maximum current and maximum capacity limits for line transmission. The constraints on line current and transmission capacity are as follows:

[0140] (36)

[0141] (37)

[0142] In the formula, This is the upper limit of the square term of the line current.

[0143] ④ Load reduction constraints

[0144] (38)

[0145] (39)

[0146] In the formula, Indicates distribution node In the scene Down The operational status at any given moment.

[0147] ⑤ Second-order cone constraint

[0148] For the nonlinear constraint between voltage, current and power shown in equation (37), it can be converted into a second-order cone constraint using the second-order cone relaxation principle as shown below:

[0149] (40)

[0150] 2) Determine whether all typical scenarios have been simulated. If not, continue the simulation. If so, calculate the risk assessment index values ​​of the impact of lightning and rainstorm combined disasters on the distribution network lines, including the load failure rate, the proportion of heavy load on distribution lines, the proportion of heavy load on transformers, and the proportion of node voltage exceeding the limit.

[0151] Loss of load rate :

[0152] (41)

[0153] In the formula, , These are the total power loss of the distribution network and the total required load power, respectively.

[0154] ② Risk of node voltage exceeding limits:

[0155] The degree of node voltage exceedance at each time point is calculated by the following formula:

[0156] (42)

[0157] (43)

[0158] In the formula, This is the voltage when the power grid is operating normally. This refers to the node voltage after a power grid fault occurs. To exceed the lower threshold, To exceed the upper limit threshold, The degree to which the node voltage falls below the lower limit, The degree to which a node exceeds the upper limit is determined. If the calculated degree is negative, it means that the node has not exceeded either the upper or lower limit.

[0159] The number of nodes exceeding voltage limits is counted, and the ratio of the number of nodes exceeding voltage limits to the total number of nodes is calculated to obtain the node voltage limit exceeding ratio. :

[0160] (44)

[0161] In the formula, Indicates the number of nodes whose voltage exceeds the limit. This represents the total number of nodes.

[0162] ③ Risk of overload on power distribution lines:

[0163] (45)

[0164] In the formula, For line load rate, This represents the upper limit of the line's transmission capacity. After calculating the line's load factor, a threshold can be set; when the line's load factor exceeds this threshold, it is considered overloaded. , The lines are respectively In time The active and reactive power.

[0165] Count the number of overloaded power distribution lines and calculate the total number of overloaded lines. Total number of lines The proportion of heavy load on the power distribution line is obtained from the ratio. :

[0166] (46)

[0167] ④ Transformer overload risk:

[0168] (47)

[0169] In the formula, Transformer load factor; For nodes exist Active power at any given time; For nodes exist Reactive power at any given moment; For nodes exist Apparent power at any given moment.

[0170] Count the number of overloaded distribution transformers and calculate the total number of overloaded transformers. With the total number of transformers The proportion is used to obtain the transformer overload ratio. :

[0171] (48)

[0172] 3) Model each risk assessment indicator using blind number theory.

[0173] To effectively integrate the four system-level risk assessment indicators obtained above, this paper first examines the impact characteristics of lightning and rainstorms on the distribution network. It points out that the fault mechanism exhibits significant randomness, fuzziness, grey effects, and uncertainty, making it difficult to accurately characterize using deterministic functions. Therefore, blind number theory is introduced to uniformly model various risk indicators: the four risk assessment indicators—load loss rate, distribution line overload ratio, transformer overload ratio, and node voltage exceedance ratio—are represented as different blind numbers. The risk measure of each risk assessment indicator is calculated through the expectation operation of the blind numbers. Then, by combining the weights of different risk assessment indicators in the risk assessment, the integrated value of the distribution network risk assessment indicators is calculated, thereby determining the risk level of the distribution network.

[0174] Blind numbering involves two parts: possible values ​​and confidence level. Let's assume an interval-type grey number set consists of interval number sequences with multiple possible values. Formation, credibility of each interval Credibility sequences distributed across multiple intervals As shown in the following formula:

[0175] (49)

[0176] Under a single indicator factor, assuming the risk assessment indicators have There are several types, and each type of risk assessment indicator has... The range of values ​​is defined as the nth interval. Type 1 The risk assessment indicators for each value range are: , ; ; Based on the information entropy method, typical failure scenarios are sampled, and the minimum, average, and maximum values ​​of each risk assessment indicator are denoted as follows: , , .

[0177] In terms of credibility calculation, it is divided into two parts: one is the credibility of a single risk indicator value, and the other is the credibility of the overall risk indicator formed by merging multiple indicators. The credibility of a single risk indicator value is calculated by sampling typical failure scenarios using information entropy, and then determining the values ​​falling within these typical failure scenarios. , , The probabilities of these three intervals are denoted as follows: Risk assessment indicators Represented as blind numbers, as shown in the following formula:

[0178] (13)

[0179] In the formula, express Possible values ​​for blind numbers; express Possible values ​​of blind numbers The corresponding credibility;

[0180] 4) Calculate the risk measure for each risk assessment indicator using the following formula. This risk metric will serve as a potential value for subsequent risk indicator fusion.

[0181] (14)

[0182] 5) Qualitative and quantitative analysis of the possible values ​​of a single risk assessment indicator is conducted using the judgment matrix method. The estimation results comprehensively reflect the weight of different risk assessment indicators in the risk assessment of the power distribution network under combined lightning and rainstorm disasters. Any pair of indicators is randomly selected from all risk assessment indicators. , To compare their importance, and ,remember right Importance rating The judgment value is given according to the 9-level scale method shown in Table 1.

[0183] Table 1

[0184] ;

[0185] Construct a judgment matrix based on the importance judgment values ​​between each pair of elements. :

[0186] (15)

[0187] In the formula, To determine the matrix The Middle Line number Column elements, , For the first The importance judgment value of various risk assessment indicators For the first The importance judgment value of each risk assessment indicator.

[0188] By constructing a judgment matrix among factors of different levels Then, the judgment matrix is ​​obtained. Eigenvectors under the largest eigenvalue The feature vectors were normalized to obtain the weights of different risk assessment indicators in the risk assessment of combined lightning and rainstorm disasters. ;

[0189] (16)

[0190] 6) Calculate the fusion value of the risk assessment index of the distribution network under the combined disaster of lightning and rainstorm using the following formula. ;

[0191] (17).

[0192] 7) Based on the integrated value of distribution network risk assessment indicators Determine the risk level of the power distribution network.

[0193] According to GB50052-1995 "Code for Design of Power Supply and Distribution Systems", load levels are classified from two aspects: safety and economic loss. This code only describes the definition of load levels. In order to clarify the impact of different risk indicators on the system, this invention, based on the above-mentioned code, classifies the fusion value of risk assessment indicators for distribution networks under combined lightning and rainstorm disasters based on blind number theory, with the value range being [0, 1]. The classification results are shown in Table 2.

[0194] Table 2

[0195] ;

[0196] In Table 2, A level 3 risk rating indicates that the consequences of the malfunction are extremely serious. A level 2 risk rating indicates that the failure will cause a significant reduction in production. Level 1 risk indicates that a short-term power outage will not cause significant losses; this invention defines levels 0-1 as low risk, levels 1-2 as medium risk, and levels 2-3 as high risk.

[0197] To verify the effectiveness and practicality of the method proposed in this invention, a simulation experiment was conducted. A power distribution system in Guangxi was selected as a case study for analysis. The power distribution network topology is as follows: Figure 2 As shown, black nodes represent load nodes, black nodes with triangles represent industrial and commercial loads, white nodes represent no-load nodes, #1 represents node number 1, S1 represents line 1, TS1 represents tie line 1, dashed lines represent normally open tie lines and their included tie switches, WT represents wind farms, PV represents photovoltaic power stations, PV1 is a centralized photovoltaic power station, and PV2-4 are distributed rooftop photovoltaic areas.

[0198] Using the method proposed in this invention, the equipment-level risk and system-level risk under a certain thunderstorm and rainstorm combined weather conditions in a power distribution system in Guangxi can be obtained, and the 12 time periods with the greatest impact of thunderstorm and rainstorm disasters on the power distribution network can be selected for simulation. Figure 3 The original value represents the probability of power line failure under a combined lightning and rainstorm disaster. Figure 4This represents the corrected probability of faults in the power distribution lines. Figure 5 To compare the wind turbine failure probabilities before and after correction. Figure 6 This represents the probability of transformer failure. Figure 7 To compare the fused values ​​of risk assessment indicators before and after the restructuring, Figure 8 To compare the risk levels before and after the restructuring, Figure 8 Levels 0-1 are considered low risk, 1-2 are considered medium risk, and 2-3 are considered high risk.

[0199] from Figure 3 and Figure 4 The comparison shows that when calculating the probability of lightning-induced faults in distribution network lines based on the strike distance method, the impact of heavy rainfall on the electrical environment around conductor insulators is taken into account. Rainwater causes the surface of the insulators to become damp and the conductivity of the pollution layer to increase, which reduces the flashover voltage and weakens the line's ability to withstand lightning strikes and induced overvoltages. Therefore, the probability of line faults increases significantly.

[0200] from Figure 5 It can be seen that during heavy rain, moisture and precipitation lead to a decrease in the insulation strength of the blades and a reduction in the interception efficiency of the lightning arrester, thus increasing the probability of lightning-induced wind turbine failure.

[0201] according to Figure 7 and Figure 8 This demonstrates the effectiveness of the method proposed in this invention. After reconstruction, the fusion value of the risk assessment index of the distribution network under the combined disaster of lightning and rainstorm significantly decreased. Figure 8 It can be seen that before the reconstruction, the distribution network was at high risk from the 8th time period, while after the reconstruction, the distribution network was at high risk only at one time, and then it was reduced to medium risk.

[0202] The above embodiments are preferred implementations of the present invention. In addition, the present invention can be implemented in other ways. Any obvious substitutions without departing from the concept of the present technical solution are within the protection scope of the present invention.

[0203] To facilitate understanding by those skilled in the art of the improvements of this invention over the prior art, some of the accompanying drawings and descriptions have been simplified, and for clarity, some other elements have been omitted from this application. Those skilled in the art should realize that these omitted elements may also constitute the content of this invention.

Claims

1. A risk assessment method for distribution networks under combined lightning and rainstorm disasters based on blind number theory, characterized by: I. Constructing a probability model for power distribution network equipment failure under combined lightning and rainstorm disasters, including: considering the impact of rainfall intensity on the flashover voltage of power distribution line insulation, constructing a probability model for power distribution line failure based on the strike distance method; considering the impact of rainfall intensity on the insulation margin of wind turbine blades, constructing a probability model for wind turbine failure based on the effective receiving area of ​​wind turbine blades struck by lightning; and constructing a probability model for transformer failure based on a two-dimensional hydraulic model. The expression for the power distribution line fault probability model is as follows: （1） In the formula, The probability of power line failure under combined lightning and rainstorm disasters; The tripping rate of the power distribution line; This represents the ratio between the probability of a power distribution line failure and the tripping rate. （2） （3） （4） （5） In the formula, Indicates the current time; The direct lightning strike trip rate of power distribution lines; The tripping rate of induced lightning on power distribution lines; The shielding factor for lightning strikes caused by trees; Lightning strike density; For the arc-building rate; The width of the projection of the topmost conductor onto the ground; This refers to the lightning strike range on one side of an overhead power distribution line. The lightning withstand level of the power distribution line; This represents the average operating voltage gradient of the insulator string; （6） （7） In the formula, Rainfall intensity; The lightning withstand voltage of the power distribution line has a negative exponential power function relationship with the rainfall intensity; , These are the characteristic coefficient and index of rainfall intensity, respectively; The expression for the wind turbine failure probability model is as follows: （8） （9） In the formula, The probability of wind turbine failure under combined lightning and rainstorm disasters; This refers to the effective receiving area of ​​the wind turbine; For the fan position factor; This is a correction factor for the impact of rainfall intensity on the damage to wind turbine blades caused by lightning strikes. This represents the probability of a single lightning strike causing a wind turbine blade to fail, assuming the wind turbine is equipped with a lightning arrester. Take 0.02, when there is no lightning arrester Take 1; The value ranges from 0.5 to 1.0, and is calibrated based on historical fault statistics for the region. This represents the lower limit of rainfall intensity during heavy rain. This represents the upper limit of rainfall intensity during periods of no rain or light rain. II. Selecting typical fault scenarios of power distribution networks under combined lightning and rainstorm disasters using the information entropy method; III. Integration and hierarchical early warning of risk assessment indicators under combined lightning and rainstorm disasters based on blind number theory: The four types of risk assessment indicators, namely, load shedding rate, distribution line overload ratio, transformer overload ratio, and node voltage overrun ratio, are represented by different blind numbers. The risk measure of each risk assessment indicator is calculated by the expectation operation of the blind numbers. Then, the weights of different risk assessment indicators in the risk assessment are combined to calculate the integrated value of the distribution network risk assessment indicators, and then the risk level of the distribution network is determined. The process of fusing risk assessment indicators under combined lightning and rainstorm disasters based on blind number theory includes: 1) Simulate the power grid operation status under typical fault scenarios on the simulation platform, and determine whether there are isolated nodes in the power grid. If so, calculate the load loss of the isolated node first, and then perform power flow calculation. If not, perform power flow calculation directly. 2) Determine whether all typical scenarios have been simulated. If not, continue the simulation. If yes, calculate the risk assessment index values ​​of the impact of lightning and rainstorm combined disasters on the distribution network lines, including the load failure rate, the proportion of heavy load on distribution lines, the proportion of heavy load on transformers, and the proportion of voltage exceeding the limit at nodes. 3) Modeling each risk assessment indicator using blind number theory: Assuming the risk assessment indicators have There are several types, and each type of risk assessment indicator has... The range of values ​​is defined as the nth interval. Type 1 The risk assessment indicators for each value range are: , ; ; Based on the information entropy method, typical failure scenarios are sampled, and the minimum, average, and maximum values ​​of each risk assessment indicator are denoted as follows: , , And the values ​​in typical fault scenarios fall within , , The probabilities of these three intervals are denoted as follows: Risk assessment indicators Represented as blind numbers, as shown in the following formula: （13） In the formula, Represents the possible values ​​of the blind number; Indicates possible values The corresponding credibility; 4) Calculate the risk measure for each risk assessment indicator using the following formula. ; （14） 5) Select any pair of indicators from all risk assessment indicators. , To compare their importance, or and Construct a judgment matrix based on the importance judgment values ​​between each pair of elements. Find the judgment matrix Eigenvectors under the largest eigenvalue The feature vectors were normalized to obtain the weights of different risk assessment indicators in the risk assessment of combined lightning and rainstorm disasters. ; （15） （16） In the formula, To determine the matrix The Middle Line number Column elements, , For the first The importance judgment value of various risk assessment indicators For the first The importance judgment value of various risk assessment indicators; 6) Calculate the fusion value of the risk assessment index of the distribution network under the combined disaster of lightning and rainstorm using the following formula. ; （17）。 2. The method for risk assessment of distribution networks under combined lightning and rainstorm disasters based on blind number theory according to claim 1, characterized in that: In the power distribution network equipment failure probability model under the combined disaster of lightning and rainstorm: The expression for the transformer failure probability model is as follows: （10） In the formula, The probability of transformer failure under combined lightning and rainstorm disasters; These are the coefficients of the transformer fault probability model; The depth of water accumulation in the area where the power distribution equipment is located; The design height for flood protection of power distribution equipment.

3. The method for risk assessment of distribution networks under combined lightning and rainstorm disasters based on blind number theory according to claim 2, characterized in that: The process of sampling typical fault scenarios of power distribution networks under combined lightning and rainstorm disasters using the information entropy method includes: 1) Collect current meteorological and power grid data for the area to be evaluated; 2) Divide the assessment period and calculate the failure probability of power distribution lines, wind turbines and transformers under the combined disaster of lightning and rainstorm according to the failure probability model of power distribution network equipment under the combined disaster of lightning and rainstorm. 3) Based on the calculated failure probabilities of power distribution lines, wind turbines, and transformers, the entropy value corresponding to different failure scenarios is calculated using the information entropy method. Typical failure scenarios are selected by sampling from the interval with the highest probability of entropy value occurrence. （11） （12） In the formula, The entropy value of the fault scenario; , These are the upper and lower limits of the interval where the entropy value has the highest probability of occurring, respectively. This indicates the time it takes for extreme weather to travel through the distribution network area; for Real-time distribution network equipment The probability of failure, the equipment includes power distribution lines, fans, transformers; for Power distribution lines Did the malfunction just happen? For the malfunction to occur, To prevent malfunctions, The value of follows the distribution of the failure probability of distribution network equipment; For distribution network line collection.

4. The method for risk assessment of distribution networks under combined lightning and rainstorm disasters based on blind number theory according to claim 3, characterized in that: Based on the fusion value of distribution network risk assessment indicators Determine the risk level of the power distribution network: A level 3 risk rating indicates that the consequences of the malfunction are extremely serious. A level 2 risk rating indicates that the failure will cause a significant reduction in production. A Level 1 risk rating indicates that a short-term power outage will not cause significant losses.

5. The method for risk assessment of distribution networks under combined lightning and rainstorm disasters based on blind number theory according to claim 4, characterized in that: In the process of integrating system-level risk assessment indicators under combined lightning and rainstorm disasters based on blind number theory, Distflow is used for power flow calculation. The constraints of this power flow calculation include: power balance constraints, node voltage constraints, line current and transmission capacity constraints, load shedding constraints, and second-order cone constraints. The second-order cone constraints are obtained by converting the nonlinear constraints between voltage, current, and power in the line current and transmission capacity constraints through the second-order cone relaxation principle.

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