A multi-pole weather distribution network distributed power source resilience planning method

Abstract

The application relates to the technical field of power distribution network planning, and discloses a kind of multi-extreme weather under power distribution network distributed power source flexibility planning method, comprising: constructing power distribution network element comprehensive failure probability model and generating initial extreme disaster scene set;Adopt clustering algorithm to obtain typical scene set by reducing initial extreme disaster scene set;Combined with typical scene set, power distribution network investment cost and maintenance cost, establish distributed power source planning joint model and configure limit load reduction and power flow balance post-disaster power distribution network operation constraint model to execute solving, output each candidate node distributed power source in power distribution network optimal installation location and capacity decision instruction.The application integrates distributed power source site selection, post-disaster output scheduling and network topology reconstruction into joint model to solve uniformly, guarantees planning accuracy under the premise of controlling calculation scale, balances power distribution network economic investment and load recovery demand under natural disaster conditions.

Description

Technical Field

[0001] This invention relates to the field of distribution network planning technology, specifically to a method for distributed power source resilience planning in distribution networks under multiple extreme weather conditions. Background Technology

[0002] Distribution networks directly connect upstream power sources to end users. A large portion of these facilities are exposed to the natural environment, making them vulnerable to damage from extreme weather events such as strong winds, heavy rains, landslides, and snow and ice. Natural disasters can cause multiple lines or equipment to fail simultaneously, leading to power outages and localized power losses. Distribution network resilience emphasizes the network's ability to prevent, withstand, respond to, and recover from natural disasters. Existing methods for enhancing distribution network resilience mainly include pre-disaster planning and post-disaster recovery. Pre-disaster planning reduces the risk of power outages caused by natural disasters through line reinforcement and distributed power source configuration. Post-disaster recovery restores critical loads through fault isolation, network topology reconfiguration, and distributed resource scheduling. Distributed power sources can provide local power support when existing power supply paths are interrupted, and network reconfiguration utilizes sectionalizing switches and tie switches to change the load power supply path.

[0003] Existing distribution network resilience planning methods typically establish fault models for a single type of disaster, such as strong winds, heavy rain, or icing. These methods fail to comprehensively describe the impact of different disaster-causing factors, including wind speed, rainfall, geological hazards, and line icing, on the probability of distribution network line faults. Enumerating all fault combinations leads to an exponential increase in the number of scenarios with the scale of the lines, increasing the computational burden on the distribution network model. Planning with a small number of pre-defined scenarios may miss typical scenarios with high probability of occurrence or significant load loss. Traditional scenario reduction methods, based on fault location or scenario occurrence probability, fail to reflect the power supply impact of different fault scenarios, resulting in the retention of repetitive scenarios with similar power loss characteristics in the selection results.

[0004] Existing distribution network resilience planning methods have shortcomings in coordinating distributed generation planning and post-disaster recovery. These methods only determine the installation locations of distributed generation sources without further optimizing their capacity. Some existing methods rely primarily on network reconfiguration to restore load, failing to integrate pre-disaster distributed generation site selection and capacity determination with post-disaster switching actions, topology reconfiguration, and power output scheduling. Traditional distribution network planning emphasizes investment costs, while post-disaster recovery strategies focus on load recovery indicators, lacking a comprehensive balancing mechanism for distributed generation investment costs, maintenance costs, post-disaster operating costs, and power outage losses. Current distribution network planning technologies cannot simultaneously consider fault scenario representativeness, model solution efficiency, planning economics, and post-disaster power restoration capabilities. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a distributed power source resilience planning method for distribution networks under multiple extreme weather conditions. This method solves the problems of existing methods being unable to comprehensively describe the impact of multiple extreme weather disaster factors on the probability of distribution network line failures, retaining repetitive scenarios during the scenario reduction process, and being unable to uniformly coordinate the economic investment of distribution network planning with post-disaster load recovery capabilities.

[0006] To achieve the above objectives, this invention provides a method for resilience planning of distributed generation sources in distribution networks under multiple extreme weather conditions, comprising the following steps: The data processing terminal constructs a comprehensive failure probability model for power distribution network components under multiple extreme weather conditions; A comprehensive fault probability model of distribution network components under multiple extreme weather conditions is used to generate multiple initial extreme disaster scenario sets containing different survival and fault states of distribution network components. A clustering algorithm is then used to reduce and cluster the initial extreme disaster scenario sets to obtain a reduced typical scenario set. A joint model for distributed power source resilience planning is established by combining the reduced set of typical scenarios with the investment and operation and maintenance costs of the distribution network. Establish a post-disaster distribution network resilience operation constraint model for the joint model of distributed power source resilience planning; The post-disaster distribution network resilience operation constraint model is incorporated into the distributed power source resilience planning joint model for numerical solution. Based on the solution results of the distributed power source resilience planning joint model, the optimal installation location and capacity decision instructions for each candidate node distributed power source in the distribution network are output.

[0007] The data processing terminal obtains the failure probability of distribution network components under windy, rainy, landslide, and icing weather conditions. The comprehensive failure probability of distribution network components under multiple extreme weather conditions is the sum of the failure probabilities of components under windy weather, rainy or landslide weather, and icing weather, weighted by a set weighting coefficient.

[0008] The failure probability of components under strong winds is calculated using the empirical fitting proportional constant, empirical fitting exponential constant, and equivalent load intensity of the line exposed to strong winds obtained by fitting historical data to a strong wind failure model.

[0009] Preferably, the failure probability of components under rainfall or landslide geological disasters is obtained by multiplying the probability of spatial geological disaster occurrence by the probability of tower structure damage, thus completing the coupled calculation of the probability of geological disaster occurrence and the probability of tower structure damage. The probability of spatial geological disaster occurrence is determined based on the relationship between the effective rainfall and the rainfall threshold. When the effective rainfall is greater than or equal to zero and less than the rainfall threshold, the probability of spatial geological disaster occurrence is calculated by combining the geological disaster probability fitting constant obtained from historical data with the effective rainfall; when the effective rainfall is greater than or equal to the rainfall threshold, the probability of spatial geological disaster occurrence is equal to one. Obtaining the failure probability of components under icing disasters involves calculating the ratio of the cumulative equivalent ice thickness to the maximum designed ice resistance thickness of the line to obtain the equivalent ice thickness ratio. This ratio is then used to perform an exponential operation with the icing failure probability fitting coefficient and the equivalent ice thickness ratio to obtain the failure probability of components under icing disasters.

[0010] Preferably, a clustering algorithm is used to reduce the initial extreme disaster scenario set through clustering, including calculating the expected power shortage of all nodes in the distribution network to construct a load reduction vector for the entire network. By calculating the clustering objective function, the clustering algorithm minimizes the sample distance, calculates the cluster center and scenario probability, and compares the decline rate of the clustering objective function with the cluster number convergence threshold to determine the optimal number of clusters.

[0011] Preferably, the data processing terminal generates random numbers based on Monte Carlo sampling, compares the relationship between the random numbers and the overall failure probability of the components to determine the survival status and failure status of the components, and outputs the status of the distribution network components. Based on the distribution network topology connectivity status under the initial extreme disaster scenario, the active power reduction of important loads and interruptible loads when each node loses power from the main grid is evaluated through islanding. The expected power supply shortage of the nodes is calculated by summing the total operating time period of the distribution network and the unit time interval. Based on the constructed load reduction vector of the entire network, a distribution network loss threshold is set to eliminate low-impact scenarios to complete the initial screening. The initial extreme disaster scenarios with high losses are retained to form an initial reduction scenario set, and clustering and reduction processing of massive disaster scenarios is performed.

[0012] Preferably, establishing a joint model for distributed generation resilience planning includes constructing a comprehensive planning objective function and defining an overall cost minimization objective. The overall cost minimization objective constrains the optimization direction of the joint model for distributed generation resilience planning, striving to minimize the value of the solved comprehensive planning objective function. Calculating the comprehensive planning objective function involves obtaining the investment cost corresponding to the planning scheme, the operation and maintenance cost associated with the normal state of the distribution network, and the expected post-disaster operating loss cost associated with extreme disaster scenarios. The comprehensive planning objective function equals the sum of the investment cost, operation and maintenance cost, and expected post-disaster operating loss cost.

[0013] Preferably, the distributed power source resilience planning joint model includes setting distributed power source planning constraints. These constraints include setting a maximum total number of installations allowed across the entire network and boundary constraints on the installation capacity of each node. The boundary constraints on the installation capacity of each node are used to establish inequalities based on the node's planned installation status, the lower limit of the node's installation capacity, and the upper limit of the node's installation capacity.

[0014] Preferably, establishing a post-disaster distribution network resilience operation constraint model includes calculating post-disaster distribution network operation indicators and setting resilience baseline constraints. The resilience baseline constraints are limited by establishing an inequality between the post-disaster distribution network operation indicators and the highest baseline threshold of the resilience operation indicators. Establishing the post-disaster distribution network resilience operation constraint model also includes establishing network topology connectivity and radial constraints, setting reactive power compensation and power factor linkage constraints, and calculating the reactive power reduction amount in accordance with the linkage between constant power factor and active power reduction amount.

[0015] Preferably, handling the fault isolation area includes determining the status of faulty branches, forcibly setting the connectivity of branches belonging to the faulty branch set to zero, and disconnecting the corresponding connection paths. Determining that the post-disaster reconstructed network maintains a loop-free radial virtual power flow includes establishing a radial virtual power flow identity for the associated node set, constraining the virtual load balance of nodes, and setting upper and lower limit intervals for the virtual power flow of branches. Establishing power flow safety and line capacity limit constraints includes linearizing the nonlinear voltage drop of the lines, establishing linearized polygonal constraints for the thermal stability limit of the apparent power of branches, and transforming the quadratic constraints of the apparent power of the lines into polygonal linear capacity constraints.

[0016] Preferably, the numerical solution process involves inputting the integrated planning objective function and operational constraints into a mixed-integer linear programming solver. After receiving the joint model's operational parameters, the mixed-integer linear programming solver performs a global optimization calculation to obtain the optimal solution. It then analyzes the optimal solution to extract the node planning and installation status and node planning and installation capacity, generating optimal installation location and capacity decision instructions for each candidate node's distributed power source.

[0017] Preferably, the data processing terminal packages the distributed power source installation location data and distributed power source capacity data to generate an optimal decision instruction containing location and capacity information, and outputs the optimal decision instruction to the external display terminal so that external devices can deploy the corresponding distributed power source equipment at the node indicated by the distributed power source installation location data.

[0018] This invention provides a method for resilience planning of distributed generation sources in power distribution networks under multiple extreme weather conditions. It has the following beneficial effects: 1. This invention constructs comprehensive failure probability models for power distribution network components under windy weather, rainy or landslide geological disaster weather, and icing weather, respectively. It calculates the failure probability of components under windy weather using line length and maximum average wind speed, calculates the failure probability of components under rainy or landslide geological disaster weather using effective rainfall and landslide impact energy, and calculates the failure probability of components under icing weather using line icing load rate. This avoids using a single fixed value to describe the destructive state of extreme weather and reflects the differentiated impact of different disaster-causing factors on power distribution line failures.

[0019] 2. This invention eliminates low-impact scenarios where the post-disaster operational loss cost is less than the scenario impact threshold by setting a scenario impact threshold, and calculates the cumulative power loss of distribution network nodes to form a scenario feature vector. A clustering algorithm is used to perform reduction clustering on the scenario feature vector to obtain a typical scenario set, reducing the number of scenarios with the same power supply consequences and retaining typical scenarios with obvious differences in the spatial distribution of load loss. Under the premise of controlling the calculation scale of the distributed power resilience planning joint model, the accuracy of distributed power resilience planning scenario calculation is guaranteed.

[0020] 3. This invention establishes a joint model for distributed power source resilience planning by adding the annualized investment cost, equipment maintenance cost, and expected operating cost of distributed power sources in multiple scenarios to form a comprehensive planning objective function. It also incorporates the post-disaster distribution network resilience operation constraint model, which limits the operating costs of distributed power sources and load reduction losses, into the joint model for global optimization calculation. The invention integrates distributed power source location planning, capacity configuration, post-disaster power output scheduling, line switch state switching, and network topology reconstruction into the joint model for unified solution, completing the collaborative calculation of pre-disaster resource allocation and post-disaster power supply restoration control, and balancing the economic investment of distribution network planning with the power loss load restoration requirements under multiple line fault conditions. Attached Figure Description

[0021] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a diagram illustrating the architecture of the comprehensive fault probability model for power distribution network components under multiple extreme weather conditions according to the present invention. Figure 3 This is a flowchart of the extreme disaster scenario set generation and reduction clustering process of the present invention; Figure 4 This is a diagram of the joint model architecture for distributed power resilience planning of the present invention; Figure 5 This is a flowchart of the component failure probability determination under rainfall or landslide geological disasters according to the present invention; Figure 6 This is a comparison chart of the running data between the traditional scenario-free reduction planning method of the present invention and the method of the present invention; Figure 7This is a diagram of the improved IEEE-33 node distribution network structure of the present invention. Detailed Implementation

[0022] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0023] See attached document Figure 1 This invention provides a method for resilience planning of distributed power sources in distribution networks under multiple extreme weather conditions: S1. The data processing terminal constructs a comprehensive failure probability model for power distribution network components under multiple extreme weather conditions; S2. Using a comprehensive fault probability model of distribution network components under multiple extreme weather conditions, generate multiple initial extreme disaster scenario sets containing different survival and fault states of distribution network components. Then, use a clustering algorithm to reduce and cluster the initial extreme disaster scenario sets to obtain a reduced typical scenario set. S3. Establish a joint model for distributed power source resilience planning by combining the reduced set of typical scenarios with the investment and operation and maintenance costs of the distribution network. S4. Establish a post-disaster distribution network resilience operation constraint model for the distributed power source resilience planning joint model. S5. Incorporate the post-disaster distribution network resilience operation constraint model into the distributed power source resilience planning joint model for numerical solution, and output the optimal installation location and capacity decision instructions for each candidate node distributed power source in the distribution network based on the solution results of the distributed power source resilience planning joint model.

[0024] See attached document Figure 2 For S1, the data processing terminal constructs a comprehensive failure probability model for distribution network components under multiple extreme weather conditions. It obtains the failure probabilities of distribution network components under windy weather, rainy or landslide-prone weather, and icing weather. The comprehensive failure probability of a component is the weighted sum of the failure probabilities under windy weather, rainy or landslide-prone weather, and icing weather, according to a set weighting coefficient. The formula for calculating the comprehensive failure probability of distribution network components under multiple extreme weather conditions is as follows: ; In the formula, Represents the overall failure probability of a component. This represents the probability of component failure under windy conditions. This represents the probability of component failure under conditions of rainfall or landslides. This represents the probability of component failure under icing conditions. The weighting coefficient represents the impact of severe wind disasters. The weighting coefficients represent the weighting factors under rainfall or landslide disasters. This represents the weighting coefficient under ice cover disaster.

[0025] The weighting coefficients for windstorm disasters, rainfall or landslide disasters, and icing disasters are added together to form a weighting coefficient of 1. The following formula satisfies the constraint that the sum of the weighting coefficients must be 1: ; The data processing terminal constructs a fault probability assessment model for distribution network lines and towers caused by strong winds. This model reflects the mapping relationship between the equivalent load intensity of lines exposed to strong winds and the fault probability of components under strong wind conditions. Using the empirical fitting proportional constant and empirical fitting exponential constant of the strong wind fault model obtained through historical data fitting, along with the equivalent load intensity of lines exposed to strong winds, the fault probability of components in distribution network lines and towers under strong wind conditions is calculated. The formula for the strong wind fault model is as follows: ; In the formula, This represents the probability of component failure under windy conditions. The empirical fitting proportionality constant representing the high wind fault model. This represents the equivalent load intensity of the line exposed to strong winds. The empirical fitting exponential constant represents the fault model of strong winds.

[0026] See attached document Figure 5 To determine the failure probability of components under rainfall or landslide geological hazards, it is necessary to quantify cumulative rainfall and effective rainfall. Landslides and debris flows caused by continuous rainfall are affected by the cumulative effect of previous and current rainfall. Effective rainfall is calculated by combining previous cumulative rainfall and the cumulative effect of current rainfall. Effective rainfall equals the sum of the previous cumulative rainfall plus the product of the rainfall attenuation weighting coefficient and the actual rainfall. The formula for calculating effective rainfall is as follows: ; In the formula, Represents effective rainfall. Represents the cumulative rainfall in the previous period. Represents the total number of days observed. Represents the number of days variable. Represents the rainfall attenuation weighting coefficient. Representing the The actual rainfall of the day.

[0027] The data processing terminal determines the relationship between the effective rainfall and the rainfall threshold based on the rainfall threshold, and judges the probability of space geological disasters occurring. When the effective rainfall is greater than or equal to 0 and less than the rainfall threshold, the probability of space geological disasters occurring is calculated by combining the geological disaster probability fitting constant obtained from historical data with the effective rainfall. When the effective rainfall is greater than or equal to the rainfall threshold, the probability of space geological disasters occurring is equal to 1. The piecewise formula for the probability of space geological disasters occurring is as follows: ; In the formula, Represents the probability of space geological disasters occurring. Represents the fitting constant for the probability of geological disasters. Represents the fitting constant for the probability of geological disasters. Represents effective rainfall. Represents the fitting constant for the probability of geological disasters. This represents the rainfall threshold.

[0028] The data processing terminal calculates the maximum force that the tower can withstand by combining the tower's elastic modulus, moment of inertia, deflection limit, debris flow impact height, and total tower height, thus completing the mechanical verification of the debris flow impact energy and the tower's tensile damage limit. The formula for the maximum force on the tower is as follows: ; In the formula, This represents the maximum force that the tower can withstand. Represents the elastic modulus of the tower. Represents the moment of inertia. Represents the deflection limit. Represents the height of debris flow. This represents the total height of the tower.

[0029] After calculating the maximum force that the tower can withstand, the comprehensive kinetic energy parameters of the debris flow are calculated. These parameters characterize the work done by the debris flow. The calculation of these parameters involves considering the debris flow mass, velocity, gravitational acceleration, drop height, friction coefficient, and slope angle. The formula for the comprehensive kinetic energy parameters of the debris flow is as follows: ; In the formula, Represents the comprehensive kinetic energy parameters of debris flow. Represents the quality of debris flow. Represents flow rate, Represents gravitational acceleration. Represents the height difference. Represents the coefficient of friction. Represents the slope angle.

[0030] By combining the tower's elastic modulus, moment of inertia, and the maximum force the tower can withstand, the work done by the maximum bending moment is calculated. The formula for the work done by the maximum bending moment is as follows: ; In the formula, This represents the work done by the maximum bending moment. This represents the maximum force that the tower can withstand. Represents the elastic modulus of the tower. Represents the moment of inertia.

[0031] The probability of foundation damage to the tower structure is obtained by calculating the work done by the maximum bending moment. A correlation is established between the comprehensive kinetic energy parameter of the debris flow and the work done by the maximum bending moment. When the comprehensive kinetic energy parameter of the debris flow is greater than or equal to the work done by the maximum bending moment, it means that the impact energy of the debris flow exceeds the tower's bearing capacity, and the probability of foundation damage to the tower structure is 1. When the comprehensive kinetic energy parameter of the debris flow is less than the work done by the maximum bending moment, the probability of foundation damage to the tower structure is 0. The formula for the probability of foundation damage to the tower structure is as follows: ; In the formula, This represents the probability of foundation damage to the tower structure. Represents the comprehensive kinetic energy parameters of debris flow. This represents the work done by the maximum bending moment.

[0032] By multiplying the probability of spatial geological disasters by the probability of tower structure damage, the coupled calculation of the probability of geological disasters and the probability of tower structure damage is completed, and the failure probability of components under rainfall or landslide geological disasters is obtained.

[0033] After obtaining the failure probability of components under rainfall or landslide geological hazards, the failure probability of components under icing hazards is then obtained. Obtaining the failure probability of components under icing hazards involves calculating the cumulative equivalent ice thickness under the spatial distribution of the micro-meteorological environment. Calculating the cumulative equivalent ice thickness involves integrating the icing growth rate constant, the spatial Gaussian distribution coordinates of the micro-meteorological environment, the spatial scale parameters of the micro-meteorological environment, the integration time variable, and the target observation time. The integral formula for the cumulative equivalent ice thickness is as follows: ; In the formula, Represents the cumulative equivalent ice thickness. Represents the target observation time. Represents the icing growth rate constant. Represents the spatial Gaussian distribution coordinates of the micrometeorological environment. Represents the spatial Gaussian distribution coordinates of the micrometeorological environment. Represents spatial scale parameters of the micrometeorological environment. Represents spatial scale parameters of the micrometeorological environment. Represents spatial scale parameters of the micrometeorological environment. Represents spatial scale parameters of the micrometeorological environment. This represents the time variable for integration.

[0034] After calculating the cumulative equivalent ice thickness, the equivalent icing thickness ratio is then calculated. This ratio is the ratio of the calculated cumulative equivalent ice thickness to the maximum designed ice resistance thickness of the line. The formula for the equivalent icing thickness ratio is as follows: ; In the formula, Represents the ratio of equivalent icing thickness. Represents the cumulative equivalent ice thickness. This represents the maximum anti-icing thickness of the line design.

[0035] After calculating the equivalent icing thickness ratio, a mapping calculation is performed between the equivalent icing thickness ratio and the occurrence rate of icing failure. This mapping calculation involves an exponential operation combining the icing failure probability fitting coefficient and the equivalent icing thickness ratio to obtain the icing failure probability. The formula for the icing failure probability is as follows: ; In the formula, Represents the probability of icing failure. The coefficients represent the fitting coefficients for the probability of icing failure. Represents the ratio of equivalent icing thickness. This represents the fitting coefficient for the probability of icing failure.

[0036] See attached document Figure 3 For S2, the data processing terminal uses a comprehensive fault probability model of distribution network components under multiple extreme weather conditions to generate multiple initial extreme disaster scenario sets containing different survival and fault states of distribution network components. Random numbers are generated based on Monte Carlo sampling, and the survival or fault state of the component is determined by comparing the relationship between the random numbers and the comprehensive fault probability of the component. The distribution network component status is then output. The formula for determining the random number of a component's survival or fault state is as follows: ; In the formula, Represents the status of power distribution network components. Represents a fault status. Indicates the state of being alive. Represents a random number. This represents the overall failure probability of a component.

[0037] The data processing terminal quantitatively assesses power outage losses in a single extreme disaster scenario. Based on the distribution network topology connectivity under the initial extreme disaster scenario, it evaluates the active power reduction of critical loads and interruptible loads when each node loses main grid power through islanding. Combining the total operating time period of the distribution network with unit time intervals, it performs a summation calculation to calculate the expected power shortage at each node. The expected power shortage at a node represents the expected value of power shortage at a distribution network node within the total operating time period of the distribution network. The expected power shortage at a node equals the sum of the active power reduction of critical loads and the active power reduction of interruptible loads, multiplied by the unit time interval, and accumulated over the total operating time period of the distribution network. The formula for the expected power shortage at a node is as follows: ; In the formula, The representative node expects a power shortage. Represents the total operating time period of the distribution network. Represents a time-period variable. This represents the active power reduction of critical loads. This represents the amount of active power reduction for interruptible loads. The unit of time is the time interval.

[0038] After calculating the expected power shortage at each node, a load reduction vector for the entire network is constructed. Constructing this vector involves extracting the expected power shortage for all nodes within the distribution network, and then arranging these expected power shortages into column vectors according to the node numbers to form the overall network load reduction vector. The formula for constructing the overall network load reduction vector is as follows: ; In the formula, Represents the load reduction vector of the entire network. The node representing the first node expects to lack power. The node representing the second node is expected to lack power. Representing the Each node expects a power shortage. Represents the total number of nodes.

[0039] Based on the constructed load reduction vector of the entire network, the distribution network loss threshold is set to eliminate low-impact scenarios to complete the initial screening. The expected power shortage of the total nodes of the entire network for each initial extreme disaster scenario is calculated. Scenarios with the expected power shortage of the total nodes of the entire network lower than the distribution network loss threshold are eliminated, and the initial extreme disaster scenarios with high losses are retained to form the initial reduction scenario set.

[0040] After removing low-impact scenarios, a massive number of disaster scenarios are clustered and reduced from the initial reduction scenario set. This process involves calculating a clustering objective function and using a clustering algorithm to minimize sample distances, thereby calculating cluster centers and scenario probabilities. The clustering objective function represents the sum of the squares of the vector L2 distances between the total network load reduction vector of a scenario sample and the representative vector of the cluster center across all cluster sets. Minimizing the sample distance is achieved by finding the minimum value of the clustering objective function. The formula for minimizing the clustering objective function is as follows: ; In the formula, Represents the clustering objective function. Represents the total number of cluster centers. Represents the cluster center variable. Representing the A cluster set, Represents the variables of the scene sample. Representing the The network load reduction vector for each scenario sample Representing the Representative vectors of each cluster center The L2 norm distance represents the distance between vectors.

[0041] Calculate the minimum value of the clustering objective function and determine the first... After representing the cluster centers with their representative vectors, the reduced scenario occurrence probabilities are synthesized. The synthesized reduced scenario occurrence probabilities involve summing the initial occurrence probabilities of all scenario samples belonging to the same cluster set, resulting in the reduced scenario occurrence probability for that cluster set. The formula for the reduced scenario occurrence probability is as follows: ; In the formula, This represents the probability of the scenario occurring after the reduction. Representing the A cluster set, Represents the variables of the scene sample. Representing the The initial occurrence probability of each scene sample.

[0042] The probability of the scenario occurring after reduction is calculated. The optimal number of clusters is determined through dynamic judgment criteria. The decline rate of the cluster objective function corresponding to the number of adjacent clusters, which reflects the attenuation caused by the increase in the number of cluster centers, is calculated. The difference between the cluster objective function when the number of cluster centers is reduced by one and the cluster objective function corresponding to the number of cluster centers is obtained. The decline rate of the cluster objective function is obtained by dividing the difference between the cluster objective function and the cluster objective function when the number of cluster centers is reduced by one.

[0043] After calculating the decline rate of the clustering objective function, it is compared with the cluster number convergence threshold. When the decline rate of the clustering objective function is less than or equal to the cluster number convergence threshold, the inequality for determining the optimal number of clusters is satisfied. When the inequality for determining the optimal number of clusters is satisfied, the currently calculated number of cluster centers is output as the optimal number of clusters, and the incremental calculation of the number of cluster centers is stopped. The formula for the inequality for determining the optimal number of clusters is as follows: ; In the formula, This represents the clustering objective function when the number of cluster centers is reduced by one. The clustering objective function representing the number of cluster centers. This represents the threshold for the number of clusters to converge.

[0044] See attached document Figure 4 For S3, the data processing terminal establishes a joint model for distributed power source resilience planning. A comprehensive objective function is constructed, defining the overall cost minimization objective. This overall cost minimization objective constrains the optimization direction of the joint model, minimizing the value of the output comprehensive objective function. It comprehensively considers investment costs, operation and maintenance costs, and expected post-disaster operating loss costs. Calculating the comprehensive objective function involves obtaining the investment cost corresponding to the planning scheme, the operation and maintenance costs associated with the normal state of the distribution network, and the expected post-disaster operating loss costs associated with extreme disaster scenarios. The comprehensive objective function equals the sum of the investment cost, operation and maintenance cost, and expected post-disaster operating loss cost. The formula for the comprehensive objective function is as follows: ; In the formula, The representative programming objective function, Represents investment cost, Represents operation and maintenance costs. This represents the expected operating losses and costs after a disaster.

[0045] After establishing the comprehensive objective function of the planning model, investment costs and capital recovery are calculated. This calculation involves determining the conversion relationships between the planned installation capacity of each node and the fixed investment cost, the unit capacity investment cost, and the service life. The investment cost calculation includes summing the fixed investment cost, the planned installation status of each node, the unit capacity investment cost, the planned installation capacity of each node, and the investment capital recovery coefficient over the total number of nodes. The investment cost equals the product of the fixed investment cost and the planned installation status of each node, plus the product of the unit capacity investment cost and the planned installation capacity of each node, multiplied by the cumulative investment capital recovery coefficient. The investment cost calculation formula is as follows: ; In the formula, Represents investment cost, Represents the total number of nodes. Represents node variables, Represents fixed investment costs. This indicates the planned installation status of the node. Represents the unit capacity investment cost. Representative node planned installation capacity, This represents the return on investment.

[0046] To determine the investment cost, the investment recovery factor needs to be calculated beforehand. Calculating the investment recovery factor involves combining the discount rate and the useful life. The investment recovery factor equals the discount rate multiplied by the discount rate plus one raised to the power of the useful life, then divided by the difference between the discount rate plus one raised to the power of the useful life and one. The formula for the investment recovery factor is as follows: ; In the formula, Represents the return on investment. Represents the discount rate. Indicates service life.

[0047] After calculating the investment cost and investment recovery coefficient, the operation and maintenance costs and expected post-disaster operational loss costs are quantified. Quantifying operation and maintenance costs includes calculating the unit operation and maintenance cost. This calculation involves summing the unit operation and maintenance cost, distributed generation output, and unit time interval over the total number of nodes and the total operating time period of the distribution network. The operation and maintenance cost is equal to the sum of the products of the unit operation and maintenance cost, distributed generation output, and unit time interval. The operation and maintenance cost formula is as follows: ; In the formula, Represents operation and maintenance costs. Represents the total number of nodes. Represents node variables, Represents the total operating time period of the distribution network. Represents a time-period variable. Represents unit operation and maintenance costs. Represents the output of distributed power sources. The unit of measurement is the time interval.

[0048] After calculating the operation and maintenance costs, the expected post-disaster operational loss cost is quantified. Quantifying the expected post-disaster operational loss cost includes converting post-disaster resilience operation indicators under various typical scenarios. The conversion of post-disaster resilience operation indicators involves combining the probability of scenario occurrence after reduction, the unit loss cost of critical loads, the post-disaster active power reduction of critical loads, the unit loss cost of interruptible loads, the post-disaster active power reduction of interruptible loads, and the unit time interval.

[0049] The expected post-disaster operating loss cost equals the product of the unit loss cost of critical loads and the active power reduction of critical loads after the disaster, plus the product of the unit loss cost of interruptible loads and the active power reduction of interruptible loads after the disaster. This sum is multiplied by the probability of the reduced scenario occurring and the unit time interval, and then summed over the total number of cluster centers, the total number of nodes, and the total operating time period of the distribution network. The formula for the expected post-disaster operating loss cost is as follows: ; In the formula, Represents the expected operating losses after a disaster. Represents the total number of cluster centers. Represents the cluster center variable. Represents the total number of nodes. Represents node variables, Represents the total operating time period of the distribution network. Represents a time-period variable. This represents the probability of the scenario occurring after the reduction. Represents the unit loss cost of critical loads. This represents the reduction in active power of critical loads after a disaster. This represents the unit loss cost of interruptible load. This represents the amount of active power reduction that can be interrupted after a disaster. The unit of time is the time interval.

[0050] After quantifying the expected post-disaster operating loss cost, constraints are set for distributed generation planning. These constraints include setting a maximum total number of distributed generation units allowed across the entire network and boundary constraints on the installation capacity of each node. The maximum total number of distributed generation units allowed across the entire network includes limiting the total number of nodes within the distribution network that can have distributed generation units installed. A constraint relationship is established by combining the total number of nodes, the planned installation status of nodes, and the upper limit of the total number of units, ensuring that the sum of the planned installation statuses of all nodes is less than or equal to the upper limit of the total number of units. The formula for the upper limit of the total number of units is as follows: ; In the formula, Represents the total number of nodes. Represents node variables, This indicates the planned installation status of the node. This represents the maximum number of units that can be installed.

[0051] After setting the maximum total number of installations allowed across the entire network, boundary constraints for node installation capacity are set. These boundary constraints limit the range of distributed power supply installation capacity for each node. An inequality is established by combining the planned installation status of nodes, the lower limit of node installation capacity, and the upper limit of node installation capacity. This requires that the planned installation capacity of a node be greater than or equal to the product of its planned installation status and the lower limit of its installation capacity, and less than or equal to the product of its planned installation status and the upper limit of its installation capacity. The formulas for the upper and lower limits of node installation capacity are as follows: ; In the formula, This indicates the planned installation status of the node. This represents the lower limit of the node installation capacity. Representative node planned installation capacity, This represents the maximum capacity that can be installed on a node.

[0052] For S4, the data processing terminal establishes a post-disaster distribution network resilience operation constraint model, calculates post-disaster distribution network operation indicators and sets resilience baseline constraints. The post-disaster distribution network operation indicators characterize the operation loss costs associated with extreme disaster scenarios.

[0053] The calculation of post-disaster distribution network operation indicators involves summing the unit loss cost of critical loads, the active power reduction of critical loads after the disaster, the unit loss cost of interruptible loads, the active power reduction of interruptible loads after the disaster, and the unit time interval, over the total number of nodes and the total operating time period of the distribution network. The post-disaster distribution network operation indicator equals the sum of the product of the unit loss cost of critical loads and the active power reduction of critical loads after the disaster, plus the sum of the product of the unit loss cost of interruptible loads and the active power reduction of interruptible loads after the disaster, multiplied by the unit time interval. The formula for the post-disaster distribution network operation indicator is as follows: ; In the formula, Representing the Post-disaster power distribution network operation indicators of each cluster center Represents the total number of nodes. Represents node variables, Represents the total operating time period of the distribution network. Represents a time-period variable. Represents the unit loss cost of critical loads. This represents the reduction in active power of critical loads after a disaster. This represents the unit loss cost of interruptible load. This represents the amount of active power reduction that can be interrupted after a disaster. The unit of time is the time interval.

[0054] After calculating the post-disaster distribution network operation indicators, resilience baseline constraints are set. These constraints include limiting the maximum permissible boundaries of the post-disaster distribution network operation indicators. An inequality is established by combining the post-disaster distribution network operation indicators with the maximum baseline threshold for resilience operation indicators, requiring that the post-disaster distribution network operation indicators be less than or equal to the maximum baseline threshold for resilience operation indicators. The formula for the resilience operation indicator baseline constraint is as follows: ; In the formula, Representing the Post-disaster power distribution network operation indicators of each cluster center This represents the highest baseline threshold for resilience indicators.

[0055] After setting resilience baseline constraints, network topology connectivity and radial constraints are established. Establishing these constraints includes handling fault isolation regions and determining the virtual power flow to maintain a loop-free radial shape in post-disaster network reconstruction. Handling fault isolation regions involves determining the status of faulty branches. Combining time period variables, cluster center variables, and the set of faulty branches, the connectivity status of branches belonging to the set of faulty branches is forcibly set to zero, disconnecting the corresponding connection paths. The formula for the faulty branch status is as follows: ; In the formula, Represents the connection status of the branch. Represents the first node variable. Represents the variable at the end node. Represents a time-period variable. Represents the cluster center variable. This represents the set of faulty branches.

[0056] After forcibly setting the connection status of branches belonging to the faulty branch set to zero, the total number of branch connection statuses is calculated. Combining the distribution network branch set, the total number of nodes, and the total number of islanded microgrids, the sum of all branch connection statuses within the distribution network branch set is required to equal the difference between the total number of nodes and the total number of islanded microgrids, thus restricting the distribution network from forming a closed-loop connection. The constraint formula for the total number of branch connection statuses is as follows: ; In the formula, Represents the set of distribution network branches. Represents the connection status of the branch. Represents the total number of nodes. This represents the total number of isolated microgrids.

[0057] After calculating the total number of branch connectivity states, it is determined that the post-disaster reconstructed network maintains a loop-free radial virtual power flow. Determining that the post-disaster reconstructed network maintains a loop-free radial virtual power flow involves establishing a radial virtual power flow identity for the associated node set. Establishing this identity includes constraining the virtual load balance of nodes and setting upper and lower limits for branch virtual power flow. Combining the associated node set, the branch virtual power flow of inflow nodes, the branch virtual power flow of outflow nodes, the node virtual load, and the maximum constant, the difference between the branch virtual power flow of inflow nodes and the branch virtual power flow of outflow nodes is set to equal the node virtual load, and the branch virtual power flow of outflow nodes is bounded by the product of the maximum constant and the branch connectivity state. The radial virtual power flow identity for the associated node set is as follows: ; ; ; In the formula, Represents the set of associated nodes. Represents the associated node variable, Represents node variables, Represents a time-period variable. Represents the cluster center variable. Virtual power flow representing the inflow node in the branch. Virtual power flow representing the outflow node in the branch. Represents the virtual load of nodes. This represents the preset maximum constant. This represents the connection status of the branch.

[0058] Establishing node power balance constraints requires setting boundary constraints for power output and load reduction. A safety boundary inequality constraint for active power output is established by combining the node active power output with the node planned installed capacity obtained within the joint model of distributed power resilience planning. This constraint limits the post-disaster operational output based on planning decisions. Node active power output must be greater than or equal to zero, and less than or equal to the node's planned installed capacity. The formulas for the upper and lower limits of active power output are as follows: ; In the formula, The node represents the contribution of the node. This represents the upper limit of one's contribution. Represents node variables, Represents a time-period variable. This represents the cluster center variable.

[0059] After setting the safety boundary for active power output, a safety boundary for critical load reduction is then set. Setting the safety boundary for critical load reduction involves establishing an inequality between the post-disaster active power reduction of critical loads and the demand for critical loads at nodes. It is required that the post-disaster active power reduction of critical loads is greater than or equal to zero, and less than or equal to the demand for critical loads at nodes. The formulas for the upper and lower limits of critical load reduction are as follows: ; In the formula, This represents the reduction in active power of critical loads after a disaster. Represents the critical load demand of nodes. Represents node variables, Represents a time-period variable. This represents the cluster center variable.

[0060] After setting safety boundaries for critical load reduction, safety boundaries for interruptible load reduction are then set. Setting these safety boundaries involves establishing an inequality between post-disaster active power reduction of interruptible loads and node interruptible load demand. It is required that post-disaster active power reduction of interruptible loads is greater than or equal to zero, and that post-disaster active power reduction of interruptible loads is less than or equal to node interruptible load demand. The formulas for the upper and lower limits of interruptible load reduction are as follows: ; In the formula, This represents the amount of active power reduction that can be interrupted after a disaster. The interruptible load demand of the representative node. Represents node variables, Represents a time-period variable. This represents the cluster center variable.

[0061] After setting a safety boundary for interruptible load reduction, constraints are established to link reactive power compensation and power factor. Setting these constraints includes calculating the power factor proportionality coefficient. This calculation involves dividing the node's reactive power load demand by its active power load demand. The power factor proportionality coefficient is equal to the quotient obtained by dividing the node's reactive power load demand by its active power load demand. The power factor formula is as follows: ; In the formula, Represents the power factor proportionality coefficient. Represents the reactive power load demand of the node. Represents the active power load demand of the node. Represents node variables, Represents a time-period variable.

[0062] After calculating the power factor proportionality coefficient, the reactive power reduction is calculated as a function of the constant power factor and active power reduction. This calculation includes establishing a linkage relationship between reactive power reduction and active power reduction for critical loads. Combining the post-disaster active power reduction of critical loads with the power factor proportionality coefficient, the post-disaster reactive power reduction of critical loads is set to the product of the power factor proportionality coefficient and the post-disaster active power reduction. The formula for the linkage of reactive power reduction for critical loads is as follows: ; In the formula, This represents the amount of reactive power reduction for critical loads after a disaster. Represents the power factor proportionality coefficient. This represents the reduction in active power of critical loads after a disaster. Represents node variables, Represents a time-period variable. This represents the cluster center variable.

[0063] After establishing the reactive power reduction linkage relationship for critical loads, establish the reactive power reduction linkage relationship for interruptible loads. Combining the reactive power reduction amount of interruptible loads after a disaster with the power factor ratio, set the reactive power reduction amount of interruptible loads after a disaster equal to the product of the power factor ratio and the reactive power reduction amount of interruptible loads after a disaster. The reactive power reduction linkage formula for interruptible loads is as follows: ; In the formula, This represents the amount of reactive power reduction that can be interrupted after a disaster. Represents the power factor proportionality coefficient. This represents the amount of active power reduction that can be interrupted after a disaster. Represents node variables, Represents a time-period variable. This represents the cluster center variable.

[0064] After establishing the linkage relationship for reactive power reduction of interruptible loads, an approximate derivation of capacitor reactive power compensation is performed. This approximate derivation involves calculating the capacitor reactive power compensation amount by combining the rated reactive power capacity of the capacitor with the square value of the node voltage. The capacitor reactive power compensation amount is equal to the product of the rated reactive power capacity of the capacitor and the square value of the node voltage. The approximate formula for capacitor reactive power compensation is as follows: ; In the formula, This represents the reactive power compensation of the capacitor. This represents the rated reactive power of the capacitor. Represents the square value of the node voltage. Represents node variables, Represents a time-period variable. This represents the cluster center variable.

[0065] After completing the approximate derivation of capacitor reactive power compensation, the balance constraints between node net injection and branch transmission are established. Establishing these constraints involves calculating the node net active power injection. This calculation combines node active power output, node active power load demand, post-disaster active power reduction for critical loads, and post-disaster active power reduction for interruptible loads. The node net active power injection formula is equal to the difference between node active power output and node active power load demand, plus the post-disaster active power reductions for critical loads and interruptible loads. ; In the formula, Represents the net active power injected into the node. The node represents the contribution of the node. Represents the active power load demand of the node. This represents the reduction in active power of critical loads after a disaster. This represents the amount of active power reduction that can be interrupted after a disaster. Represents node variables, Represents a time-period variable. This represents the cluster center variable.

[0066] After calculating the net active power injection at each node, the net reactive power injection at each node is calculated. This calculation involves combining the node's reactive power output, capacitor reactive power compensation, node reactive power load demand, and post-disaster reactive power reduction for critical loads and interruptible loads. The net reactive power injection at each node equals the sum of the node's reactive power output and capacitor reactive power compensation, minus the node's reactive power load demand, plus the post-disaster reactive power reduction for critical and interruptible loads. The formula for net reactive power injection is as follows: ; In the formula, The representative node has net reactive power injection. The node represents no reactive power output. This represents the reactive power compensation of the capacitor. Represents the reactive power load demand of the node. This represents the amount of reactive power reduction for critical loads after a disaster. This represents the amount of reactive power reduction that can be interrupted after a disaster. Represents node variables, Represents a time-period variable. This represents the cluster center variable.

[0067] After calculating the net reactive power injection at each node, an active power balance relationship is established for connected branches. Establishing this relationship involves combining the net reactive power injection at each node, the active power transmission of branches flowing out of the node, the active power transmission of branches flowing into the node, and the set of associated nodes to create an equation. The net reactive power injection at each node is set to the sum of the active power transmission of branches flowing out of the node within the associated node set, minus the sum of the active power transmission of branches flowing into the node within the associated node set. The formula for active power balance in connected branches is as follows: ; In the formula, Represents the net active power injected into the node. Represents the associated node variable, Represents the set of associated nodes. The active power transmission volume of the branch representing the outflow node. The active power transmission volume of the branch representing the inflow node. Represents node variables, Represents a time-period variable. This represents the cluster center variable.

[0068] After establishing the active power balance relationship of connected branches, the reactive power balance relationship of connected branches is established. Establishing the reactive power balance relationship of connected branches involves establishing an equation based on the net reactive power injection of the nodes, the reactive power transmission of the outflowing nodes, the reactive power transmission of the inflowing nodes, and the associated node set. Let the net reactive power injection of a node equal to the sum of the reactive power transmission of the outflowing nodes within the associated node set, minus the sum of the reactive power transmission of the inflowing nodes within the associated node set. The reactive power balance formula for connected branches is as follows: ; In the formula, The representative node has net reactive power injection. Represents the associated node variable, Represents the set of associated nodes. The reactive power transmission of the branch representing the outflow node. The reactive power transmission of the branch that flows into the node. Represents node variables, Represents a time-period variable. This represents the cluster center variable.

[0069] After establishing the reactive power balance relationship of connected branches, power flow safety and line capacity limit constraints are established. Establishing these constraints requires linearizing the nonlinear voltage drop of the line. A line voltage drop inequality constraint is established by combining the maximum constant, branch connectivity, the square of the node voltage, the square of the associated node voltage, branch resistance, the active power transmission of the branch at the outflow node, and the reactive power transmission of the branch with the branch reactance. The formula is: subtract the square of the associated node voltage from the square of the node voltage, then subtract twice the product of the branch resistance and the active power transmission of the branch at the outflow node, and then subtract twice the product of the branch reactance and the reactive power transmission of the branch at the outflow node. The calculated result is greater than or equal to the negative of the product of the maximum constant and 1 minus the difference between the branch connectivity and the current state, and less than or equal to the product of the maximum constant and 1 minus the difference between the branch connectivity and the current state. The line voltage drop inequality constraint formula is as follows: ; In the formula, This represents the preset maximum constant. Represents the connection status of the branch. Represents the square value of the node voltage. Represents the squared value of the associated node voltage. Represents the branch resistance. The active power transmission volume of the branch representing the outflow node. Represents branch circuit reactance. The reactive power transmission of the branch representing the outflow node. Represents node variables, Represents the associated node variable, Represents a time-period variable. This represents the cluster center variable.

[0070] After establishing the line voltage drop inequality constraint, upper and lower limits for the actual active power transmission of branches are set. Setting these limits involves establishing inequalities based on the active power transmission of the branch at the outflow node, the upper limit of the branch's active power transmission, and the branch's connectivity status. It is required that the active power transmission of the branch at the outflow node is greater than or equal to the negative of the product of the upper limit of the branch's active power transmission and the branch's connectivity status, and that the active power transmission of the branch at the outflow node is less than or equal to the product of the upper limit of the branch's active power transmission and the branch's connectivity status. The formulas for the upper and lower limits of the actual active power transmission of branches are as follows: ; In the formula, This represents the upper limit of active power transmission in the branch. Represents the connection status of the branch. The active power transmission volume of the branch representing the outflow node. Represents node variables, Represents the associated node variable, Represents a time-period variable. This represents the cluster center variable.

[0071] After setting the upper and lower limits for the actual active power transmission of a branch, the upper and lower limits for the actual reactive power transmission of the branch are then set. Setting these limits involves establishing an inequality based on the reactive power transmission amount of the branch at the outflow node, the upper limit of the branch's reactive power transmission, and the branch's connectivity status. It is required that the reactive power transmission amount of the branch at the outflow node is greater than or equal to the negative of the product of the upper limit of the branch's reactive power transmission and the branch's connectivity status, and that the reactive power transmission amount of the branch at the outflow node is less than or equal to the product of the upper limit of the branch's reactive power transmission and the branch's connectivity status. The formulas for the upper and lower limits of the actual reactive power transmission of a branch are as follows: ; In the formula, Represents the upper limit of reactive power transmission in the branch. Represents the connection status of the branch. Represents the reactive power transmission of the branch at the outgoing node. Represents node variables, Represents the associated node variable, Represents a time-period variable. This represents the cluster center variable.

[0072] After setting the upper and lower limits of actual reactive power transmission in the branches, the node voltage safety boundary constraints are set. Setting the node voltage safety boundary constraints includes setting the root node reference voltage. Setting the root node reference voltage includes establishing the root node voltage identity. An equation is established by combining the square of the root node voltage and the rated reference voltage, setting the square of the root node voltage equal to the square of the rated reference voltage. The root node voltage identity is as follows: ; In the formula, This represents the square of the root node voltage. Represents the rated reference voltage. Represents a time-period variable. This represents the cluster center variable.

[0073] After setting the root node reference voltage, the boundary limits for the voltage amplitude of all nodes in the network are then set. Setting these boundary limits involves establishing inequalities between the lower and upper safe limits of node voltages. The requirement is that the squared value of a node voltage is greater than or equal to the lower safe limit, and less than or equal to the upper safe limit. The formulas for the safe upper and lower limits of node voltages are as follows: ; In the formula, This represents the lower limit of the safe voltage at the node. Represents the square value of the node voltage. Represents the upper limit of node voltage safety. Represents node variables, Represents a time-period variable. This represents the cluster center variable.

[0074] After setting boundary limits for the voltage amplitude of all network nodes, a linearized polygon constraint is established for the thermal stability limit of branch apparent power. Establishing this constraint includes establishing a quadratic constraint for line apparent power. This constraint combines the active power transfer of branches at outgoing nodes, the reactive power transfer of branches at outgoing nodes, the branch apparent power thermal stability limit, and the branch connectivity state to establish an inequality. The requirement is that the sum of the squares of the active power transfer and reactive power transfer of branches at outgoing nodes must be less than or equal to the square of the product of the branch apparent power thermal stability limit and the branch connectivity state. The formula for the quadratic apparent power constraint is as follows: ; In the formula, The active power transmission volume of the branch representing the outflow node. Represents the reactive power transmission of the branch at the outgoing node. This represents the apparent power thermal stability limit of the branch. Represents the connection status of the branch. Represents node variables, Represents the associated node variable, Represents a time-period variable. This represents the cluster center variable.

[0075] After establishing the quadratic constraint on the apparent power of the line, the quadratic constraint on the apparent power of the line is transformed into a polygonal linear capacity constraint. Combining the active power transmission of the branch at the outflow node, the thermal stability limit of the branch's apparent power, and the branch's connectivity state, the first inequality of the polygonal linearized capacity constraint is established. This requires that the active power transmission of the branch at the outflow node is greater than or equal to the negative of the product of the thermal stability limit of the branch's apparent power and the branch's connectivity state, and that the active power transmission of the branch at the outflow node is less than or equal to the product of the thermal stability limit of the branch's apparent power and the branch's connectivity state. The formula for the first inequality of the polygonal linearized capacity constraint is as follows: ; In the formula, This represents the apparent power thermal stability limit of the branch. Represents the connection status of the branch. The active power transmission volume of the branch representing the outgoing node. Represents node variables, Represents the associated node variable, Represents a time-period variable. This represents the cluster center variable.

[0076] After establishing the first inequality for polygonal linearized capacity constraints, a second inequality for polygonal linearized capacity constraints is established by combining the reactive power transmission of branches at outflow nodes, the apparent power thermal stability limit of branches, and the branch connectivity state. This requires that the reactive power transmission of branches at outflow nodes be greater than or equal to the negative of the product of the apparent power thermal stability limit of branches and the branch connectivity state, and that the reactive power transmission of branches at outflow nodes be less than or equal to the product of the apparent power thermal stability limit of branches and the branch connectivity state. The formula for the second inequality for polygonal linearized capacity constraints is as follows: ; In the formula, This represents the apparent power thermal stability limit of the branch. This represents the connection status of the branch. Represents the reactive power transmission of the branch at the outgoing node. Represents node variables, Represents the associated node variable, Represents a time-period variable. This represents the cluster center variable.

[0077] After establishing the second inequality for polygonal linearized capacity constraints, the third inequality is established by combining the active power transmission of the outflowing node's branch, the reactive power transmission of the outflowing node's branch, the square root of two constants, the apparent power thermal stability limit of the branch, and the branch connectivity state. This requires that the sum of the active power transmission and reactive power transmission of the outflowing node's branch is greater than or equal to the negative of the product of the square root of two constants, the apparent power thermal stability limit of the branch, and the branch connectivity state; and that the sum of the active power transmission and reactive power transmission of the outflowing node's branch is less than or equal to the product of the square root of two constants, the apparent power thermal stability limit of the branch, and the branch connectivity state. The formula for the third inequality for polygonal linearized capacity constraints is as follows: ; In the formula, This represents the apparent power thermal stability limit of the branch. Represents the connection status of the branch. The active power transmission volume of the branch representing the outflow node. Represents the reactive power transmission of the branch at the outgoing node. Represents node variables, Represents the associated node variable, Represents a time-period variable. This represents the cluster center variable.

[0078] For S5, after establishing linearized polygonal constraints for the apparent power thermal stability limit of the branches, the joint model is solved and the resilience planning scheme is output. The solution to the joint model and the resilience planning scheme output include the solution to the execution planning model. The solution to the execution planning model includes the summary objective function and operational constraints. The objective function is the comprehensive planning objective function. The operational constraints include distributed generation planning constraints, resilience baseline constraints, network topology connectivity and radial constraints, node power balance constraints, and power flow safety and line capacity limit constraints.

[0079] After summarizing the objective function and operational constraints, the integrated planning objective function, along with operational constraints including distributed generation planning constraints, resilience baseline constraints, network topology connectivity and radial constraints, node power balance constraints, and power flow safety and line capacity limit constraints, is input into the mixed-integer linear programming solver. The mixed-integer linear programming solver receives the joint model's operational parameters and performs a global optimization calculation. Within the boundary range satisfying the distributed generation planning constraints, resilience baseline constraints, network topology connectivity and radial constraints, node power balance constraints, and power flow safety and line capacity limit constraints, the global optimization calculation calculates the optimal solution that minimizes the value of the integrated planning objective function. The optimal solution includes planning decision variables related to the distributed generation resilience planning scheme, including node planning installation status and node planning installation capacity. The mixed-integer linear programming solver outputs the optimal solution.

[0080] The data processing terminal analyzes the optimal solution to extract the node planning and installation status and the node planning and installation capacity, generating distributed power supply installation location data and distributed power supply capacity data. The distributed power supply installation location data indicates the nodes corresponding to non-zero node planning and installation status values, and the distributed power supply capacity data indicates the specific capacity value corresponding to the node planning and installation capacity. The data processing terminal packages the distributed power supply installation location data and distributed power supply capacity data to generate an optimal decision instruction containing location and capacity information, and outputs the optimal decision instruction to the external display terminal, allowing external devices to deploy the corresponding distributed power supply equipment at the nodes indicated by the distributed power supply installation location data.

[0081] Specific application examples: See attached document Figure 7Based on specific improvements to the IEEE-33 node distribution network structure, the distribution network comprises 33 nodes and 37 branches. The 37 branches include 32 normally closed branches and 5 normally open tie lines. The base voltage is set at 12.66 kV, and the total load is set at 3715 kW + j2300 kVar. Under normal operating conditions, normally closed branches are closed, and tie lines are open. Parallel capacitors are configured at nodes 7, 14, 23, and 29. The maximum allowed total number of distributed generation sources installed across the entire network is set to 4, with the capacity of a single node ranging from 100 kW to 700 kW. The corresponding voltage amplitude boundary limits for all nodes are set from 0.93 pu to 1.05 pu.

[0082] The data processing terminal constructs a comprehensive failure probability model for distribution network components under multiple extreme weather conditions. Specifically, for windy weather, the terminal builds a failure probability assessment model for wind disasters affecting distribution network lines and towers, and calculates the failure probability of components under windy weather using the windy weather failure model formula.

[0083] The data processing terminal extracts the empirical fitting ratio constant of the strong wind fault model. Empirical fit exponential constant And the equivalent load strength of the line exposed to strong winds is Substitute the above parameters into the formula to calculate: ; The calculation shows that the probability of component failure in strong winds affecting power distribution lines and towers during windy weather is 3.62%.

[0084] In response to rainfall-induced or landslide geological disasters, the data processing terminal calculates the effective rainfall by combining the previous cumulative rainfall and the current cumulative effect of rainfall. It then combines this with the maximum stress the tower can withstand and the comprehensive kinetic energy parameters of the debris flow to obtain the failure probability of components under rainfall-induced or landslide geological disasters. Calculations determined that lines 1 to 5 have the highest failure probability of components under rainfall-induced or landslide geological disasters, corresponding to a value of 12.65%.

[0085] For icing weather, a spatial Gaussian distribution coordinate center for the micrometeorological environment was set at 50km x 50km x 50km, moving at a speed of 2km / h along a 45-degree direction. The data processing terminal calculated the cumulative equivalent ice thickness and performed an occurrence rate mapping calculation, obtaining a component failure probability of approximately 15.63% under icing disasters. Based on the set weighting coefficients, the final weighted summation yielded the overall component failure probability.

[0086] The data processing terminal utilizes a comprehensive failure probability model of distribution network components under multiple extreme weather conditions. It generates random numbers based on Monte Carlo sampling and performs 2000 random samplings. The relationship between the random numbers and the comprehensive failure probability of the components is compared to determine the survival status and failure status of the components. The data processing terminal limits the number of faulty lines in each scenario to no more than three, generating a total of 742 initial extreme disaster scenario sets containing different survival and failure statuses of distribution network components.

[0087] The distribution network loss threshold is set to 500. The expected power shortage of the total number of nodes in the entire network under each initial extreme disaster scenario is calculated. Scenarios with the expected power shortage of the total number of nodes in the entire network lower than the distribution network loss threshold are eliminated, and 215 high-loss initial extreme disaster scenarios are retained to form the initial reduction scenario set.

[0088] For the initial reduction of the scene set, the data processing terminal calculates the clustering objective function and uses the clustering algorithm to minimize the sample distance, reducing the 215 effective scenes into 50 typical scene sets after reduction, and synthesizing the occurrence probability of the reduced scenes.

[0089] Based on the expected power shortage of each node under the condition of no distributed power supply, the data processing terminal selects nodes 7, 13, 23, 24, 29, 31 and 32 as candidate nodes.

[0090] The data processing terminal inputs the overall planning objective function, along with operational constraints including distributed power planning constraints, resilience baseline constraints, network topology connectivity and radial constraints, node power balance constraints, and power flow safety and line capacity limit constraints, into the mixed-integer linear programming solver. After receiving the joint model's operational parameters, the mixed-integer linear programming solver performs a global optimization calculation and outputs the optimal solution.

[0091] The data processing terminal analyzes the optimal solution and generates distributed power source installation location data indicating the corresponding nodes 29 and 31; it also generates distributed power source capacity data indicating that the planned installation capacity of the node configured at node 29 is 700kW and the planned installation capacity of the node configured at node 31 is 427kW. The data processing terminal packages the above data to generate the optimal decision instruction and outputs it to the external display terminal.

[0092] For the post-disaster distribution network resilience operation constraint model, lines 6, 10, and 25 are assumed to simultaneously belong to the fault branch set. The data processing terminal determines the status of the fault branches and forcibly sets the branch connectivity of lines 6, 10, and 25 to zero. The data processing terminal performs topology reconstruction on the distribution network, disconnecting lines 21 and 31 and closing 5 interconnecting lines.

[0093] To determine whether the post-disaster reconstructed network maintains a loop-free radial shape, the data processing terminal will calculate the total number of distribution network nodes. The total number of isolated microgrids formed after the introduction of distributed power sources. Substitute into the constraint formula for the total number of branch connectivity states: ; The calculated cumulative sum of branch connectivity states within the distribution network branch set is equal to 30. The data processing terminal calls the distributed power sources configured at nodes 29 and 31 to provide active power output support for the fault isolation area. The reconstructed network satisfies network topology connectivity and radial constraints, as well as node power balance constraints.

[0094] The experiment compared the planning and operation data of the traditional scenario-free reduction planning method and the method of this invention in an improved IEEE-33 node distribution network. The experimental data are shown in Table 1.

[0095] Table 1. Comparison of operational data between traditional scenario-free reduction planning methods and the method of this invention. See attached document Figure 6 And Table 1, Appendix Figure 6 This paper compares the expected power shortage at nodes and the model solution time for two planning methods when dealing with extreme disasters. Figure 6 The horizontal axis represents the method type, the left vertical axis represents the expected power shortage at the node, and the right vertical axis represents the model solution time. Traditional scenario-free reduction planning methods do not use clustering algorithms to reduce and cluster the initial extreme disaster scenario set. The input of massive scenarios leads to an excessive computational burden on the solver. The line graph indicates that the model solution time reaches 48.5 hours. Furthermore, it does not perform co-optimization for the post-disaster distribution network resilience operation constraint model, and the bar graph indicates that the expected power shortage at the node remains at a high level of 245.2 MWh.

[0096] The method of this invention employs a clustering algorithm to obtain a set of 50 reduced typical scenarios, thereby lowering the computational dimensionality and shortening the model solution time (indicated by the line chart) to 2.4 hours. Simultaneously, based on the optimal solution output, the method determines the optimal capacity configuration for nodes 29 and 31, coordinating topology connectivity and power output during the post-disaster distribution network resilience operation phase, reducing the expected power shortage at nodes (indicated by the bar chart) to 85.6 MWh. The results show that the method of this invention balances the accuracy of the overall planning objective function with the computational efficiency of global model optimization.

Claims

1. A method for resilience planning of distributed generation sources in distribution networks under multiple extreme weather conditions, characterized in that, Includes the following steps: The data processing terminal constructs a comprehensive failure probability model for power distribution network components under multiple extreme weather conditions; Using the comprehensive failure probability model of distribution network components under multiple extreme weather conditions, multiple initial extreme disaster scenario sets containing different survival and failure states of distribution network components are generated. Clustering algorithms are then used to reduce and cluster the initial extreme disaster scenario sets to obtain a reduced typical scenario set. A joint model for distributed power source resilience planning is established by combining the reduced set of typical scenarios with the investment and operation and maintenance costs of the distribution network. A post-disaster distribution network resilience operation constraint model is established for the aforementioned distributed power source resilience planning joint model; The post-disaster distribution network resilience operation constraint model is incorporated into the distributed power source resilience planning joint model for numerical solution. Based on the solution results of the distributed power source resilience planning joint model, the optimal installation location and capacity decision instructions for each candidate node distributed power source in the distribution network are output.

2. The method for resilience planning of distributed power sources in distribution networks under multiple extreme weather conditions according to claim 1, characterized in that, The comprehensive failure probability model of distribution network components under multiple extreme weather conditions is constructed to obtain the failure probability of distribution network components under windy weather, rain or landslide geological disaster weather and icing weather. The comprehensive failure probability of the distribution network components under multiple extreme weather conditions is the sum of the failure probabilities of components under strong winds, under rain or landslide geological disasters, and under ice accumulation disasters, weighted by a set weighting coefficient.

3. The method for resilience planning of distributed power sources in distribution networks under multiple extreme weather conditions according to claim 2, characterized in that, The failure probability of the components under strong winds is calculated by combining the empirical fitting ratio constant, the empirical fitting exponential constant, and the equivalent load intensity of the line exposed to strong winds, obtained by fitting historical data to the strong wind failure model. The failure probability of the component under the geological disaster of rainfall or landslide includes multiplying the probability of the occurrence of the spatial geological disaster with the probability of damage to the tower structure foundation to complete the coupled calculation of the probability of the occurrence of the geological disaster and the probability of damage to the tower structure, so as to obtain the failure probability of the component under the geological disaster of rainfall or landslide.

4. The distributed power generation resilience planning method for distribution networks under multiple extreme weather conditions according to claim 3, characterized in that, The probability of the occurrence of the space geological disaster is determined by analyzing the relationship between the effective rainfall and the rainfall threshold. When the effective rainfall is greater than or equal to zero and less than the rainfall threshold, the probability of the occurrence of the space geological disaster is calculated by combining the geological disaster probability fitting constant obtained through historical data with the effective rainfall. When the effective rainfall is greater than or equal to the rainfall threshold, the probability of the occurrence of the space geological disaster is equal to one.

5. The distributed power generation resilience planning method for distribution networks under multiple extreme weather conditions according to claim 2, characterized in that, Obtaining the failure probability of components under the aforementioned icing disaster includes calculating the ratio of the cumulative equivalent ice thickness to the maximum anti-icing thickness of the line design to obtain the equivalent ice thickness ratio. The failure probability of the component under the icing disaster is obtained by performing an exponential calculation by combining the fitting coefficient of the icing failure probability with the ratio of the equivalent icing thickness.

6. The method for resilience planning of distributed power sources in distribution networks under multiple extreme weather conditions according to claim 1, characterized in that, The process of reducing and clustering the initial extreme disaster scenario set using a clustering algorithm includes calculating the expected power shortage of all nodes in the distribution network to construct a load reduction vector for the entire network. The clustering objective function is calculated, the clustering algorithm is used to minimize the sample distance, the cluster center and scene probability are calculated, the cluster objective function decline rate and the cluster number convergence threshold are compared to determine the optimal number of clusters, and the incremental calculation of the number of cluster centers is stopped to obtain the reduced typical scene set.

7. The method for resilience planning of distributed generation in distribution networks under multiple extreme weather conditions according to claim 1, characterized in that, The establishment of the distributed power source resilience planning joint model includes constructing a planning comprehensive objective function and defining an overall cost minimization objective. The overall cost minimization objective constrains the optimization direction of the distributed power source resilience planning joint model, prompting the solution output planning comprehensive objective function to be minimized. The calculation of the comprehensive objective function of the planning includes obtaining the distribution network investment cost corresponding to the planning scheme, the operation and maintenance cost associated with the normal state of the distribution network, and the expected post-disaster operation loss cost associated with extreme disaster scenarios. The comprehensive objective function of the planning is equal to the sum of the distribution network investment cost, the operation and maintenance cost, and the expected post-disaster operation loss cost.

8. The distributed power generation resilience planning method for distribution networks under multiple extreme weather conditions according to claim 7, characterized in that, The distributed power resilience planning joint model includes setting distributed power planning constraints. The distributed power planning constraints include setting the maximum total number of installations allowed across the entire network and the boundary constraints of the installation capacity of each node. The boundary constraints of the installation capacity of each node are combined with the node's planned installation status, the lower limit of the node's installation capacity, and the upper limit of the node's installation capacity to establish an inequality.

9. The method for resilience planning of distributed generation in distribution networks under multiple extreme weather conditions according to claim 1, characterized in that, The establishment of the post-disaster distribution network resilience operation constraint model includes calculating the post-disaster distribution network operation indicators and setting resilience baseline constraints. The resilience baseline constraints are limited by establishing an inequality between the post-disaster distribution network operation indicators and the highest baseline threshold of the resilience operation indicators. The established post-disaster distribution network resilience operation constraint model also includes establishing network topology connectivity and radial constraints, setting reactive power compensation and power factor linkage constraints, and calculating the reactive power reduction amount based on the linkage between the constant power factor and the active power reduction amount.

10. A method for resilience planning of distributed power sources in distribution networks under multiple extreme weather conditions, as described in claim 8, is characterized in that, The numerical solution process involves inputting the planning objective function and the operational constraints, including the distributed power planning constraints, resilience baseline constraints, network topology connectivity and radial constraints, node power balance constraints, power flow safety and line capacity limit constraints, into a mixed-integer linear programming solver. The mixed-integer linear programming solver receives the joint model running parameters and performs global optimization calculation to obtain the optimal solution. It then analyzes the optimal solution to extract the node planning and installation status and the node planning and installation capacity, and generates the optimal installation location and capacity decision instructions for each candidate node distributed power source.

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