Method for reliability evaluation of distribution network under ice and snow weather based on probability model

Abstract

The application discloses a power distribution network reliability evaluation method under ice and snow weather based on a probability model, belongs to the technical field of power system distribution network reliability evaluation, and comprises the following steps: S1, constructing a random state model considering ice and snow weather; S2, establishing a time-varying fault probability model of power distribution network equipment under ice and snow weather; S3, based on a sequential Monte Carlo simulation method; and S4, statistically evaluating power distribution network system-level and load point-level reliability indexes; the application decouples seasonal Markov chain and Weibull distribution modeling, on one hand, accurately captures seasonal distribution characteristics of ice and snow weather through a seasonal transition probability matrix, and on the other hand, replaces a traditional geometric distribution with a Weibull distribution, solves the problem of underestimating long-duration extreme ice and snow events by a classical Markov chain, and the weather sequence generated by the model is highly consistent with historical observation in statistical characteristics such as occurrence frequency, duration and seasonal distribution, and can truly reflect the random evolution law of ice and snow disasters.

Description

Technical Field

[0001] This invention belongs to the field of power system distribution network reliability assessment technology, specifically involving a method for assessing the reliability of distribution networks under icy and snowy weather based on a probabilistic model. Background Technology

[0002] The power distribution network is a critical link in the power system that directly faces users. Its power supply reliability is directly related to the normal operation of social production and life. Snow and ice weather is one of the most important natural disasters affecting the reliability of the power distribution network. Low temperature, freezing rain, wet snow and other meteorological conditions can lead to faults such as line icing, tower overload, and insulator flashover, causing large-scale power outages and resulting in huge economic losses and social impact.

[0003] Existing methods for assessing the reliability of power distribution networks treat equipment failure rates as a constant, completely ignoring the time-varying high risks brought about by severe environments such as snow and ice. This seriously underestimates the impact of extreme weather on system reliability, resulting in a large deviation between the assessment results and actual operating conditions. Weather models also lack accuracy: existing weather models mostly use simple probability distributions to describe the occurrence patterns of snow and ice weather, without considering the seasonal characteristics of weather evolution and the true distribution characteristics of state duration. The geometric distribution duration assumption implicit in the classic Markov chain will significantly underestimate the probability of long-duration severe icing events, and cannot accurately characterize the risks of extreme snow and ice disasters. Summary of the Invention

[0004] The purpose of this invention is to provide a method for assessing the reliability of power distribution networks under icy and snowy weather based on a probabilistic model, so as to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for assessing the reliability of power distribution networks under icy and snowy weather based on a probabilistic model, comprising the following steps: S1. Construct a stochastic state model that considers snow and ice weather, and divide the weather into: baseline state A0, snow and ice warning state A1, and high stress state of snow and ice A2. A seasonal discrete-time Markov chain is used to describe the state transition pattern, and a two-parameter Weibull distribution is used to independently fit the duration of each weather state to generate a long-term weather state time series. S2. Establish a time-varying fault probability model for power distribution network equipment under icy and snowy weather, construct a conductor fault probability model and a tower fault probability model respectively, and obtain the overall fault probability of the power distribution line based on the reliability theory of series system. S3. Based on the sequential Monte Carlo simulation method, combined with the weather state time series and the time-varying failure probability of equipment, the time sequence process of power distribution network fault occurrence, fault isolation, load outage and equipment repair is simulated step by step. S4. Statistically analyze the reliability indicators at the system level and load point level of the distribution network, and make convergence judgments to complete the quantitative assessment of the reliability of the distribution network under snowy weather.

[0006] In a preferred embodiment, in step S1, the probability density function of the two-parameter Weibull distribution is:

[0007] In the formula: t is the duration of the state, k > 0 is the shape parameter, >0 is a scale parameter, if <1 indicates that the failure rate decreases over time. =1, the Weibull distribution simplifies to an exponential distribution, and the failure rate is constant. >1 indicates that the failure rate increases over time.

[0008] As a preferred embodiment, the weather state in step S2 is defined as: Baseline state A0: meteorological conditions without significant ice and snow additional stress, and the equipment failure rate is a basic stable value; Snow and ice warning status A1: Low temperature and high humidity with slight icing conditions, equipment failure rate is higher than the baseline status; High-stress ice and snow condition A2: There are meteorological conditions with active icing or wet snow accumulation and strong winds, and the equipment failure rate is significantly higher than the first two conditions.

[0009] As a preferred implementation, the specific steps for generating the weather state time series in step S2 are as follows: S21 Season division: Divide the year into multiple seasons according to the regional climate characteristics, and each season corresponds to a set of independent transition probability matrices; S22 Initial State Determination: The weather state distribution at the start of the simulation is set based on historical statistical data; S23 State Duration Sampling: When the system enters a certain state, the duration D of the current state is sampled from the two-parameter Weibull distribution corresponding to that state; S24 State Transition: After the duration D ends, the next weather state is determined by sampling based on the transition probability matrix corresponding to the current season; S25 Repeat steps S23-S24 to generate a complete long-term weather state time series.

[0010] As a preferred implementation, the specific steps for calculating the conductor fault probability in step S3 are as follows: dynamically calculate the increment of the equivalent ice thickness of the conductor using the Jones model.

[0011] In the formula: and The densities of ice and water are respectively. Let be the precipitation rate at time t, expressed in mm / h, representing the intensity of freezing rain or wet snow. Wind speed, in m / s. The moisture content in ambient air, expressed in g / m³. 3 .

[0012] As a preferred implementation, the specific steps for calculating the tower failure probability in step S3 are as follows: Calculate the icing load borne by the tower:

[0013] In the formula, Where d is the unit vertical load on the conductor, and d is the outer diameter of the conductor. For correction factor, For the ice load on the tower, This refers to the span between the two sides of the tower. The height of the suspension positions at both ends of the line. and This refers to the horizontal tension of the lines on both sides of the tower.

[0014] The probability of tower failure is calculated using an exponential function model: In the formula, The probability of tower icing failure. Design the towers to withstand icing loads. It is a constant coefficient.

[0015] In a preferred embodiment, the overall line fault probability in step S3 is:

[0016] In the formula, This represents the probability of a wire failure. Let be the probability of tower failure, assuming that conductor failures and tower failures are independent of each other.

[0017] As a preferred implementation, the specific steps of system state timing simulation in step S4 are as follows: S41 Initialization: Set the total simulation duration and time step, initialize all devices to normal operating status, and initialize cumulative index variables; S42 Time-Step Scan: For each time step, a Bernoulli test is performed based on the current equipment failure probability to determine whether the equipment has failed. S43 Fault Event Handling: If a device malfunctions, record the fault information, determine the affected load points through network topology analysis, record the power outage start time, and determine the power outage duration based on the recovery strategy; S44 Repair Process Simulation: The repair duration is obtained by sampling the equipment repair time distribution, and the equipment remains in a shutdown state during the repair period; S45 Status Update: Updates the system's operating status and proceeds to the next time step of the simulation.

[0018] As a preferred implementation, the reliability indicators in step S5 include: the system average outage frequency index SAIFI, the system average outage duration index SAIDI, the user average outage duration index CAIDI, the average power availability index ASAI, and the expected power shortage EENS.

[0019] As a preferred implementation, the specific method for determining convergence in step S5 is as follows: calculate the coefficient of variation of the key reliability index, and determine that the simulation result is converged when the coefficient of variation is less than or equal to 0.05.

[0020] Compared with the prior art, the beneficial effects of the present invention are: This invention decouples seasonal Markov chains from Weibull distributions in its modeling. On the one hand, it accurately captures the seasonal distribution characteristics of snow and ice weather through a seasonal transition probability matrix. On the other hand, it replaces the traditional geometric distribution with a Weibull distribution, solving the problem of classical Markov chains underestimating long-duration extreme snow and ice events. The weather sequences generated by this model are highly consistent with historical observations in terms of statistical characteristics such as frequency of occurrence, duration, and seasonal distribution. They can truly reflect the stochastic evolution of snow and ice disasters and provide an accurate input basis for reliability assessment.

[0021] This invention constructs a physical process-based equipment failure probability model. It dynamically simulates the icing growth process using the Jones model, comprehensively considers the coupling effect of ice load and wind load, and uses piecewise exponential functions and exponential functions to characterize the nonlinear relationship between the failure probability of conductors and towers and mechanical load. This model breaks through the limitations of traditional empirical statistical models, can dynamically reflect the changes in equipment failure risk under different meteorological conditions, and accurately quantify the impact of snow and ice weather on equipment reliability.

[0022] This invention employs a sequential Monte Carlo simulation method, which can naturally embed the temporal dependence of weather processes and the time-varying characteristics of equipment failure probabilities. It accurately simulates the clustering and persistent characteristics of failures under icy and snowy weather. This method can clearly distinguish the contribution of different weather states to system reliability, accurately quantify the power outage risk caused by extreme icy and snowy disasters, and solve the problem that traditional non-sequential simulation methods cannot accurately assess the impact of persistent external events. The credibility and practicality of the assessment results are significantly enhanced.

[0023] This invention can not only output conventional reliability indicators at the system and load point levels, but also further analyze the contribution of different weather conditions and seasons to reliability, identify weak links in the system, and the evaluation results can provide comprehensive decision support for the planning and design of the distribution network (such as line selection and tower reinforcement), operation and scheduling (such as snow and ice weather warning and load transfer), and disaster prevention and mitigation (such as the formulation of ice melting strategies), effectively improving the distribution network's ability to cope with snow and ice disasters and reducing power outage losses. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the flowchart structure of the power distribution network reliability assessment system of the present invention; Figure 2 This is a schematic diagram illustrating the steps of the distribution network reliability assessment method based on a probability model under icy and snowy weather according to the present invention. Detailed Implementation

[0025] The present invention will be further described below with reference to embodiments.

[0026] The following embodiments are used to illustrate the present invention, but should not be used to limit the scope of protection of the present invention. The conditions in the embodiments can be further adjusted according to specific conditions, and simple improvements to the method of the present invention under the premise of the concept of the present invention are all within the scope of protection claimed by the present invention.

[0027] Please see Figure 1 and Figure 2 This invention provides a method for assessing the reliability of power distribution networks under icy and snowy weather based on a probabilistic model. Based on the development stages of icy and snowy weather and the level of physical stress exerted on power equipment, this invention defines three core states: Baseline State A0: This state encompasses all meteorological conditions that do not impose significant additional stress from ice and snow on power grid equipment. Typical scenarios include high temperatures with no risk of freezing or low temperatures but dry air with no condensation conditions. Under this state, the failure risk of equipment such as lines, towers, and transformers is primarily determined by their inherent aging, wear, and conventional electrical and mechanical loads, and their failure rate can be considered a relatively stable baseline value. This state represents the most common operating environment for the system.

[0028] Snow and Ice Warning Status A1: This status indicates that meteorological conditions have entered a sensitive period that may increase equipment vulnerability. Its typical characteristics are a combination of low temperature and high humidity, which may lead to freezing fog, tiny supercooled water droplets, or initial frost and light icing. At this time, although the ice layer accumulated on conductors or insulators is thin and insufficient to cause severe mechanical overload, it already presents two key risks: first, the insulation performance of the equipment insulation surface begins to decline; second, it builds a foundation for subsequent, more severe icing. From a reliability perspective, the probability of equipment failure should be higher in Status A1 than in Status A0, reflecting the initial intensification of environmental stress.

[0029] High-stress state A2 due to ice and snow: This state poses a direct and significant threat to the power grid. It characterizes an active icing or wet snow accumulation process, typically caused by freezing rain, sleet, or wet snow. Under this state, the observed or simulated equivalent ice thickness will clearly increase. This process is often accompanied by wind speed, causing equipment to be subjected to the combined effects of static gravity loads and dynamic wind loads. State A2 directly corresponds to a high incidence of fault modes such as increased line sag, excessive tower stress, and insulator flashover. Its failure probability should be significantly higher than A0 and A1, reflecting a high failure rate under extreme environmental stress.

[0030] The division into these three states is achieved through a set of thresholds determined by joint analysis of historical meteorological data and power grid fault records.

[0031] Each state corresponds to a relatively homogeneous risk level in an engineering sense, providing a clear input label for the subsequent establishment of differentiated failure probability models.

[0032] Once discrete states are defined, a mathematical model is needed to describe how these states change randomly over time. Discrete-time Markov chains (DTMCs) provide a powerful framework for this purpose.

[0033] The dynamic properties of a Markov chain are entirely determined by its transition probability matrix. For a system with three states {A0, A1, A2}, its transition probability matrix is... P for:

[0034] Elements in the matrix It has a clear probabilistic meaning: it represents the state of the system at the known current moment. Under the condition that, the system transitions to state in the next moment. The conditional probability of . Expressed mathematically as: According to the definition of probability, a matrix P The sum of the elements in each row must equal 1, that is... For all This means that starting from any state, the next step will inevitably lead to one of the possible states.

[0035] However, weather patterns exhibit strong seasonality, with icing occurring far more frequently in winter than in summer. To capture this key characteristic, we introduce a seasonal transition probability matrix, assuming we divide the year into... Each season has different climatic characteristics, so for the first season... Each season, we have a specific TPM, denoted as .in, Indicates the first During the season, from the state to state The transition probability.

[0036] These probability parameters need to be learned from historical data. Given a historical dataset containing timestamps and corresponding weather state labels, we can estimate them using an intuitive method like maximum likelihood estimation. The specific approach is to statistically analyze the data on the [number]th [day / month]. Throughout all historical records of seasons, it was observed that from state Transition to state The number of times, recorded as Then, the estimated value of the transition probability. This refers to the proportion of this type of transfer to the total number of transfers:

[0037] in, Indicates the first Seasons, all from state The total number of departure transfer events.

[0038] Classical Markov chains implicitly assume that the duration of each state follows a geometric distribution, which may deviate from the persistence of real-world weather events. The memoryless nature of the geometric distribution may lead to an underestimation of the probability of long-duration weather events. To simulate more realistically, we decouple state transitions from state durations. After generating the state transition sequence, we independently sample the duration of each state from a fitted distribution.

[0039] Analysis shows that the duration of weather conditions better conforms to a Weibull distribution or a log-normal distribution, which can better describe the duration data of this meteorological feature. This paper uses a two-parameter Weibull distribution to characterize the weather condition. Duration .

[0040] In a classic Markov chain, once a state is entered, the probability of leaving that state at each time step is fixed. This causes the dwell time in that state to follow a geometric distribution, which implies that the probability of a state lasting longer decays rapidly in a fixed proportion. This may not perfectly match reality. Actual observations have shown that, for states like A2, although the probability of severe icing events lasting several days gradually decreases, the decay rate may be slower than predicted by the geometric distribution.

[0041] To more realistically simulate the duration of each state, we made a significant improvement to the model: decoupling "state transition" from "state dwell." During the simulation, when the system enters a state, such as A2, we do not use [state dwell time] at every time step. Instead of determining whether to leave, we first assign a duration to this state, which is randomly drawn from a dwell time probability distribution specifically fitted to this state.

[0042] The Weibull distribution is well-suited for describing this type of duration data; it is more flexible than the geometric distribution and can characterize different risk features through its shape parameters. We define each state... Define a Weibull distribution Its probability density function is:

[0043] In the formula: t is the duration of the state, k > 0 is the shape parameter, >0 is a scale parameter, if <1 indicates that the failure rate decreases over time. =1, the Weibull distribution simplifies to an exponential distribution, and the failure rate is constant. A value greater than 1 indicates that the failure rate increases over time. Corresponding to A2, the longer the icing time, the greater the possibility that the system will break out of this state due to factors such as melting ice and changes in wind force.

[0044] parameter It can be obtained by statistically fitting samples of the duration of each state event identified in historical data.

[0045] The assumption of a constant failure rate in traditional assessments completely ignores the time-varying stress of the external environment. This is particularly detrimental to understanding the impact of complex icy and snowy weather. Complex weather is not a single meteorological disaster, but rather an interweaving and coupling of multiple factors in time and space, such as low temperature, high humidity, freezing rain or wet snow, icing, and strong winds. For example, low temperature promotes icing conditions, icing changes the aerodynamic shape of conductors and induces galloping, while strong winds simultaneously increase mechanical loads and galloping excitation, and high humidity may prematurely degrade insulation. This interaction of multiple physical processes makes equipment failure risk exhibit highly nonlinear dynamic characteristics. Therefore, the core task of this section is to establish a refined, mechanism-driven time-varying failure probability model for equipment.

[0046] Based on the above approach, an overhead power distribution line can be regarded as a system consisting of conductors and towers connected in series. This invention establishes fault probability models for conductor units and tower units respectively, and finally integrates them through the reliability theory of series systems.

[0047] Conductor Failure Probability Model: The failure of conductor units is the most active failure point under complex icy and snowy weather, involving multiple coupled processes such as icing growth, mechanical overload, and aerodynamic galloping.

[0048] (a) Dynamic growth model of icing thickness Equivalent ice thickness under complex ice and snow conditions It is the most crucial dynamic variable in calculating mechanical loads. Its growth is not simply linear, but closely related to multiple factors such as precipitation intensity, wind speed, and temperature. To accurately simulate this complex physical process, this study employs the Jones model or its modified form, widely used in electrical engineering, to correlate meteorological conditions with the dynamic growth of ice thickness. This model is based on the microscopic mechanism of supercooled water droplet collision, capture, and freezing, and its incremental form is expressed as:

[0049] In the formula: and The densities of ice and water are respectively. Let be the precipitation rate at time t, expressed in mm / h, representing the intensity of freezing rain or wet snow. Wind speed, in m / s. The moisture content in ambient air, expressed in g / m³. 3 .

[0050] (b) Calculation of multi-factor mechanical loads Based on dynamic ice thickness and wind speed This allows for the calculation of time-varying mechanical loads borne by the conductor. Ice load per unit length of conductor. Determined by the weight of the ice layer:

[0051] Horizontal wind load This is determined by wind speed, conductor diameter, and the windward area after icing.

[0052] In the formula, These are the conductor diameter, wind load shape coefficient, and span coefficient, respectively.

[0053] Total comprehensive load borne by the conductor It is the vector sum of the two, taking into account the most dangerous wind direction:

[0054] (c) Conductor Fault Probability Model Obtain mechanical stress This study establishes a mapping between the fault probability and the mechanical load. A piecewise exponential fault probability multiplier model is used. When the mechanical load is lower than the design allowable load of the conductor... At that time, the risk of failures caused by ice and snow remained at a low level. When the load exceeds At this point, the risk of failure begins to increase non-linearly; when the load reaches the ultimate failure load... At that time, the equipment will almost certainly fail.

[0055] Tower failure probability model: (a) Calculation of tower icing load The icing load on the tower mainly refers to the tension generated by the conductor suspended from the tower at both ends. It depends on the vertical loads such as the conductor's own weight and the weight of the conductor covered by ice. The specific expression is as follows.

[0056]

[0057] In the formula, d represents the unit vertical load on the conductor; d is the outer diameter of the conductor. This is a correction factor; For the ice load on the tower, The span on both sides of the tower, The height of the suspension positions at both ends of the line; and This refers to the horizontal tension of the lines on both sides of the tower.

[0058] (b) Tower failure probability model The relationship between tower icing load and tower failure probability is characterized by an exponential function, expressed as follows:

[0059] In the formula, The probability of tower icing failure. Design the towers to withstand icing loads; and It is a constant coefficient.

[0060] Overall Fault Probability Model for Power Distribution Lines: Assuming that conductor and tower faults are independent, the power distribution line is equivalent to a series connection of conductors and towers. Its overall fault probability... It can be calculated based on the reliability theory of series systems as follows:

[0061] The power distribution network reliability assessment process proposed in this invention mainly includes the following five steps: S1. Input data preparation: including historical meteorological data, equipment parameters, network topology, load data, reliability parameters, etc. S2. Weather State Sequence Simulation: Based on the seasonal Markov chain and state duration model, long-term weather state time series are generated. S3. Calculation of Time-Varying Failure Probability of Equipment: Based on weather conditions and equipment type, dynamically calculate the failure probability of each piece of equipment at each time step. S4. System State Timing Simulation: The sequential Monte Carlo method is used to simulate the system's fault and repair process, and power outage events at load points are recorded. S5. Reliability Indicator Statistics: Based on multiple simulation results, calculate the reliability indicators at the system level and load point level, and perform convergence judgment.

[0062] Weather state sequence simulation Based on the weather state model established above, long-term weather state time series are generated. The specific steps are as follows: X1. Seasonal Division: The year is divided into several seasons (such as winter, transition season, etc.) based on climate characteristics, and each season corresponds to a set of transition probability matrices; X2. Initial State Determination: Based on historical statistics, the weather state distribution at the start of the simulation is set, and the transition direction between states is determined by the seasonal transition probability matrix established in Section 1.1.2. X3. State duration sampling: When the system enters a certain state, the duration D is sampled from the Weibull distribution of that state; X4. State Transition: After the duration D ends, the next state is determined by sampling based on the transition probability matrix corresponding to the current season. X5. Repeat steps 3-4 to generate a complete weather status time series.

[0063] And the calculation of time-varying failure probability of equipment At each time step of the simulation, the real-time failure probability of each device is calculated based on the current weather conditions and meteorological conditions: Meteorological condition assignment: Based on the weather conditions, assign corresponding meteorological parameters (such as precipitation rate, wind speed, temperature, etc.) for each time step. Calculation of conductor failure probability: The equivalent ice thickness is dynamically updated using the Jones model, the mechanical load is calculated, and the failure probability of the conductor is obtained based on the piecewise exponential model. Tower failure probability calculation: Based on the conductor load transfer and tower icing load model, the failure probability of the tower is calculated using an exponential function model. Overall line failure probability: Based on the reliability theory of series systems, the failure probabilities of conductors and towers are combined to obtain the comprehensive failure probability of each distribution line at the current time step.

[0064] System state timing simulation and index statistics Simulation of system operation and failure process based on time-series Monte Carlo method: Initialization: Set the total simulation duration and time step, initialize all devices to normal operating status, and initialize cumulative indicator variables; Time-step scanning: For each time step, Bernoulli test is used to determine whether a fault has occurred based on the current fault probability of each device; Fault event handling: If equipment malfunctions, record the time of malfunction, the equipment malfunctioning, and the type of malfunction. Based on the system topology and fault location, the affected load points are determined through power flow analysis or impact analysis; Record the start time of power outage at each load point and determine the duration of power outage based on the fault isolation and recovery strategy; Repair process simulation: The repair duration is obtained by sampling the repair time distribution of the equipment. During the repair period, the equipment is in a downtime state. Status Update: Update the system status and continue the simulation to the next time step; Reliability Indicator Statistics: At the end of each simulation year, the reliability indicators of each load point and the system are cumulatively calculated, including: System Average Outage Frequency (SAIFI); System Average Outage Duration (SAIDI); User Average Outage Duration (CAIDI); Average Power Availability (ASAI); Expected Power Shortage (EENS), etc. Convergence judgment: As the number of simulation years increases, the relative error of key indicators is calculated. When the relative error of key indicators converges to the set threshold or reaches the set simulation period, the simulation stops and the final indicator results are output.

[0065] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for assessing the reliability of power distribution networks under icy and snowy weather based on a probabilistic model, characterized in that, Includes the following steps: S1. Construct a stochastic state model that considers snow and ice weather, and divide the weather into: baseline state A0, snow and ice warning state A1, and high stress state of snow and ice A2. A seasonal discrete-time Markov chain is used to describe the state transition pattern, and a two-parameter Weibull distribution is used to independently fit the duration of each weather state to generate a long-term weather state time series. S2. Establish a time-varying fault probability model for power distribution network equipment under icy and snowy weather, construct a conductor fault probability model and a tower fault probability model respectively, and obtain the overall fault probability of the power distribution line based on the reliability theory of series system. S3. Based on the sequential Monte Carlo simulation method, combined with the weather state time series and the time-varying failure probability of equipment, the time sequence process of power distribution network fault occurrence, fault isolation, load outage and equipment repair is simulated step by step. S4. Statistically analyze the reliability indicators at the system level and load point level of the distribution network, and make convergence judgments to complete the quantitative assessment of the reliability of the distribution network under snowy weather.

2. The method for assessing the reliability of power distribution networks under icy and snowy weather based on a probabilistic model according to claim 1, characterized in that: In step S1, the probability density function of the two-parameter Weibull distribution is: ； In the formula: t is the duration of the state, k > 0 is the shape parameter, >0 is a scale parameter, if <1 indicates that the failure rate decreases over time. =1, the Weibull distribution simplifies to an exponential distribution, and the failure rate is constant. >1 indicates that the failure rate increases over time.

3. The method for assessing the reliability of power distribution networks under icy and snowy weather based on a probabilistic model according to claim 1, characterized in that: The weather state in step S2 is defined as: Baseline state A0: Under meteorological conditions without significant additional stress from ice and snow, the equipment failure rate is a basic stable value; Snow and ice warning status A1: Low temperature and high humidity with slight icing conditions, equipment failure rate is higher than the baseline status; High-stress ice and snow condition A2: There are meteorological conditions with active icing or wet snow accumulation and strong winds, and the equipment failure rate is significantly higher than the first two conditions.

4. The method for assessing the reliability of distribution networks under icy and snowy weather based on a probabilistic model according to claim 1, characterized in that: The specific steps for generating the weather state time series in step S2 are as follows: S21 Season division: Divide the year into multiple seasons according to the regional climate characteristics, and each season corresponds to a set of independent transition probability matrices; S22 Initial State Determination: The weather state distribution at the start of the simulation is set based on historical statistical data; S23 State Duration Sampling: When the system enters a certain state, the duration D of the current state is sampled from the two-parameter Weibull distribution corresponding to that state; S24 State Transition: After the duration D ends, the next weather state is determined by sampling based on the transition probability matrix corresponding to the current season; S25 Repeat steps S23-S24 to generate a complete long-term weather state time series.

5. The method for assessing the reliability of power distribution networks under icy and snowy weather based on a probabilistic model according to claim 1, characterized in that: The specific steps for calculating the conductor fault probability in step S3 are as follows: The Jones model is used to dynamically calculate the increment of the equivalent ice thickness of the conductor. ； In the formula: and The densities of ice and water are respectively. Let be the precipitation rate at time t, expressed in mm / h, representing the intensity of freezing rain or wet snow. Wind speed, in m / s. The moisture content in ambient air, expressed in g / m³. 3 .

6. The method for assessing the reliability of distribution networks under icy and snowy weather based on a probabilistic model according to claim 1, characterized in that: The specific steps for calculating the tower failure probability in step S3 are as follows: Calculate the icing load borne by the tower: ； In the formula, Where d is the unit vertical load on the conductor, and d is the outer diameter of the conductor. For correction factor, For the ice load on the tower, This refers to the span between the two sides of the tower. The height of the suspension positions at both ends of the line. and The horizontal tension of the lines on both sides of the tower; The probability of tower failure is calculated using an exponential function model: In the formula, The probability of tower icing failure. Design the towers to withstand icing loads. It is a constant coefficient.

7. The method for assessing the reliability of distribution networks under icy and snowy weather based on a probabilistic model according to claim 1, characterized in that: The overall line fault probability mentioned in step S3 is: ； In the formula, This represents the probability of a wire failure. Let be the probability of tower failure, assuming that conductor failures and tower failures are independent of each other.

8. The method for assessing the reliability of distribution networks under icy and snowy weather based on a probabilistic model according to claim 1, characterized in that: The specific steps of system state timing simulation in step S4 are as follows: S41 Initialization: Set the total simulation duration and time step, initialize all devices to normal operating status, and initialize cumulative index variables; S42 Time-Step Scan: For each time step, a Bernoulli test is performed based on the current equipment failure probability to determine whether the equipment has failed. S43 Fault Event Handling: If a device malfunctions, record the fault information, determine the affected load points through network topology analysis, record the power outage start time, and determine the power outage duration based on the recovery strategy; S44 Repair Process Simulation: The repair duration is obtained by sampling the equipment repair time distribution, and the equipment remains in a shutdown state during the repair period; S45 Status Update: Updates the system's operating status and proceeds to the next time step of the simulation.

9. The method for assessing the reliability of distribution networks under icy and snowy weather based on a probabilistic model according to claim 1, characterized in that: The reliability indicators mentioned in step S5 include: the system average outage frequency index SAIFI, the system average outage duration index SAIDI, the user average outage duration index CAIDI, the average power availability index ASAI, and the expected power shortage EENS.

10. The method for assessing the reliability of distribution networks under icy and snowy weather based on a probabilistic model according to claim 1, characterized in that: The specific method for determining convergence in step S5 is as follows: calculate the coefficient of variation of the key reliability index, and determine that the simulation results are converged when the coefficient of variation is less than or equal to 0.05.

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