A power distribution system disaster risk management method, device, equipment and storage medium

Abstract

The application provides a power distribution system disaster risk management method, device and equipment and a storage medium, and belongs to the power distribution risk management field. The method comprises the following steps: determining the annual occurrence exceeding probability of each disaster scene; evaluating the vulnerability of the power distribution system under each typical disaster scene, determining the component function loss and direct economic loss metric; determining a first target and a second target to be optimized, establishing a double-target optimization model considering the first target and the second target; the decision variable of the double-target optimization model comprises the implementation decision of the risk control measure and the risk financing measure; the double-target optimization model is solved to obtain an optimal Pareto frontier representing the trade-off relationship between the power supply capacity and the risk cost of the power distribution system, and a management scheme is determined. In this way, the disaster prevention and mitigation management of the power distribution system can be effectively guided, and the unified optimization of the social target and the commercial target is realized.

Description

Technical Field

[0001] This invention belongs to the field of power distribution risk management, and specifically relates to a method, device, equipment and storage medium for disaster risk management of power distribution systems. Background Technology

[0002] Urban flooding and torrential rain disasters are becoming increasingly widespread and frequent, posing a serious threat to the safe operation of urban power distribution systems. Power distribution facilities are widely distributed and have low disaster prevention design standards, making them prone to failure during urban flooding and torrential rain disasters. This can lead to prolonged power outages for users, and after the disaster, power companies need to repair and replace a large amount of damaged equipment, resulting in significant direct economic losses. Therefore, conducting flood disaster risk management of power distribution systems and carrying out scientific disaster prevention and mitigation measures are urgent technical and economic issues that need to be addressed.

[0003] To enhance the ability of power distribution systems to cope with rain and flood disasters, a typical technical solution involves selecting appropriate management methods, setting optimization objectives, and obtaining a disaster risk management plan through optimization methods, as detailed below: Existing management methods focus on risk control, namely, reducing the probability of power distribution system failures and losses after failures during urban rainstorms and floods through technical means. This includes relocating power distribution substations, installing remote control switches to rationally partition the power distribution system to reduce faulty sections, and configuring distributed backup power sources to form microgrids in non-faulty sections to supply power to important users.

[0004] In optimizing the objectives of stormwater disaster risk management in power distribution systems, existing technologies fall into two categories. One approach is to use either outage-related indicators or economic loss indicators alone, neither of which can fully reflect the social and commercial functions of the power distribution system. For example, using only outage indicators only reflects the social function of supplying electricity to users, not its commercial function; similarly, using only economic loss indicators only reflects the commercial function of the system's role in business operations, not its social function. To integrate these two aspects, another approach is to use a comprehensive indicator, specifically converting outage indicators into economic losses. However, this method still has significant drawbacks. When performing the conversion, existing technologies often assign large coefficients (such as GDP per kilowatt-hour) to outage indicators to reflect their social function, resulting in a lower coefficient for direct economic losses compared to the actual situation, thus weakening the economic losses recorded by power companies. Therefore, existing technologies cannot achieve a unified optimization of the social and commercial objectives of stormwater disaster risk management in power distribution systems. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides a method, apparatus, equipment, and storage medium for disaster risk management of power distribution systems.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A method for disaster risk management of power distribution systems, the method comprising: Construct a set of typical urban stormwater disaster scenarios, and for each scenario in the set, determine its annual occurrence probability and the maximum water accumulation depth of each power distribution node under that scenario; Based on the maximum water accumulation depth of each power distribution node, determine the functional loss status of the components and the degree of direct economic loss of each node; Based on the component functional loss, the mathematical expectation of the annual cumulative number of users experiencing power outages due to disasters is determined. Minimizing the mathematical expectation of the annual cumulative number of users experiencing power outages is taken as the first objective, and minimizing the annualized risk cost is taken as the second objective. The risk cost includes the expected loss cost calculated based on direct economic losses and the annual probability of exceeding the limit, as well as the management cost incurred in implementing risk management measures. A dual-objective optimization model considering the first objective and the second objective is established; the decision variables of the dual-objective optimization model include the implementation decisions of risk control measures and risk financing measures; the risk control measures include risk avoidance measures and risk suppression measures, and the risk financing measures include risk transfer measures and risk retention measures; Solving the bi-objective optimization model yields the optimal Pareto front, which characterizes the trade-off between the power distribution system's supply capacity and risk costs. From this optimal Pareto front, a scheme is selected to guide the disaster prevention and mitigation management of the power distribution system.

[0007] Optionally, the construction of a set of typical urban stormwater disaster scenarios, for each scenario in the set, determining its annual occurrence probability and the maximum water accumulation depth at each power distribution node under that scenario, includes: Based on the preset urban rainstorm intensity formula, the annual exceedance probability curve of the average rainfall intensity of the rainstorm process in the target city is determined; The annual exceedance probability curve is discretized to obtain a set of typical disaster scenarios consisting of discrete points. Each scenario in the set corresponds to a rainfall intensity and its annual exceedance probability. For each scenario, the average rainfall intensity is extended into a rainfall process curve based on typical rainfall patterns; Based on the rainfall process curve, the maximum water depth at each power distribution node location is determined through hydrological and hydrodynamic model simulation in this scenario.

[0008] Optionally, determining the component functional loss status and direct economic loss degree of each distribution node based on the maximum water accumulation depth of each node includes: Based on whether the maximum water depth at the power distribution node exceeds the preset critical water level, determine whether the node needs to be shut down urgently in order to determine the loss of component function; Based on the flood vulnerability curve, the degree of direct economic loss at the distribution node is assessed according to the maximum water depth at the node.

[0009] Optionally, establishing a bi-objective optimization model considering both the first objective and the second objective includes: The risk avoidance measures are modeled as a logical constraint relationship between the decision variables for relocating and modifying substations and the availability status of nodes. The risk mitigation measures are modeled as a recovery sub-model for the post-disaster reconstruction of the power distribution system with the objective of minimizing the weighted number of power outage users. The constraints of the recovery sub-model include the safe operation constraints of the power distribution system and the radial topology operation constraints, and the recovery capability is determined by the backup power supply and remote control switch decision variables configured in advance. The risk transfer measures are modeled as asset insurance decision variables, premium calculation functions, and insurance payout functions that take into account deductibles; The risk retention measures are modeled as capital reserves and their opportunity cost functions based on direct economic losses in extreme disaster scenarios.

[0010] Optionally, solving the bi-objective optimization model includes: Solve the single-objective optimization problems of minimizing the first objective and minimizing the second objective respectively, and obtain the extreme values ​​of the two objectives; Select a set of values ​​within the extreme range of the second target. ε Threshold; For each ε The threshold is used to find an optimization objective that minimizes the first objective while incorporating the second objective as a constraint, requiring that it does not exceed the current threshold. ε A single-objective optimization problem for the threshold; All Combinations ε The solutions corresponding to the threshold form the optimal Pareto front and the corresponding Pareto solution set.

[0011] A power distribution system disaster risk management device, the device comprising: The acquisition module is used to construct a set of typical urban stormwater disaster scenarios. For each scenario in the set, the annual occurrence probability and the maximum water accumulation depth of each power distribution node under that scenario are determined. The determination module determines the functional loss status and direct economic loss of each node's components based on the maximum water accumulation depth of each distribution node. The preset module determines the expected number of users experiencing power outages due to disasters in a given year based on the functional loss of the components. It takes minimizing the expected number of users experiencing power outages in a given year as the first objective and minimizing the annualized risk cost as the second objective. The risk cost includes the expected loss cost calculated based on direct economic losses and the annual probability of exceeding the limit, as well as the management cost incurred in implementing risk management measures. A construction module is used to establish a dual-objective optimization model that considers the first objective and the second objective; the decision variables of the dual-objective optimization model include the implementation decisions of risk control measures and risk financing measures; the risk control measures include risk avoidance measures and risk suppression measures, and the risk financing measures include risk transfer measures and risk retention measures; The optimization module is used to solve the bi-objective optimization model to obtain the optimal Pareto front that characterizes the trade-off between the power distribution system's power supply capacity and risk costs. From the optimal Pareto front, a scheme is selected to guide the disaster prevention and mitigation management of the power distribution system.

[0012] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned method for disaster risk management of a power distribution system.

[0013] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the aforementioned method for disaster risk management of a power distribution system.

[0014] The disaster risk management method for power distribution systems provided by this invention has the following beneficial effects: This invention constructs a set of typical urban stormwater disaster scenarios and calculates the annual exceedance probability, enabling precise understanding of disaster occurrence patterns, assessment of the vulnerability of power distribution systems in various scenarios, and determination of relevant loss metrics, thus clearly quantifying the impact of disasters on the system. By minimizing the expected number of users experiencing annual power outages and the annualized risk cost as dual objectives, it considers not only power supply capacity but also direct economic losses and risk management costs, comprehensively taking into account both disaster impact and response costs. A dual-objective optimization model is established, incorporating various risk control and financing measures as decision variables. Response strategies are planned from multiple dimensions, and the optimal Pareto front is obtained by solving the model. This front intuitively presents the trade-off between power distribution system supply capacity and risk costs. Finally, the solution is selected from the frontier, effectively guiding the disaster prevention and mitigation management of the power distribution system and achieving unified optimization of the social and commercial goals of power supply security. Attached Figure Description

[0015] To more clearly illustrate the embodiments and design schemes of the present invention, the accompanying drawings required for this embodiment will be briefly described below. The drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a flowchart illustrating a disaster risk management method for a power distribution system according to an exemplary embodiment of the present invention.

[0017] Figure 2 This is a schematic diagram of the optimal Pareto front for disaster risk management of a power distribution system, provided as an exemplary embodiment of the present invention.

[0018] Figure 3 This is a block diagram of a power distribution system disaster risk management device according to an exemplary embodiment of the present invention. Detailed Implementation

[0019] To enable those skilled in the art to better understand and implement the technical solutions of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and should not be construed as limiting the scope of protection of the present invention.

[0020] The technical solutions provided by the various embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0021] First, this invention provides a method for disaster risk management in power distribution systems, specifically as follows: Figure 1 As shown, it includes the following steps: S101. Construct a set of typical urban stormwater disaster scenarios. For each scenario in the set, determine its annual occurrence probability and the maximum water accumulation depth of each power distribution node in the scenario.

[0022] In this step, firstly, based on a pre-defined formula for urban rainstorm intensity, the annual exceedance probability curve of the average rainfall intensity during a rainstorm event in the target city is determined. The annual exceedance probability curve is then discretized to obtain a set of typical disaster scenarios composed of discrete points. Each scenario in the set corresponds to a rainfall intensity and its annual exceedance probability. For each scenario in the set of typical disaster scenarios, the average rainfall intensity is extended into a rainfall process line based on typical rainfall patterns. Based on the rainfall process line, the maximum water accumulation depth at each power distribution node location under the scenario is determined through hydrological and hydrodynamic model simulation.

[0023] In one embodiment, the annual exceedance probability curve of the average rainfall intensity of urban storms is derived based on the urban storm intensity formula. The urban storm intensity formula is a statistical formula reflecting the relationship between rainfall intensity, regression return period, and rainfall duration:

[0024] ; In the formula, This represents the average rainfall intensity during a rainfall event; Indicates the recurrence interval; The duration of a rainfall event is often selected in short-duration rainfall analysis. As a typical parameter; These are statistical parameters used in the formula for urban rainstorm intensity, and are verified by the municipal departments of each city.

[0025] The annual exceedance probability represents the probability of all possible events exceeding a certain scale occurring in a year, and it is equal to the reciprocal of the regression return period: ; In the formula, The exceedance probability function represents the maximum rainfall intensity in an urban rainstorm that occurs within a year. The probability, based on Function drawing The relationship curve is the annual exceedance probability curve of the average rainfall intensity of urban rainstorms.

[0026] The annual probability exceedance curve of rainfall intensity is discretized. A set of heavy rainfall intensity data is selected. The annual exceedance probability is obtained by using the exceedance probability function. This leads to the discretized transcendental probability curve. And record , used to represent a set of typical disaster scenarios.

[0027] For each point on the discretized transcendental probability curve The Chicago rain pattern, based on a unimodal rainfall model, extends the average rainfall intensity of a rainfall event into a rainfall hydrograph. The rainfall hydrograph can be represented as the instantaneous rainfall intensity at each moment within the rainfall duration:

[0028] ; ; In the formula, and Representing disaster scenarios Time before the end of the peak Post-peak time The instantaneous rainfall intensity; This represents the peak rainfall coefficient, which is obtained by statistically analyzing the locations of peak rainfall events throughout historical rainfall events.

[0029] Solving the two-dimensional shallow water equation yields the maximum water depth at each power distribution node under various typical disaster scenarios. The two-dimensional shallow water equation serves as the governing equation for urban stormwater inundation simulation, and its form is:

[0030] ; In the formula, Indicates water depth; and express direction and Flow velocity in the direction; It is the acceleration due to gravity; For the scene The instantaneous rainfall intensity is given through a rainfall process curve; Typical parameters for different land use types are used to determine the infiltration rate; The drainage rate is given by the design standards of the drainage network in the study area; The elevation is the surface elevation, provided by the digital elevation model of the study area. The coefficient is the Manning coefficient, using typical parameters for different land use types.

[0031] For each scenario in the set of typical disaster scenarios The finite volume method is used to solve the two-dimensional shallow water equation, obtaining the water depth at various locations within the study area at different times. By matching the latitude and longitude of the power distribution nodes, the maximum water depth at each power distribution node under various typical disaster scenarios is obtained. ,in Indicating typical disaster scenarios Downstream distribution node The maximum water depth at the location, This is the set of power distribution nodes.

[0032] S102. Based on the maximum water accumulation depth of each power distribution node, determine the functional loss status of the components and the degree of direct economic loss of each node.

[0033] In this step, it is determined whether the node needs to be shut down urgently based on whether the maximum water depth at the distribution node exceeds the preset critical water level, so as to determine the functional loss of the components; based on the flood vulnerability curve, the degree of direct economic loss of the node is assessed according to the maximum water depth at the distribution node.

[0034] In one embodiment, the first step is to determine the functional loss of the components: Faced with impending flooding in a substation, one measure implemented by the power company is a proactive emergency shutdown to prevent the electrical equipment from exploding upon contact with water, thus threatening personal safety. Therefore, when the water depth at the distribution node exceeds the critical water level of the equipment's flood protection design standard, the node is shut down urgently.

[0035] ; In the formula, Representing a scene Downstream distribution node The 0-1 parameter indicating whether an emergency shutdown is required; Indicates distribution node Critical water level height requiring emergency shutdown; This indicates an indicator function.

[0036] Secondly, the direct economic losses were determined: the FEMA-HAZUS flood vulnerability curve was used to assess the extent of direct economic losses to the substation due to flooding. ; In the formula, Representing a scene Downstream distribution node The extent of direct economic loss, i.e., the scenario Downstream distribution node The ratio of the repair cost to its replacement value; The critical water depth at which all equipment in the power distribution station is lost and there is no value in repairing it.

[0037] S103. Based on the functional loss of components, determine the expected number of users with annual power outages caused by disasters. Take minimizing the expected number of users with annual power outages as the first objective and minimizing the annualized risk cost as the second objective. Establish a dual-objective optimization model that considers the first and second objectives.

[0038] Among them, risk cost includes the expected loss cost calculated based on the degree of direct economic loss and the annual probability of exceeding the limit, as well as the management cost incurred in implementing risk management measures; the decision variables of the bi-objective optimization model include the implementation decisions of risk control measures and risk financing measures; risk control measures include risk avoidance measures and risk suppression measures, and risk financing measures include risk transfer measures and risk retention measures.

[0039] In this step, it is necessary to establish the constraint and mapping relationships between the variables in the optimization model. For example, risk avoidance measures are modeled as logical constraints between the substation relocation decision variables and the node availability status; risk mitigation measures are modeled as a sub-model for the post-disaster reconstruction and recovery of the power distribution system with the objective of minimizing the weighted number of outage users. The sub-model is constrained by the safe operation constraints of the power distribution system and the radial topology operation constraints, and its recovery capability is determined by the pre-configured backup power supply and remote control switch decision variables; risk transfer measures are modeled as asset insurance decision variables, premium calculation functions, and insurance payment functions considering deductibles; risk retention measures are modeled as capital reserves and their opportunity cost functions based on direct economic losses in extreme disaster scenarios.

[0040] In one embodiment, a mathematical model is established for four risk management measures of power distribution system under urban rainstorm disasters, based on the measurement of functional loss and direct economic loss of power distribution system components under typical disaster scenarios, taking into account risk avoidance and risk suppression measures in risk control, as well as risk transfer and risk retention measures in risk financing.

[0041] Risk avoidance refers to the conscious avoidance of a specific risk by a risk management unit. It refers to measures taken to reduce the frequency of a specific loss, which can reduce the probability of the risk occurring to zero.

[0042] Relocating flood-prone substations is a common risk mitigation measure used by power distribution systems to cope with urban stormwater disasters. It can effectively prevent substations from shutting down due to flooding. ; ; ; In the formula, Representing a scene Downstream distribution node Are 0-1 variables available? Indicates distribution node The 0-1 variable for whether or not to relocate. The above three formulas respectively represent: (1) If the power distribution node is relocated, it will not be shut down due to flooding; (2) If the water depth at the power distribution node does not reach the critical water level for emergency shutdown, it will not be shut down; (3) If the power distribution node is not relocated and the water depth is higher than the critical water level, the power distribution node will be shut down.

[0043] Risk mitigation refers to various measures or behaviors that reduce the expected cost of loss by minimizing the extent of the loss. It refers to the degree to which measures are taken to reduce losses after a risk event has occurred. Risk mitigation is a reactive measure; although many measures are designed in advance, their implementation and effectiveness only occur after the loss has taken place.

[0044] After a power distribution system failure, distributed backup power network construction and reconfiguration are the main ways to reduce the impact of the failure. The goal is to reduce the affected sections and the scope of the outage, thereby minimizing the weighted number of affected users. ; In the formula, Representing a scene Weighted number of users experiencing power outages in the sub-distribution system; Representing a scene Next node A 0-1 variable indicating whether the user is receiving power normally; Represents a node User importance level; Represents a node The number of users connected at that location.

[0045] Although reconfiguration and recovery are performed after a failure, distributed backup power supplies and remote control switches need to be configured before the failure to enable the power distribution system to have reconfiguration and recovery capabilities. ; ; ; In the formula, Indicates distribution node Should it be installed? The 0-1 variable of the backup power supply model; Indicates power distribution lines Whether to install a remote control switch at the starting end (0-1 variable); For the collection of power distribution lines; It is a collection of power distribution lines that have been equipped with remote control switches. The above three formulas respectively indicate that: (1) each power distribution node is limited to installing only one type of backup power supply; (2) lines that have been equipped with switches do not need to be re-installed; (3) lines that have not been equipped with remote control switches can only be in a connected state.

[0046] In addition, numerous safety constraints need to be met during reconstruction and recovery: ; ; ; ; ; ; In the formula, and Representing the scene respectively Downline The active and reactive power; and Representing a scene Next node The active and reactive power output of the power source; and Represents a node The active and reactive power of the load; Representing a scene Downline A 0-1 variable indicating whether the switch is closed; Representing a scene Next node The square of the voltage amplitude; and Indicates the line Resistance and reactance; Indicates the line Maximum capacity; and Represents a node The lower and upper limits of voltage amplitude; It is a sufficiently large positive number. The above 6 formulas are: (1) the active power balance equation of the node; (2) the reactive power balance equation of the node; (3) the line voltage drop equation; (4) and (5) are used to constrain the line capacity; (6) is used to constrain the node voltage amplitude.

[0047] Power distribution system reconfiguration and recovery rely on the actions of remote control switches to change the power distribution network topology, which needs to satisfy radial topology constraints: ; ; ; ; In the formula, and These are non-negative continuous variables used for modeling radial topology constraints in power distribution systems. It is a set of substation nodes.

[0048] Because the number of switches used for fault isolation within the power distribution system is limited, the impact of an emergency shutdown of a power distribution station will propagate within a certain area: ; ; ; ; ; In the formula, Representing a scene Next node A 0-1 variable indicating whether the faulty section needs to be isolated; and Represents a node The upper limit of active and reactive power output of the existing power source; and express The upper limit of active and reactive power output of the backup power supply of the model. The above 5 formulas respectively represent the following meanings: (1) If the distribution node is shut down in an emergency, it must be in the fault section that needs to be isolated; (2) If the line is in a closed state, the isolation state of the nodes at both ends is the same, so the distribution node that needs to be isolated can be deduced from the switch state of the distribution line; (3) and (4) indicate that the power supply in the fault section cannot be connected to the grid; (5) indicates that the node in the fault section cannot be restored.

[0049] Risk transfer refers to the transfer of potential losses or the financial consequences of loss compensation from one risk management unit to another. The primary financing method for risk transfer is insurance financing, whereby the risk management unit uses insurance contracts and other means to raise funds to compensate for losses. Unlike risk control measures, risk transfer measures cannot eliminate the potential losses caused by risk events; they can only help avoid the consequences and financial burdens of such events through risk financing, allowing other entities to bear the losses.

[0050] All risks property insurance for power grids is a type of insurance purchased by power companies to protect their power grid assets. It allows them to transfer the repair costs and losses of vulnerable assets to the insurance company. As the price receiver, the premium that the power company needs to pay for insuring vulnerable assets is:

[0051] ; In the formula, Indicates distribution node Whether or not insurance is purchased is a 0-1 variable; Indicates distribution node Replacement value of existing assets; This indicates the insurance premium rate for all-risk property insurance for power grids; This indicates the insurance premiums that the power system needs to pay.

[0052] All risks property insurance for power grids typically includes a deductible clause: if the loss is below a certain limit, the insurance company will not provide compensation; if the loss exceeds the limit, the insurer will only pay the excess. The actual compensation received by the insured in a single loss event is:

[0053] ; In the formula, This indicates the deductible specified in the insurance contract; Disaster scenario The amount of compensation below; Disaster scenario Actual losses of sub-insured power distribution assets: ; Through linearization, the actual compensation received by the insured in a single loss event is... It can be modeled as: ; ; In the formula, An auxiliary 0-1 variable indicating whether the actual loss of the insured assets meets the compensation requirements.

[0054] Risk retention is a method in which a risk-bearing entity assumes the losses caused by a risk event itself, and makes up for the losses through internal financing. Risk retention can be proactive, meaning that the risk management entity, after assessing the consequences of the loss, plans to assume part or all of the risk.

[0055] Risk retention not only requires bearing the economic losses caused by disasters but also the cost of reserving funds to cover those losses. Risk capital reserves are funds set aside to cope with extreme losses, typically assessed based on the maximum possible loss in a once-in-a-century scenario. The retained loss corresponding to the probability of exceeding the expected value in a given year. This portion of funds is not necessarily spent when a loss occurs, but it does require capital, thus incurring opportunity cost or capital cost:

[0056] ; In the formula, Cost of capital; The cost of capital representing risk retention; Representing a scene The following direct economic losses: ; In the formula, express The purchase cost of the backup power supply for this model; This indicates the cost of installing remote control switches on power distribution lines.

[0057] The objectives of stormwater disaster risk management for power distribution systems are determined. Based on the annual exceedance probability of typical disaster scenarios, the mathematical expectation of the annual cumulative number of power outage users and the mathematical expectation of the annual cumulative retained economic loss are obtained through the properties of the composite Poisson distribution. These are then added to the annualized risk management cost to obtain the annualized risk cost function.

[0058] Maximizing power supply capacity is the social goal of stormwater disaster risk management for power distribution systems. The power supply capacity of a power distribution system under urban stormwater disasters can be characterized by the mathematical expectation of the annual cumulative number of users experiencing power outages due to urban stormwater disasters:

[0059] ; In the formula, This represents the expected number of users experiencing power outages annually due to urban stormwater disasters.

[0060] Minimizing risk costs is the business objective of stormwater disaster risk management for power distribution systems. Annualized risk cost includes the annual cumulative expected loss cost and the annualized management risk cost.

[0061] ; In the formula, The lifespan of disaster prevention and mitigation projects. The discount rate for disaster prevention and mitigation projects. This represents all costs required to carry out special disaster prevention and mitigation projects: ; In the formula, Indicates distribution node The cost of relocation.

[0062] Finally, an optimization model for stormwater disaster risk management of the power distribution system is established: ; st(1) Risk avoidance measures; (2) Risk suppression measures; (3) Risk transfer measures; (4) Risk retention measures.

[0063] S104. Solve the bi-objective optimization model to obtain the optimal Pareto front that characterizes the trade-off between the power supply capacity and risk cost of the power distribution system. Select a scheme from the optimal Pareto front to guide the disaster prevention and mitigation management of the power distribution system.

[0064] based on ε The constraint method solves the optimization model of stormwater disaster risk management of the power distribution system, and obtains the optimal Pareto front for the power supply capacity and risk cost of the power distribution system. Each point on the front represents an optimal solution for stormwater disaster risk management of the power distribution system.

[0065] In this step, we solve the single-objective optimization problems of minimizing the first objective and minimizing the second objective respectively, and obtain the extreme values ​​of the two objectives; we then select a set of extreme values ​​within the range of the second objective. ε Threshold; for each ε The threshold is used to solve a problem that optimizes a first objective by minimizing the second objective, while also incorporating the second objective as a constraint, requiring that the threshold not exceed the current threshold. ε A single-objective optimization problem for thresholds; combining all ε The solutions corresponding to the threshold form the optimal Pareto front and the corresponding Pareto solution set.

[0066] For example, we first solve for the extrema of each objective separately. The solver then solves the following single-objective optimization problem:

[0067] ; st(1) Risk avoidance measures; (2) Risk suppression measures; (3) Risk transfer measures; (4) Risk retention measures.

[0068] Obtain the optimal solution Substitute to obtain That is, the objective function. The maximum value of . Secondly, the following single-objective optimization problem is solved using a solver:

[0069] ; st(1) Risk avoidance measures; (2) Risk suppression measures; (3) Risk transfer measures; (4) Risk retention measures.

[0070] Obtain the optimal solution and optimal value That is, the objective function. The minimum value of .

[0071] In the interval Select one group value: .

[0072] For each The value is used to solve the following single-objective optimization problem through a solver: ; st(1) (2) Risk avoidance measures; (3) Risk suppression measures; (4) Risk transfer measures; (5) Risk retention measures.

[0073] Obtain the optimal solution and optimal value Substitute to obtain .

[0074] Combining to obtain This refers to the Pareto frontier for stormwater disaster risk management in power distribution systems, and its corresponding... This is the Pareto solution set, where each... All of these represent optimal solutions for managing stormwater disaster risks in power distribution systems, allowing decision-makers to weigh the social objectives of such management. and business goals Then select a suitable optimal risk management plan. .

[0075] In one embodiment, an improved IEEE 33-node distribution system is used as the test system, mapped to a coastal city area in southern China as a test case. For the test case, the relevant parameter values ​​are as follows: In the urban rainstorm intensity formula, statistical parameters... , , , When selecting typical disaster scenarios, the duration of rainfall is considered. Number of scenes In the Chicago rain pattern, the peak rainfall coefficient is... In solving the two-dimensional shallow water equation, the infiltration rate The calculation uses the Horton model, and the displacement rate Surface elevation Using AW3D30 digital terrain model, Manning coefficient Based on different land use types (arable land 0.035, water area 0.022, building land 0.013), the critical water depth for functional loss of each node component in the vulnerability assessment is determined. The critical water depth at which all station equipment is lost. When calculating the weighted average number of users experiencing power outages, the number of users connected to each node is calculated based on the corresponding active load per household. The proportional conversion and importance levels are all set to... The replacement value of the distribution node is based on the typical cost of a distribution network project, PB-1 typical design. The relocation cost is calculated based on the replacement value, amounting to tens of thousands of yuan; backup diesel generator power supply is considered. , , , , Five models, purchase cost They are respectively , , , , Ten thousand yuan; cost of adding remote control switchgear 10,000 yuan; all-risk property insurance for power grids, low premium rate. Deductible 10,000 yuan; life cycle of disaster prevention and mitigation projects Annual discount rate Cost of capital .

[0076] The linearized mixed-integer linear programming model was modeled and solved using Gurobi 12.0.3 and Python 3.13.5, yielding the Pareto front for stormwater disaster risk management of the test power distribution system, as shown below. Figure 2As shown by the dotted lines, each circular marker represents an optimal solution for managing stormwater disaster risks in a power distribution system. Decision-makers can select the optimal disaster risk management solution based on budget constraints and a trade-off between the two objectives. The power distribution system disaster risk management method provided by this invention combines four types of measures: risk avoidance, risk mitigation, risk transfer, and risk retention. The solutions obtained are all on the optimal Pareto front, and the solutions on the optimal Pareto front are all derived from the solutions obtained by the proposed method. That is, no other solution can outperform the proposed method in both social and commercial objectives.

[0077] The disaster risk management method for power distribution systems provided by this invention is compared with conventional risk management methods that rely solely on independent risk management approaches: While risk avoidance alone can effectively prevent power distribution stations from being flooded, thus reducing the annual number of users experiencing power outages, it incurs high relocation and reconstruction costs, making it less economically viable. Figure 2 As indicated by the diamond markings; risk mitigation measures alone can reduce the number of users experiencing power outages to some extent, but configuring distributed backup power supplies and installing remote control switches can only prevent power outages in non-faulty sections and cannot solve the power outage problem in faulty sections. Therefore, it can only reduce the annual cumulative number of users experiencing power outages to a certain level, such as... Figure 2 As indicated by the triangle markers in the diagram; risk transfer alone can financially mitigate disaster risk by reducing expected retained losses and reserve capital costs, thereby lowering the annualized risk cost, but it cannot improve power outages for users in the distribution system, such as... Figure 2 As indicated by the hexagonal markings in the diagram; employing only risk retention measures is equivalent to not taking any additional countermeasures, and the annual cumulative number of power outage users and annualized risk costs remain unchanged, such as... Figure 2 The octagonal marking is shown in the figure.

[0078] The power distribution system disaster risk management method provided by this invention is compared with conventional technical means that only employ risk control: While technical means alone can reduce the annual cumulative number of power outages to a low level when the engineering construction budget is large, they cannot control the annualized risk cost when the risk management budget is small. Figure 2 As indicated by the square markers in the diagram; the proposed method can comprehensively utilize risk control measures (risk avoidance and risk mitigation measures) and risk financing measures (risk transfer and risk retention measures), complementing each other. When the risk management budget is tight, risk financing measures can effectively reduce risk costs, while when the risk management budget is ample, risk control measures can effectively enhance the power distribution system's supply capacity. Figure 2As indicated by the circular markers in the diagram. Furthermore, the power distribution system disaster risk management method provided by this invention takes minimizing the expected number of users experiencing annual power outages and the annualized risk cost as dual objectives, encompassing both expected loss costs and management costs. It comprehensively considers the impact of disasters and response costs, and obtains the optimal Pareto front through a combination of response strategies such as risk avoidance, risk mitigation, risk transfer, and risk retention. This visually presents the trade-off between the power distribution system's supply capacity and risk costs, achieving a unified optimization of the social and commercial objectives of power distribution system stormwater disaster risk management.

[0079] Therefore, the method provided by this invention, by constructing a set of typical urban stormwater disaster scenarios and calculating the annual exceedance probability, can accurately grasp the disaster occurrence patterns, assess the vulnerability of the power distribution system in each scenario, and determine relevant loss metrics, thus clearly quantifying the system's disaster impact. By minimizing the expected number of users experiencing annual power outages and the annualized risk cost as dual objectives, it not only considers power supply capacity but also covers direct economic losses and risk management costs, comprehensively considering the disaster impact and response costs. A dual-objective optimization model is established, incorporating various risk control and financing measures as decision variables. Response strategies are planned from multiple dimensions, and the optimal Pareto front is obtained by solving the model. This front intuitively presents the trade-off between the power distribution system's supply capacity and risk costs. Finally, the solution is selected from the frontier, effectively guiding the disaster prevention and mitigation management of the power distribution system and achieving unified optimization of the social and commercial goals of power supply security.

[0080] Secondly, the present invention also provides a power distribution system disaster risk management device, such as... Figure 3 As shown, it includes: The acquisition module 201 is used to construct a set of typical urban stormwater disaster scenarios. For each scenario in the set, the annual occurrence probability and the maximum water accumulation depth of each power distribution node in the scenario are determined.

[0081] Module 202 determines the functional loss status and direct economic loss of each node's components based on the maximum water accumulation depth at each power distribution node.

[0082] The preset module 203 determines the mathematical expectation of the annual cumulative number of users experiencing power outages due to disasters based on component functional losses. It takes minimizing the mathematical expectation of the annual cumulative number of users experiencing power outages as the first objective and minimizing the annualized risk cost as the second objective. The risk cost includes the expected loss cost calculated based on direct economic losses and the annual probability of exceeding the limit, as well as the management cost incurred in implementing risk management measures.

[0083] Module 204 is used to establish a dual-objective optimization model that considers the first objective and the second objective. The decision variables of the dual-objective optimization model include the implementation decisions of risk control measures and risk financing measures. Risk control measures include risk avoidance measures and risk suppression measures, and risk financing measures include risk transfer measures and risk retention measures.

[0084] The optimization module 205 is used to solve the bi-objective optimization model to obtain the optimal Pareto front that characterizes the trade-off between the power supply capacity and risk cost of the power distribution system. From the Pareto front, a scheme is selected to guide the disaster prevention and mitigation management of the power distribution system.

[0085] The present invention also provides a computer-readable storage medium storing a computer program that can be used to execute the above-described... Figure 1 The steps of the provided disaster risk management method for power distribution systems.

[0086] This invention also provides a computer device. At the hardware level, the computer device includes a processor, an internal bus, a network interface, memory, and non-volatile memory, and may also include other hardware required for various operations. The processor reads the corresponding computer program from the non-volatile memory into memory and then executes it to achieve the above-mentioned functions. Figure 1 The steps of the provided disaster risk management method for power distribution systems.

[0087] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0088] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0089] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0090] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0091] It should be noted that the specific embodiments described above enable those skilled in the art to more fully understand the present invention, but do not limit the present invention in any way. Therefore, although the present invention has been described in detail in this specification, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the present invention; and all technical solutions and improvements that do not depart from the spirit and scope of the present invention are covered within the protection scope of the patent of the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. A method for disaster risk management in a power distribution system, characterized in that, The method includes: Construct a set of typical urban stormwater disaster scenarios, and for each scenario in the set, determine its annual occurrence probability and the maximum water accumulation depth of each power distribution node under that scenario; Based on the maximum water accumulation depth of each power distribution node, determine the functional loss status of the components and the degree of direct economic loss of each node; Based on the component functional loss, the mathematical expectation of the annual cumulative number of users experiencing power outages due to disasters is determined. Minimizing the mathematical expectation of the annual cumulative number of users experiencing power outages is taken as the first objective, and minimizing the annualized risk cost is taken as the second objective. The risk cost includes the expected loss cost calculated based on direct economic losses and the annual probability of exceeding the limit, as well as the management cost incurred in implementing risk management measures. A dual-objective optimization model considering the first objective and the second objective is established; the decision variables of the dual-objective optimization model include the implementation decisions of risk control measures and risk financing measures; the risk control measures include risk avoidance measures and risk suppression measures, and the risk financing measures include risk transfer measures and risk retention measures; Solving the bi-objective optimization model yields the optimal Pareto front, which characterizes the trade-off between the power distribution system's supply capacity and risk costs. From this optimal Pareto front, a scheme is selected to guide the disaster prevention and mitigation management of the power distribution system.

2. The method according to claim 1, characterized in that, The construction of a set of typical urban stormwater disaster scenarios, for each scenario in the set, determines its annual occurrence probability and the maximum water accumulation depth at each power distribution node under that scenario, including: Based on the preset urban rainstorm intensity formula, the annual exceedance probability curve of the average rainfall intensity of the rainstorm process in the target city is determined; The annual exceedance probability curve is discretized to obtain a set of typical disaster scenarios consisting of discrete points. Each scenario in the set corresponds to a rainfall intensity and its annual exceedance probability. For each scenario, the average rainfall intensity is extended into a rainfall process curve based on typical rainfall patterns; Based on the rainfall process curve, the maximum water depth at each power distribution node location is determined through hydrological and hydrodynamic model simulation in this scenario.

3. The method according to claim 2, characterized in that, Based on the maximum water accumulation depth at each power distribution node, the functional loss status and direct economic loss of each node are determined, including: Based on whether the maximum water depth at the power distribution node exceeds the preset critical water level, determine whether the node needs to be shut down urgently in order to determine the loss of component function; Based on the flood vulnerability curve, the degree of direct economic loss at the distribution node is assessed according to the maximum water depth at the node.

4. The method according to claim 1, characterized in that, The establishment of the bi-objective optimization model considering both the first and second objectives includes: The risk avoidance measures are modeled as a logical constraint relationship between the decision variables for relocating and modifying substations and the availability status of nodes. The risk mitigation measures are modeled as a recovery sub-model for the post-disaster reconstruction of the power distribution system with the objective of minimizing the weighted number of power outage users. The constraints of the recovery sub-model include the safe operation constraints of the power distribution system and the radial topology operation constraints, and the recovery capability is determined by the backup power supply and remote control switch decision variables configured in advance. The risk transfer measures are modeled as asset insurance decision variables, premium calculation functions, and insurance payout functions that take into account deductibles; The risk retention measures are modeled as capital reserves and their opportunity cost functions based on direct economic losses in extreme disaster scenarios.

5. The method according to claim 1, characterized in that, Solving the bi-objective optimization model includes: Solve the single-objective optimization problems of minimizing the first objective and minimizing the second objective respectively, and obtain the extreme values ​​of the two objectives; Select a set of values ​​within the extreme range of the second target. ε Threshold; For each ε The threshold is used to find an optimization objective that minimizes the first objective while incorporating the second objective as a constraint, requiring that it does not exceed the current threshold. ε A single-objective optimization problem for the threshold; All Combinations ε The solutions corresponding to the threshold form the optimal Pareto front and the corresponding Pareto solution set.

6. A disaster risk management device for a power distribution system, characterized in that, The device includes: The acquisition module is used to construct a set of typical urban stormwater disaster scenarios. For each scenario in the set, the annual occurrence probability and the maximum water accumulation depth of each power distribution node under that scenario are determined. The determination module determines the functional loss status and direct economic loss of each node's components based on the maximum water accumulation depth of each distribution node. The preset module determines the expected number of users experiencing power outages due to disasters in a given year based on the functional loss of the components. It takes minimizing the expected number of users experiencing power outages in a given year as the first objective and minimizing the annualized risk cost as the second objective. The risk cost includes the expected loss cost calculated based on direct economic losses and the annual probability of exceeding the limit, as well as the management cost incurred in implementing risk management measures. A construction module is used to establish a dual-objective optimization model that considers the first objective and the second objective; the decision variables of the dual-objective optimization model include the implementation decisions of risk control measures and risk financing measures; the risk control measures include risk avoidance measures and risk suppression measures, and the risk financing measures include risk transfer measures and risk retention measures; The optimization module is used to solve the bi-objective optimization model to obtain the optimal Pareto front that characterizes the trade-off between the power distribution system's power supply capacity and risk costs. From the optimal Pareto front, a scheme is selected to guide the disaster prevention and mitigation management of the power distribution system.

7. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the method described in any one of claims 1 to 5.

8. A computer device, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method described in any one of claims 1 to 5.

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