Power distribution system resilience evaluation method and system for urban rainstorm waterlogging disaster

Abstract

The application discloses a kind of power distribution system to respond to urban rainstorm waterlogging disaster elasticity evaluation method and system, according to rainfall and rainfall process to construct rainstorm model, obtain time series rainfall intensity;Constitute runoff model and confluence model, according to the time series rainfall intensity determined surface water depth variation process obtained, obtain surface water depth simulation result;Based on surface water depth simulation result, model simulation outdoor equipment submergence and indoor equipment submergence process are constructed, and the disaster scene of power distribution system and damaged equipment set are obtained;Based on the disaster scene of power distribution system and damaged equipment set, road network model is constructed, and the mobile resource path problem under urban waterlogging is modeled as time-dependent vehicle routing problem;Based on time-dependent vehicle routing problem, mixed integer linear programming model is constructed as power distribution system response model, and the elasticity of power distribution system is quantified using elasticity measurement index, based on the obtained elasticity index R t The elasticity of urban rainstorm waterlogging disaster is evaluated.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of disaster prevention and mitigation of power distribution systems, and particularly relates to a method and system for evaluating the resilience of a power distribution system in response to urban rainstorm waterlogging disasters. BACKGROUND

[0002] Frequent urban rainstorm waterlogging disasters pose a huge risk to the safe and stable operation of power distribution systems. The extensive spatial distribution and low standard design of power distribution system facilities increase the vulnerability of power distribution systems, making them prone to failure. The resilience of a power distribution system reflects its ability to resist, absorb, adapt, and recover in a timely and efficient manner during disasters. Quantifying resilience is the basis for developing effective disaster prevention and mitigation strategies, and existing technologies mainly focus on evaluating the potential power outage scale under flood disasters.

[0003] To evaluate the impact of rain and flood disasters on power systems, existing technologies combine hydrological models with power system models. For power distribution systems, power distribution nodes such as substations, switch cabinets, ring network cabinets, and distribution transformers are considered as vulnerable components, and the evaluation indicators mainly focus on equipment failure probability, number of outages, load loss, and economic loss. Existing research mainly focuses on estimating the potential power outage scale under flood threats. However, the severity of power outages not only includes the scale, but also the speed of recovery. It is necessary to consider the recovery aspect in the evaluation. Due to insufficient consideration of post-disaster recovery processes, existing research has failed to fully assess the recovery capacity of power distribution systems under flood disaster conditions.

[0004] In terms of post-disaster recovery modeling of power distribution systems, current research mainly combines power restoration problems with vehicle routing problems, and several mature modeling paradigms have been developed to apply various types of mobile emergency resources (MER) to post-disaster recovery of power distribution systems, including edge-based models, vertex-based models, traffic flow distribution models, and space-time network models. However, rainstorm waterlogging disasters have two distinct features that distinguish them from other disasters: the outage time of power distribution equipment is the sum of the time the element is located in the flooded area and the repair time, and element repair can only begin after the rain subsides; and the routing and scheduling of MERs largely depends on the accessibility of the site. Since road flooding is one of the most typical consequences of urban waterlogging, rain and flood will hinder the arrival of repair forces at the location of power distribution facilities, further delaying equipment maintenance and power restoration. In addition, post-disaster travel time varies with road water depth, and the optimal path between a start point and an end point pair may also change depending on the road network waterlogging situation. Therefore, existing models cannot be directly applied to the resilience evaluation of power distribution systems under urban rainstorm waterlogging disasters. SUMMARY

[0005] The technical problems to be solved by the present application are to provide a power distribution system resilience evaluation method and system for coping with urban rainstorm waterlogging disasters, to solve the technical problems of the prior art that the post-disaster recovery process is not considered, and the existing model cannot be directly applied to the resilience evaluation of the power distribution system in the urban rainstorm waterlogging disaster scenario.

[0006] The present application adopts the following technical solutions:

[0007] The power distribution system resilience evaluation method for coping with urban rainstorm waterlogging disasters comprises the following steps:

[0008] A rainstorm model is constructed according to the rainfall and the rainfall process, and the time-series rainfall intensity is obtained;

[0009] A runoff model and a confluence model are constructed, the surface water depth variation process is determined according to the obtained time-series rainfall intensity, and the surface water depth simulation result is obtained;

[0010] Based on the surface water depth simulation result, a model is constructed to simulate the outdoor equipment submergence and the indoor equipment submergence process, and the power distribution system disaster scenario and the damaged equipment set are obtained;

[0011] A road network model is constructed based on the power distribution system disaster scenario and the damaged equipment set, and the mobile resource path problem under urban waterlogging is modeled as a time-dependent vehicle routing problem;

[0012] A mixed integer linear programming model is constructed based on the time-dependent vehicle routing problem as a power distribution system response model, the power distribution system resilience is quantified by using the resilience measurement index, and the obtained resilience index R t The resilience evaluation of the urban rainstorm waterlogging disaster is realized.

[0013] Preferably, the construction of the rainstorm model according to the rainfall and the rainfall process is specifically:

[0014] The intensity-duration-frequency curve is constructed to obtain the average rainfall intensity; the Chicago rain type is used for rainfall process design, the peak value time of the rainfall process is represented by using the rain peak coefficient, the rainfall duration is divided into two time periods before and after the peak, and the average rainfall intensity is used to obtain the instantaneous rainfall intensity before and after the peak.

[0015] Preferably, the instantaneous intensities before and after the peak of the rainstorm process q1 and q2 are:

[0016]

[0017] Wherein, t1 and t2 respectively represent the corresponding time in the peak period before and after the rainstorm duration; r represents the peak position coefficient of the design rainstorm process derived from historical rainstorm data; A, C, b, n r are coefficients related to the city where the research area is located; and P represents the return period.

[0018] Preferably, the runoff yield model is constructed as follows:

[0019] f(t) = f0+ (f0-fs)e-βt c c -βt

[0020] wherein f(t) is the infiltration rate at time t; f0is the initial infiltration rate; fsis the stable infiltration rate of soil; β is the attenuation coefficient; c

[0021] The confluence model is as follows:

[0022]

[0023] wherein U represents the vector of conservative quantities; u x and u y respectively represent the average flow velocity of water depth in x direction and y direction; F x and F y respectively represent the flux in x direction and y direction; S represents the source term.

[0024] Preferably, the process of simulating outdoor equipment submergence and indoor equipment submergence is as follows:

[0025] The outdoor submergence model is as follows:

[0026] If the rainwater depth at the outdoor node i exceeds the critical flood control threshold value of the equipment the node is shut down urgently, and the nearby switch is disconnected to isolate the fault; let represent the set of power distribution nodes submerged outdoors, h i (t) is the water level at the outdoor node i at time t; represent the set of power distribution nodes; represent the set of indoor nodes. For each submerged outdoor node i, the time slot when the rainwater depth at the location thereof exceeds is recorded as The time slot when the rainwater is drained from the outdoor node i is recorded as

[0027] The indoor submergence model is as follows:

[0028] When the power distribution facility is located indoors, the indoor submergence depth is calculated as a function of the outdoor water depth; let represent the set of power distribution nodes with indoor waterlogging, wherein h in,i (t) is the indoor waterlogging depth of the node i at time t in the building, and the time slot when indoor waterlogging occurs is also recorded as T i flood ​​​The set of submerged distribution nodes is denoted as A binary variable η is introduced i,t denotes whether node i is normal at time t, for nodes that do not have a flood rise above the critical water level, η i,t = 1; the state of a flooded node during a storm process is as follows:

[0029]

[0030] wherein, denotes an indicator function.

[0031] Preferably, when the outdoor water depth exceeds the indoor water depth, the rainwater inflow into the building is calculated as follows:

[0032]

[0033] wherein Q is the flow rate of rainwater inflow into the building; C d is a flow coefficient set to 1 in the present application; L is the width of the building door through which water is expected to enter; h and h in respectively denote the height of the outdoor and indoor water surface;

[0034] The indoor water depth is updated as follows:

[0035] h in (t+1) = h in (t) + Q(t)Δt / S in

[0036] wherein S in is the building area of the building.

[0037] Preferably, the mobile resource routing problem under urban waterlogging is modeled as a time-dependent vehicle routing problem, specifically: a flooded road traffic model is established according to the storm water depth and the vehicle driving speed;

[0038] A discrete arrival time function is defined to meet the needs of the space-time network modeling framework;

[0039] A space-time coordinate system is established with time index as the horizontal coordinate and road network vertex as the vertical coordinate, reflecting the spatial changes of mobile resources in the road network at different times after the storm ends; based on the discrete arrival time function, the concept of space-time arc in the space-time coordinate system is defined, and the constraint conditions related to post-disaster vehicle routing are expressed under the concept of space-time arc.

[0040] Preferably, the relationship between the storm water depth and the vehicle driving speed is as follows:

[0041]

[0042] wherein, is the vehicle speed of road segment (u, v) at time t. is the normal speed of the road segment (u, v); h uv (t) is the maximum water depth of the road segment (u, v) at time t;

[0043] For define a discrete arrival time function as a function and satisfy: a is non-decreasing; a(t) ≥ t (t = T r , T min + 1, …, T max );

[0044] Given a road network and a set of time slots define a space-time arc in the space-time network as an arc from vertex (u, t) to vertex (v, τ), and satisfy: (u, v) ∈ ε or u = v; a uv (t) = τ; denote this space-time arc as (uv, t)

[0045] The constraint conditions are as follows:

[0046]

[0047]

[0048] where x m,uv,t is whether the mobile resource m is on the space-time arc (uv, t), x m,uv,τ is whether the mobile resource m is on the space-time arc (uv, τ), is the set of space-time arcs in the space-time network, t / τ is the time slot index, is the set of time slot indices after the rainstorm, is the time slot corresponding to the end of the rainstorm, is the maximum simulation time of the model, is the set of mobile emergency resources, is the set of road network nodes, is the warehouse point of the mobile resource m, is whether the mobile resource m is on the space-time arc .

[0049] Preferably, a mixed integer linear programming model is constructed as a power distribution system response model, the power distribution system elasticity is quantified by using an elasticity measurement index, and the elasticity evaluation of urban rainstorm waterlogging disasters is realized. Specifically:

[0050] The response model of the power distribution system under waterlogging is modeled as a collaborative optimization model as a whole, the proportion of the number of users with power outage lasting more than 12 hours in the total number of interrupted users is defined as the IEEE resilience index, including the user interruption automatically recovered or avoided through intelligent switch operation and microgrid technology, based on the solution result of the collaborative optimization model, the number of persistent user interruptions and the number of avoided user interruptions are counted, and the parameterized resilience index R is determined t As follows:

[0051] The resilience index R t As follows:

[0052]

[0053] Wherein, the parameter t represents the power outage duration of interest; is an indicator function for judging whether the power outage duration of the node exceeds the time t;

[0054] The collaborative optimization model is specifically as follows:

[0055]

[0056] Wherein, represents a time slot index set, represents a power distribution system node set, δ i,t represents whether the load at the node i at the time t is restored, C i represents the number of users connected to the node i, Δt represents a fixed time interval for each time slot, ε represents a relatively small positive number, represents a mobile emergency resource set, represents a space-time arc set in the space-time network, a uv (t) represents the arrival time of the route section (u, v) at the time t, x m,uv,t represents whether the mobile resource m is on the space-time arc (uv, t).

[0057] In the second aspect, the embodiment of the present application provides a power distribution system resilience evaluation system for urban rainstorm waterlogging disasters, comprising:

[0058] A rainstorm module constructs a rainstorm model according to rainfall and rainfall process to obtain time-series rainfall intensity;

[0059] A surface runoff module constructs a runoff model and a confluence model, determines a surface water depth change process according to the obtained time-series rainfall intensity, and obtains a surface water depth simulation result; an equipment flooding module constructs a model to simulate outdoor equipment flooding and indoor equipment flooding process based on the surface water depth simulation result, and obtains a power distribution system disaster scenario and a damaged equipment set;

[0060] The road flooding module constructs a road network model based on a power distribution system disaster scenario and a set of damaged equipment, and models a mobile resource path problem under urban waterlogging as a time-dependent vehicle routing problem; the system response module constructs a mixed integer linear programming model as a power distribution system response model based on the time-dependent vehicle routing problem, quantifies the flexibility of the power distribution system by using a flexibility measure index, and quantifies the flexibility of the power distribution system based on the obtained flexibility index R t The flexibility of urban rainstorm waterlogging disasters is evaluated.

[0061] In a third aspect, a computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the steps of the power distribution system flexibility evaluation method for coping with urban rainstorm waterlogging disasters when executing the computer program.

[0062] In a fourth aspect, an embodiment of the present application provides a computer readable storage medium including a computer program, and the computer program implements the steps of the power distribution system flexibility evaluation method for coping with urban rainstorm waterlogging disasters when executed by a processor.

[0063] In a fifth aspect, a chip includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the steps of the power distribution system flexibility evaluation method for coping with urban rainstorm waterlogging disasters when executing the computer program.

[0064] In a sixth aspect, an embodiment of the present application provides an electronic device including a computer program, and the computer program implements the steps of the power distribution system flexibility evaluation method for coping with urban rainstorm waterlogging disasters when executed by the electronic device.

[0065] Compared with the prior art, the present application has at least the following beneficial effects:

[0066] A power distribution system flexibility evaluation method for coping with urban rainstorm waterlogging disasters, according to four elements of disaster risk analysis, a multi-disciplinary evaluation framework for urban power distribution system coping with rainstorm waterlogging disasters based on disaster scenario simulation is proposed, five modules are used to capture the time evolution of flood disasters, and the response behavior of the power distribution system is combined to evaluate the flexibility of the system more fully and accurately.

[0067] Furthermore, heavy rainfall is a major cause of urban flooding, and constructing a heavy rainfall model is essential for quantitatively studying the impact of heavy rainfall-induced flooding on power distribution systems. Designing a heavy rainfall model involves constructing a heavy rainfall profile based on local historical heavy rainfall data. The heavy rainfall design process of this invention mainly includes two steps: rainfall intensity design and precipitation process design. Rainfall intensity is typically determined using urban heavy rainfall intensity formulas; considering that unimodal rainfall events are more likely to cause severe flooding, the Chicago rainfall pattern is adopted for rainfall process design. By constructing a heavy rainfall model, urban flooding under different rainfall intensities can be simulated, thereby assessing the potential impact of heavy rainfall-induced flooding on power distribution systems.

[0068] Furthermore, when the rate of rainwater runoff collection exceeds the rate of stormwater runoff loss, surface runoff will occur on urban surfaces. The surface runoff module consists of two parts: a runoff generation model and a runoff collection model. The runoff generation model is mainly used to calculate the amount of surface runoff generated during rainfall. Infiltration is the most critical factor in surface runoff generation. The Horton model is used to estimate the infiltration amount, treating the infiltration process as a process with a continuously decreasing rate, which can accurately reflect the dynamic changes in soil infiltration capacity. The runoff collection model uses two-dimensional shallow water equations to simulate how rainwater runoff moves on the surface after it is generated and eventually enters the drainage network through storm drains. It fully considers the influence of topography and boundary conditions on water flow, improving the accuracy and reliability of the simulation results.

[0069] Furthermore, considering that the equipment associated with the power distribution node may be located outdoors or indoors, models are established separately to simulate the flooding process of outdoor equipment and indoor equipment, and to predict the flooding risk that outdoor and indoor power distribution equipment may suffer.

[0070] Furthermore, in the context of flooding, the travel time of mobile resources between different locations is affected by road flooding conditions. Typically, after a rainstorm, travel time decreases monotonically with departure time. Therefore, the mobile resource routing problem under urban flooding can be modeled as a time-dependent vehicle routing problem. By establishing a spatiotemporal network model based on arrival time function (TSN-ATF), we can model the mobile resource routing under urban flooding conditions to characterize the time-dependent characteristics of mobile resource travel after a rainstorm and dynamically determine the optimal travel route based on the time-varying rainfall depth on the road network.

[0071] Furthermore, considering various fault handling measures such as network reconstruction, flood drainage, equipment repair, and emergency power access, the power distribution system response model is expressed as a mixed integer linear programming model. Under the consideration of multiple factors, the optimal solution is quickly found to minimize the number of households affected by power outages and the travel time of mobile emergency resources. Based on the IEEE resilience index, a parameterized IEEE resilience index is designed to more accurately quantify the recovery rate of the power distribution system in the first 12 hours.

[0072] It can be understood that the beneficial effects of the second aspect described above can be referred to the relevant description in the first aspect described above, which will not be repeated here.

[0073] In summary, the application proposes an elastic evaluation framework based on disaster scenario simulation, which focuses on the response behavior of the power distribution system, including disaster resistance and post-disaster recovery, and is more comprehensive and accurate in evaluating the elasticity of the power distribution system under the flood disaster; considering the characteristics of urban rainstorm flooding disaster, the model considers the influence of equipment flooding time and road flooding on the response and elasticity index of the power distribution system, and supplements the application of post-disaster recovery modeling of the power distribution system in the urban rainstorm flooding scenario; the parameterized IEEE elasticity index is used to more accurately quantify the recovery efficiency of the power distribution system within the first 12 hours.

[0074] The technical solutions of the application will be further described in detail below with the help of the drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0075] Figure 1 Equipment flooding and user power outage of the power distribution system under the 50-year design rainstorm;

[0076] Figure 2 Research on the flooding of the regional road network under the 50-year design rainstorm;

[0077] Figure 3 Gantt chart for post-disaster mobile emergency resource scheduling and system elasticity curve;

[0078] Figure 4 The schematic diagram of the computer device provided by an embodiment of the application;

[0079] Figure 5 The block diagram of a chip provided by the application according to an embodiment;

[0080] Figure 6 Flowchart of the application. DETAILED DESCRIPTION

[0081] The technical solutions in the embodiments of the application will be described clearly and completely below with the help of the drawings in the embodiments of the application. Obviously, the described embodiments are part of the embodiments of the application, rather than all the embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the application.

[0082] In the description of the application, it should be understood that the terms "include" and "contain" indicate the presence of described features, whole, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, whole, steps, operations, elements, components and / or sets thereof.

[0083] It should also be understood that the terms used in the specification of the application are only for the purpose of describing specific embodiments and are not intended to limit the application. As used in the specification and the appended claims of the application, the singular forms "a", "an" and "the" are intended to include the plural forms, unless the context clearly indicates otherwise.

[0084] It should be further understood that the term "and / or" used in the specification and the appended claims of the application means one or more of the associated listed items in any combination and all possible combinations, and includes these combinations, for example, A and / or B can mean A alone, A and B together, and B alone. In addition, the character " / " in the present application generally represents an "or" relationship between the front and rear associated objects.

[0085] It should be understood that although the terms first, second, third, etc. may be used in the embodiments of the application to describe the preset ranges, etc., these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from each other. For example, the first preset range can also be referred to as the second preset range, and similarly, the second preset range can also be referred to as the first preset range, without departing from the scope of the embodiments of the application.

[0086] Depending on the context, the word "if" as used herein can be interpreted to mean "when" or "while" or "in response to determining" or "in response to detecting". Similarly, depending on the context, the phrase "if determined" or "if detecting (a stated condition or event)" can be interpreted to mean "when determined" or "in response to determining" or "when detecting (a stated condition or event)" or "in response to detecting (a stated condition or event)".

[0087] Various structural diagrams according to the disclosed embodiments of the application are shown in the drawings. These figures are not drawn to scale, in which certain details are exaggerated for the purpose of clarity and certain details can be omitted. The shapes of various regions, layers and their relative size and positional relationship shown in the figures are only exemplary, and in actuality, there can be deviations due to manufacturing tolerances or technical limitations, and a person skilled in the art can additionally design regions / layers with different shapes, sizes, relative positions according to actual needs.

[0088] The application provides a power distribution system resilience evaluation method for urban rainstorm waterlogging disasters, focuses on the response behavior of the power distribution system, including disaster resistance and post-disaster recovery, and is more sufficient and accurate in evaluating the resilience of the power distribution system under the flood disaster; considering the characteristics of urban rainstorm waterlogging disasters, the model considers the influence of equipment flooding time and road flooding on the response and resilience index of the power distribution system, supplements the application of post-disaster recovery modeling of the power distribution system in the urban rainstorm waterlogging scenario; the parameterized IEEE resilience index is adopted, which more accurately quantifies the recovery efficiency of the power distribution system within the first 12 hours.

[0089] Please refer to Figure 6 The application provides a power distribution system resilience evaluation method for urban rainstorm waterlogging disasters, and specifically comprises the following steps:

[0090] S1, constructing a rainstorm model according to rainfall and rainfall process;

[0091] Designing a rainstorm model is a model for constructing a rainstorm process line based on local historical rainstorm data, which is widely used in flood control engineering.

[0092] S101, rainfall design: the rainfall intensity is usually determined by using the urban rainstorm intensity formula, also known as the intensity-duration-frequency (IDF) curve, which describes the relationship between rainfall intensity, rainfall duration and return period:

[0093]

[0094] Where q is the average rainfall intensity (mm / min); t r represents the rainfall duration (min); P represents the return period (yr); A, C, b, n r are coefficients related to the city where the research area is located.

[0095] S102, rainfall process design: the rainfall process design is carried out on the basis of the intensity-duration-frequency (IDF) curve, considering that unimodal rainfall process usually leads to serious flood disasters and has adverse effects on urban infrastructure, therefore, the Chicago rain type is used for rainfall process design. This model uses the rain peak coefficient r to represent the peak time of the rainfall process, so as to divide the rainfall duration into two periods before and after the peak.

[0096] On the basis of formula (1), the instantaneous rainfall intensities before and after the peak can be derived as:

[0097]

[0098]

[0099] wherein q1 and q2 are the pre-peak and post-peak instantaneous intensities (mm / min) of the design storm process, respectively; t1 and t2 are the corresponding times (min) in the pre-peak and post-peak periods of the storm duration, respectively; and r e (0, 1) is the peak position coefficient of the design storm process derived from historical storm data.

[0100] S2, constructing a runoff generation model and a confluence model;

[0101] Designing a surface runoff module: the runoff generation model and the confluence model together constitute a surface runoff module. When the rainwater accumulation speed exceeds the rainwater loss speed, the urban ground will generate surface runoff.

[0102] S201, design of the runoff generation model: factors affecting rainwater loss include evaporation, depression storage, interception, and infiltration, etc. It is worth noting that in the simulation of urban waterlogging caused by rainstorms, infiltration is the most critical factor of surface runoff generation, and only the ground infiltration factor is considered here. The Horton model is used to estimate the infiltration amount, which considers that the infiltration process is a process of continuously decreasing rate, and the decreasing rate is proportional to the duration of rainfall:

[0103] f (t) = f c 0 + (f c 0 - f -βt ) e c - t / β (4)

[0104] wherein f (t) is the infiltration rate at time t (mm / min); f0 is the initial infiltration rate (mm / min); f -1 is the stable infiltration rate of soil (mm / min); and β is the attenuation coefficient (min c ), which depends on the soil properties.

[0105] The above parameters f0, f x , and β are Horton infiltration parameters, which can be determined from the land cover type data of the study area.

[0106] S202, design of the confluence model: after rainwater forms on the ground, it flows from high altitude to low altitude and is finally discharged through the drainage outlet. The control equation for the simulation of rainstorm flooding is the two-dimensional shallow water equation (2D SWE);

[0107]

[0108] wherein U = [h u y h u T h] x represents the vector of conserved quantities, which is composed of the water depth h, the x-direction unit width flow u y h, and the y-direction unit width flow u x . yu and v represent the average flow velocity in the x and y directions, respectively.

[0109] Fluxes F in the x and y directions x and F y are given by

[0110]

[0111] where g is the acceleration of gravity.

[0112] The source term on the right side of equation (5) includes three parts, i.e., the net rainfall rate, the slope gravity, and the surface friction, which are denoted as

[0113]

[0114] where q, f, and w are the precipitation rate, the infiltration rate, and the drainage rate, respectively; z is the ground elevation, which is used to model the slope source term; and n is the Manning resistance coefficient, which is used to model the surface friction term. b

[0115] The two-dimensional SWE can be solved by numerical methods through the discretization of time and space. At each time interval, the following four steps are calculated for each cell:

[0116] 1) Precipitation calculation;

[0117] 2) Infiltration calculation;

[0118] 3) Drainage calculation;

[0119] 4) Confluence calculation.

[0120] The first three steps are used to calculate the net rainfall rate, in which the precipitation rate is determined by equations (2) and (3), and the infiltration rate is determined by equation (4). The drainage calculation uses the equivalent infiltration principle to estimate the drainage rate of the urban underground pipe network. Specifically, the drainage rate w is generally determined according to the actual design standard.

[0121] It should be noted that when calculating the precipitation, infiltration, and drainage terms at the beginning of each time interval dt, the net increase in water depth of each grid is represented by max{(q-f-w)dt,-h} to maintain mass conservation and ensure that the absolute water level is not lower than the ground elevation.

[0122] For the confluence calculation, the finite volume method is used to solve the fluid mechanics equations. The piecewise linear method (PLM) with a MinMod slope limiter is used for reconstruction, achieving second-order spatial accuracy. The upwind central scheme is used as the approximate Riemann solver for the numerical fluxes at the grid interfaces. The variable time step explicit forward Euler method is used for time updating, and the time interval dt is adaptively determined by the Courant-Friedrichs-Lewy (CFL) criterion to ensure numerical stability.​

[0123] S3, Constructing models to simulate the process of outdoor equipment submergence and indoor equipment submergence;

[0124] Designing equipment submergence module: The urban power distribution system is composed of underground cables, substations, switch cabinets, distribution transformers, etc. Based on the disaster data collected from literature and field, the vulnerable elements of urban power distribution system under waterlogging are mainly the distribution nodes, including various types of substation buildings, cabinets, transformers, etc. Therefore, the distribution nodes are identified as vulnerable elements.

[0125] From this step, the following model uses a fixed time step, and the duration of a time slot is Δt. Let t = 0 represent the time slot when the rainstorm starts, and t = T r represent the time slot when the rainstorm ends. Let represent the set of time slot indexes during the rainstorm. Considering that the equipment related to the distribution node may be located outdoors or indoors, models are established respectively to simulate the process of outdoor equipment submergence and indoor equipment submergence.

[0126] S301, Outdoor submergence model: One of the most effective strategies implemented by power companies in the face of an impending flood is to pre-emptively de-energize vulnerable nodes within the flood area. This strategy, while resulting in partial power interruption, ultimately shortens the recovery time by avoiding the most severe damage. Therefore, if the rainwater depth at outdoor node i exceeds the critical flood protection threshold of the equipment , the node will be shut down urgently, and the nearby switch will be disconnected to isolate the fault.

[0127] Let represent the set of outdoor submerged distribution nodes, where h i (t) is the water level at outdoor node i at time t; represent the set of distribution nodes; represent the set of indoor nodes. For each submerged outdoor node i, the time slot when the rainwater depth at its location exceeds is recorded as In addition, through the simulation of the drainage of the urban pipe network, the time slot when the rainwater is drained from outdoor node i is recorded as

[0128] S302, Indoor submergence model: When the distribution facilities are located indoors, the indoor submergence depth is calculated as a function of the outdoor water depth;

[0129] When the outdoor water depth exceeds the indoor water depth, the calculation formula for the rainwater inflow into the building is:

[0130]

[0131] where Q is the flow rate of rainwater into the building (m 3 / s); C d is the flow coefficient set to 1 in the present application; L is the width of the building gate expected to be flooded, set to 0.75 m; h and h in respectively represent the height of the outdoor and indoor water surface (m).

[0132] The indoor water depth can be updated by the following formula:

[0133] h in (t+1) = h in (t) + Q(t)At / S in (9)

[0134] where S in is the building area (m 2 ) of the building, which can be calculated according to the building boundary polygon.

[0135] Similarly, let represent the set of power distribution nodes of the indoor waterlogging, where h in,i (t) is the indoor water depth of the building at time t where node i is located, and the corresponding time slot when the indoor waterlogging occurs is also recorded as

[0136] Here, the set of submerged power distribution nodes can be recorded as A binary variable η i,t is introduced to represent whether node i is normal at time t, i.e., not submerged. For nodes that do not rise above the critical water level, η i,t = 1.

[0137] For the flooded nodes, their state during the rainstorm process can be determined by the following formula:

[0138]

[0139] where, indicates the indicator function.

[0140] S4, modeling the mobile resource path problem under urban waterlogging as a time-dependent vehicle routing problem;

[0141] Design a road flooding module: the road network is represented as a directed graph where represents the set of road network nodes containing the location of the power distribution node (i.e., ), and ε represents the set of road arcs between different adjacent nodes in the road network.

[0142] Under the background of flood disaster, the travel time of MER between different locations is affected by the road flooding condition; generally, after the rainstorm ends, the travel time monotonically decreases with the departure time. This means that the mobile resource routing problem under urban flooding can be modeled as a time-dependent vehicle routing problem.

[0143] Suppose that the MER is on standby in the warehouse during the rainstorm to ensure the personal safety of the rescue personnel. After the rainstorm ends, the MER departs to perform the task; suppose denotes the set of time slot indicators after the rainstorm, where T r denotes the time slot when the rainstorm ends, T max denotes the maximum simulation time.

[0144] S401, establish a flooded road traffic model;

[0145] According to existing research, the relationship between storm water depth and vehicle travel speed is represented as:

[0146]

[0147] wherein, is the vehicle speed (km / h) of the road segment (u, v) at time t; is the normal vehicle speed (km / h) of the road segment (u, v); h uv (t) is the maximum accumulated water depth (m) of the road segment (u, v) at time t. When road flooding occurs, especially when the water depth exceeds 0.3 m, the likelihood of vehicle stalling greatly increases, and the road is considered impassable.

[0148] S402, define a discrete arrival time function: in order to adapt to the modeling framework of the space-time network, the present application gives the definition of a discrete arrival time function (ATF).

[0149] Definition 1 For a discrete arrival time function is defined as a function and satisfies:

[0150] 1. a is non-decreasing;

[0151] 2. a(t) ≥ t (t = T r , T min + 1, …, T max ).

[0152] The arrival time function a describes the arrival time a(t) depending on the departure time t, a(t)-t is the required travel time. For each road segment (u, v) and departure time is defined as follows:

[0153]

[0154] where, and the ratio of is the normal travel time of link (u, v), which can be obtained by map application; Δt is the length of each time slot; · is the ceiling function.

[0155] This function can make the MER wait for the road to recede before departure, thus satisfying the first-in first-out property. In addition, for each road network node and time define a vv (t) to represent staying at site v for one time slot.

[0156] is defined as follows:

[0157] a vv (t): = t + 1 (13)

[0158] S403, construct a time-dependent space-time network: establish a space-time coordinate system with time index as the horizontal coordinate and road network vertex as the vertical coordinate. The point set in the space-time coordinate system is represented as a Cartesian product Considering the time dependence of the MER routing, the concept of arrival time function is combined to give the definition of space-time arc in the space-time coordinate system.

[0159] Definition 2 Given a road network and a set of time slots The space-time arc in the space-time network is defined as an arc from vertex to vertex and satisfies:

[0160] 1. (u, v) ∈ ε or u = v;

[0161] 2. a uv (t) = τ, where a is defined by equations (12)-(13);

[0162] Denote this space-time arc as (uv, t).

[0163] From Definition 2, there are two types of space-time arcs, the first type is the transfer arc The second type is the parking arc The set of space-time arcs in the space-time network is

[0164] Based on the concept of space-time arc, the constraint conditions related to post-disaster vehicle routing can be expressed as equations (14)-(16). Introduce binary variable x m,uv,tIndicates whether the mobile resource m is on the spatiotemporal arc (uv,t). Spatial uniqueness constraint (14) constrains any MER to appear on only one arc in each time slot. Traffic flow continuity constraint (15) requires that the in-degree of each MER in the spatiotemporal network is equal to its out-degree. Constraint (16) indicates that when the rainstorm ends, the MER moves from its warehouse site. Set off.

[0165]

[0166] It is worth noting that the constraints (14)-(16) above do not restrict the specific routes between the start-end pair. In the context of urban flooding, the proposed model can combine all road segments between the start and end points and automatically determine the optimal path under the current road network flooding conditions by combining the objective function.

[0167] S5. Construct a mixed-integer linear programming model as the power distribution system response model, and use elasticity metrics to quantify the elasticity of the power distribution system to achieve elasticity assessment of urban rainstorm flood disasters.

[0168] The system response module is designed to handle situations where a component in the power distribution system is flooded and out of service. Emergency measures will be implemented to mitigate the impact of the fault and restore system functionality. Considering various fault handling measures such as network reconfiguration (fault isolation and load restoration), flood drainage, equipment repair, and emergency power supply access, the power distribution system response model is expressed as a mixed integer linear program (MILP) model.

[0169] Table 1 System Module Symbol Table

[0170]

[0171]

[0172]

[0173] S501, Network Reconfiguration Modeling: Network reconfiguration is used to isolate faults and restore loads in non-faulty areas. Since switching operations are performed by distribution automation devices, network reconfiguration can be performed both during and after heavy rainfall. This represents the set of time slot indices for the entire process. Distribution system network reconfiguration needs to satisfy the following operational constraints:

[0174] a) Fault propagation constraints:

[0175] When a distribution node is flooded, the nearest switch is operated to isolate and disconnect the power supply of the flooded node. The inevitable drawback of this measure is that the power outage can spread to other areas not affected by the flood due to the limited number of switch configurations in the distribution system. This power outage spreading characteristic of the distribution system is modeled as:

[0176]

[0177] where ζ i,t denotes whether node i is located in the area that needs to be isolated at time t. Constraint (17) states that a flooded node must be isolated. For a node not affected by the flood, if none of its neighboring nodes need to be isolated, then it does not need to be isolated, as shown in (18). Otherwise, if any of its neighboring nodes need to be isolated, then it also needs to be isolated, as shown in (19). The nonlinear terms in (18)-(19) can be simply linearized, and here we set M = 1.

[0178] b) Topology radial constraints:

[0179] Constraint (20) limits the connection status of distribution lines, i.e., a distribution line can only be switched if it is equipped with a switch. Constraints (21)-(24) are the topology radial constraints for the distribution system operation based on the maximum density of the graph.

[0180]

[0181] c) Power flow equations:

[0182] A linearized branch power flow model is adopted to solve the power flow of the distribution system, which includes the node active and reactive power balance equations (25)-(26) and the voltage drop calculation equation (27).

[0183]

[0184] d) System security constraints:

[0185] Constraints (28) and (29) limit the transmission capacity of the distribution lines. Constraint (30) represents the node voltage amplitude limit.

[0186]

[0187] e) Load restoration constraints:

[0188] Constraint (31) limits the pickup status of the power load, i.e., the load cannot be restored when its associated node is in the fault area that needs to be isolated. Constraint (32) represents that once a load is restored, it will not be disconnected again to avoid frequent user power outages during the restoration process after the storm.

[0189]

[0190] S502, Flood Drainage Modeling: y i,t is used to represent whether the rainwater at flooded distribution node i has receded or been drained at time t. For outdoor flooded nodes, the number of time slots required for the rainwater to recede from outdoor node i can be obtained by solving (5) For flooded distribution rooms, drainage vehicles are deployed for indoor drainage. Constraint (34) indicates that water is completely drained when the cumulative residence time of the drainage vehicle at indoor flooded node i reaches The time length required for indoor drainage can be estimated by the indoor water depth and the drainage capacity of the drainage vehicle. Constraint (35) represents the status of the flooded node after drainage.

[0191]

[0192] S503, Equipment Repair Modeling: After the storm ends, repair personnel are dispatched to the site to repair the equipment. To describe the repair personnel's working hours spent on fault clearance, φ m,i,t is used to represent whether personnel m is repairing equipment at node i at time t. According to equations (36) and (37), equipment repair is only performed when the location of the damaged facility is accessible and the water has receded or been completely drained; after personnel m starts repairing the damaged node i, the fault is cleared after time slots , its available state η i,t is changed; constraint (38) indicates that z = 1 only when personnel m spends m,i,t time slots repairing the damaged node i; constraint (39) specifies the status of the repaired node. Constraint (40) indicates that each damaged node can only be repaired by one repair personnel. The availability state of the flooded node after the storm ends can be derived from equation (41).

[0193]

[0194]

[0195] S504, Emergency Power Access Modeling: Distributed backup power sources are often used to quickly restore user power supply before the damaged equipment is repaired. During the storm, the output of the distributed backup power source is limited by (42) and (43), which indicates that the power source can only be connected if the site is not flooded. It should be noted that if node i is not equipped with any power source, then φ

[0196]

[0197] MEG is deployed to provide power support for non-faulted areas after the rainstorm. m,i,t Ψ represents whether MEG m is connected to node i at time t. Constraints (44)-(45) indicate that MEG can only be connected to accessible and non-damaged distribution nodes. Constraint (46) limits the allowed number of MEG connections. After the rainstorm, the MEG is connected to the grid, and the power output is limited by equations (47)-(50).

[0198]

[0199] S505, collaborative optimization model: the distribution system response model under waterlogging is modeled as a collaborative optimization model;

[0200]

[0201] s.t.a) fault propagation constraints (10), (17)-(19);

[0202] b) topological radiation constraints (20)-(24);

[0203] c) power flow equations (25)-(27);

[0204] d) system security constraints (28)-(30);

[0205] e) load restoration constraints (31)-(32);

[0206] f) dynamic routing constraints (14)-(16);

[0207] g) flood discharge constraints (33)-(35);

[0208] h) equipment repair constraints (36)-(41);

[0209] i) power source access constraints (42)-(50);

[0210] where C i Ψ represents the number of users connected to node i. The objective function (51) is to minimize the number of users out of power and the shortest distance of mobile emergency resources. The relative weight of the two target items can be adjusted by the parameter ε, which is set to a small value to ensure that the first target item is dominant. The first term in equation (51) represents the cumulative sum of user outage duration, so the distribution system response model aims to reduce user outages and speed up recovery, which is suitable for distribution system resilience assessment.

[0211] S506, elasticity index design: the IEEE elasticity index is defined as the proportion of the number of users with power outage exceeding 12 hours to the total number of user interruptions, including user interruptions automatically recovered or avoided through smart switch operation and microgrid technology. Based on the solution results of the power distribution system response model (51), the number of persistent user interruptions and the number of avoided user interruptions are counted, respectively denoted as C SI and C AI .

[0212] In order to more accurately quantify the recovery rate of the power distribution system within the first 12 hours, a parameterized IEEE elasticity index is adopted:

[0213]

[0214] Wherein, the parameter t represents the duration of power outage of interest; is an indicator function that determines whether the duration of node power outage exceeds time t; R t is the parameterized elasticity index.

[0215] In another embodiment of the present application, a power distribution system resilience evaluation system for urban rainstorm waterlogging disasters is provided, which can be used to implement the power distribution system resilience evaluation method for urban rainstorm waterlogging disasters. Specifically, the power distribution system resilience evaluation system for urban rainstorm waterlogging disasters includes a rainstorm module, a surface runoff module, a device inundation module, a road inundation module, and a system response module.

[0216] Wherein, the rainstorm module constructs a rainstorm model according to rainfall and rainfall process to obtain time-series rainfall intensity;

[0217] The surface runoff module constructs a runoff model and a confluence model, determines the surface water depth change process according to the obtained time-series rainfall intensity, and obtains the surface water depth simulation results; the device inundation module constructs a model to simulate the outdoor device inundation and indoor device inundation process based on the surface water depth simulation results, and obtains the power distribution system disaster scenario and the set of damaged devices;

[0218] The road inundation module constructs a road network model based on the power distribution system disaster scenario and the set of damaged devices, and models the mobile resource path problem under urban waterlogging as a time-dependent vehicle routing problem; the system response module constructs a mixed integer linear programming model as a power distribution system response model based on the time-dependent vehicle routing problem, quantifies the power distribution system resilience using the elasticity measurement index, and quantifies the power distribution system resilience based on the obtained elasticity index R t to realize the resilience evaluation of urban rainstorm waterlogging disasters.

[0219] In another embodiment of the present application, a terminal device is provided, which comprises a processor and a memory, the memory being configured to store a computer program, the computer program comprising program instructions, and the processor being configured to execute the program instructions stored in the computer storage medium. The processor can be a central processing unit (CPU), and can also be other general-purpose processors, digital signal processors (DSP), application specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc., which are the computing core and control core of the terminal, and are suitable for implementing one or more instructions, and are specifically suitable for loading and executing one or more instructions to implement a corresponding method flow or a corresponding function; the processor in the embodiments of the present application can be used for the operation of the elastic evaluation method of the power distribution system for urban rainstorm waterlogging disasters, including:

[0220] According to the rainfall and the rainfall process, a rainstorm model is constructed to obtain a time-series rainfall intensity; a runoff model and a confluence model are constructed, and the time-series rainfall intensity is used to determine a surface water depth change process to obtain a surface water depth simulation result; based on the surface water depth simulation result, a model is constructed to simulate an outdoor equipment submerging process and an indoor equipment submerging process to obtain a power distribution system disaster scenario and a damaged equipment set; based on the power distribution system disaster scenario and the damaged equipment set, a road network model is constructed, and a mobile resource path problem under urban waterlogging is modeled as a time-dependent vehicle routing problem; based on the time-dependent vehicle routing problem, a mixed integer linear programming model is constructed as a power distribution system response model, an elasticity measurement index is used to quantify the elasticity of the power distribution system, and based on the obtained elasticity index R t The elasticity of urban rainstorm waterlogging disasters is evaluated.

[0221] Please refer to Figure 4 , the terminal device is a computer device, the computer device 60 of the embodiment comprises a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61, and the computer program 63 is executed by the processor 61 to implement the fluid composition calculation method in the reservoir reconstruction wellbore in the embodiment, to avoid repetition, which will not be described here. Alternatively, the computer program 63 is executed by the processor 61 to implement the functions of each model / unit in the power distribution system for urban rainstorm waterlogging disasters elastic evaluation system, to avoid repetition, which will not be described here.

[0222] The computer device 60 can be a desktop computer, a notebook computer, a palm computer, a cloud server, and the like. The computer device 60 can include, but is not limited to, a processor 61, a memory 62. Those skilled in the art can understand that Figure 4 The computer device 60 is only an example and does not constitute a limitation on the computer device 60, and can include more or fewer components than shown, or combine certain components, or different components, for example, the computer device can also include an input / output device, a network access device, a bus, and the like.

[0223] The processor 61 can be a central processing unit (CPU), and can also be other general-purpose processors, digital signal processors (DSP), application specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, and the like. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor.

[0224] The memory 62 can be an internal storage unit of the computer device 60, such as a hard disk or a memory of the computer device 60. The memory 62 can also be an external storage device of the computer device 60, such as a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, and the like.

[0225] Further, the memory 62 can include both an internal storage unit and an external storage device of the computer device 60. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 can also be used to temporarily store data that has been output or will be output.

[0226] Please refer to Figure 5 The terminal device 600 is an electronic device, and the electronic device is in the form of a general computing device. The components of the electronic device can include, but are not limited to, at least one processing unit 610, at least one storage unit 620, a bus 630 connecting different platform components including the storage unit 620 and the processing unit 610, a display unit 640, and the like.

[0227] The storage unit stores program codes which can be executed by the processing unit 610, so that the processing unit 610 performs the steps according to various exemplary embodiments of the present application described in the above method part of the present specification. For example, the processing unit 610 can perform the steps as shown in the above method part of the present specification. Figure 6

[0228] The storage unit 620 can include a readable medium in the form of a volatile storage unit, such as a random access memory (RAM) 6201 and / or a cache memory 6202, and can further include a read-only memory (ROM) 6203.

[0229] The storage unit 620 can further include a program / utility 6204 having a set of programs / modules 6205, including an operating system, one or more application programs, other programs, and programmatic data, each or any combination thereof, which can include implementation of a network environment.

[0230] The bus 630 can represent one or more of several types of bus structures, including a storage unit bus or bus controller, a peripheral bus, a graphics acceleration port, a processing unit bus, or a local bus using any of a variety of bus architectures.

[0231] The electronic device 600 can also communicate with one or more external devices 700 such as a keyboard or pointing device, a Bluetooth device, etc.; user interfaces and / or peripheral devices such as a printer, scanner, or the like; and / or one or more devices in a communications system. Communication with one or more devices can occur via an input / output (I / O) interface 650. Still yet, the electronic device 600 can communicate with one or more networks such as a local area network (LAN), a general wide area network (WAN), and / or a public network (e.g., the Internet) via a network adapter 660. As depicted, the network adapter 660 can communicate with the other components of the electronic device 600 via the bus 630. It should be appreciated that the network adapter 660 and / or the bus 630 can be implemented using one or more types of communication media, such as IO devices, I / O device adapters, wireless links, wires, cables, and the like, including bus communication to one or more other buses.

[0232] ​In still another embodiment of the present application, the present application also provides a storage medium, specifically a computer readable storage medium, which is a memory device in the terminal device, for storing programs and data. It can be understood that the computer readable storage medium herein can include the built-in storage medium in the terminal device, and of course can also include the expansion storage medium supported by the terminal device. The computer readable storage medium provides a storage space, which stores the operating system of the terminal. Moreover, one or more instructions suitable for being loaded and executed by the processor are also stored in the storage space, and the instructions can be one or more computer programs. It should be noted that the computer readable storage medium herein can be a high-speed RAM memory, or a non-volatile memory such as at least one disk memory.

[0233] The one or more instructions stored in the computer readable storage medium can be loaded and executed by the processor to implement the corresponding steps of the method for evaluating the flexibility of the power distribution system in response to the urban rainstorm flood disaster in the above embodiments; the one or more instructions stored in the computer readable storage medium are loaded and executed by the processor to implement the following steps:

[0234] According to the rainfall and the rainfall process, a rainstorm model is constructed to obtain a time-series rainfall intensity; a runoff model and a confluence model are constructed to determine a surface water depth variation process according to the obtained time-series rainfall intensity, and to obtain a surface water depth simulation result; based on the surface water depth simulation result, a model is constructed to simulate an outdoor equipment submerging process and an indoor equipment submerging process, to obtain a power distribution system disaster scenario and a damaged equipment set; based on the power distribution system disaster scenario and the damaged equipment set, a road network model is constructed, and a mobile resource path problem under the urban waterlogging is modeled as a time-dependent vehicle routing problem; based on the time-dependent vehicle routing problem, a mixed integer linear programming model is constructed as a power distribution system response model, a power distribution system flexibility is quantified by using a flexibility measurement index, and based on the obtained flexibility index R t The flexibility of the urban rainstorm flood disaster is evaluated.

[0235] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the following will clearly and completely describe the technical solutions in the embodiments of the present application with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some but not all of the embodiments of the present application. The components of the embodiments of the present application described and shown in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0236] The improved IEEE 33-bus distribution system is adopted as the test system, and ANUGA3.1.9 and Python3.10.14 are used to model and solve 2D SWE. Gurobi 11.0.0 and Python 3.11.5 are used to model and solve the involved MILP.

[0237] For MER, 2 repair crews, 1 emergency generator truck and 1 emergency drainage truck are considered; the fault clearance time of each fault node is 90 min; the capacity of the emergency generator truck is set to 2 MVA; the drainage capacity of the emergency drainage truck is set to 500 m 3 / h. The switch configuration and distributed backup generator in the test distribution system are shown in Figure 1 The number of low-voltage users at each distribution node is estimated according to the node active load, assuming that each household has an active power of 5 kW. In the system response behavior simulation, the time slot is set to Δt = 10 min. Since the proposed model focuses on the recovery situation in the first 12 hours, the maximum simulation time is set to 12 hours after the design storm ends.

[0238] A design storm with a return period of 50 years, a duration of 120 min and a rain peak coefficient of 0.48 is generated as the simulated disaster scenario. Due to urban flooding caused by the storm, 4 outdoor distribution nodes and 2 indoor distribution nodes are flooded. At the end of the storm (t = 120 min), the total load loss is as high as 3415 kW, and 683 households experience persistent power outages, and 60 households avoid power outages by forming microgrids through distributed power sources.

[0239] To illustrate the impact of equipment node inundation duration (Factor A) and city road inundation (Factor B), three cases were designed. The factors considered in each case are detailed in Table 2. Case I does not consider any restrictions related to rainstorm, i.e. it is handled in the same way as a regular fault restoration process, involving only the deployment of repair crews and emergency generators. The results show that repair crews tend to prioritize repairing nodes or areas with a larger number of customers. The MER dispatch Gantt chart and system resilience curve are shown in Figs. 2 and 3, respectively. For Case I, it takes 7.5 h to restore power to all customers after the rainstorm disaster ends. Figure 3

[0240] Table 2 Comparison of three cases considering different factors

[0241]

[0242]

[0243] However, repair work under flood inundation is subject to whether the water in the fault area recedes. When this factor is considered in Case II, the repair sequence changes, and in some cases, repair crews have to wait on site. For example, repair crew 1 arrives at node 17 at t = 3.0 h, but the emergency drainage vehicle needs to wait until t = 3.8 h to drain the indoor water before repair work can begin. Similarly, repair crew 2 arrives at node 4 at t = 3.2 h, but equipment repair can only begin after the water recedes at t = 5.0 h. In this case, it takes 8.8 h for all customers to be restored after the rainstorm ends.

[0244] In fact, the accessibility of the fault node is also a crucial factor to be considered. When this factor is considered in Case III, the repair sequence changes again, and the paths of the emergency drainage vehicle and emergency generator also change. After the rainstorm ends, the roads shown in Fig. 4 are flooded, so mobile resources still need to wait at the vehicle warehouse before they can depart. In addition, compared to Case I, the average time for travel and on-site standby increases by 189%. The entire post-disaster recovery process lasts 10.5 h, which is 1.4 times that of Case I. Figure 2

[0245] In summary, the resilience evaluation method and system for a power distribution system to cope with urban rainstorm flooding disasters according to the present application consider the characteristics of urban rainstorm flooding disasters and the response behavior of the power distribution system in the disaster resistance and post-disaster recovery stages, take into account the impact of equipment inundation time and road inundation on the response and resilience indicators of the power distribution system, and more fully evaluate the resilience of the power distribution system under rainstorm disasters, and the evaluation results are more accurate.

[0246] ​​Those skilled in the art can clearly understand that, for the convenience and brevity of description, only the above-mentioned division of each functional unit and module is exemplified, and in actual application, the above-mentioned functions can be completed by different functional units and modules according to needs, that is, the internal structure of the device is divided into different functional units or modules to complete all or part of the functions described above. Each functional unit and module in the embodiment can be integrated in one processing unit, or each unit can be physically present separately, or two or more units can be integrated in one unit. The above-mentioned integrated unit can be realized in the form of hardware or software. In addition, the specific name of each functional unit and module is only for the convenience of mutual distinction, and does not limit the protection scope of the present application. The specific working process of the unit and module in the above system can refer to the corresponding process in the foregoing method embodiment, which will not be described here.

[0247] In the above embodiments, the description of each embodiment has its own emphasis, and the parts not described or recorded in detail in a certain embodiment can be referred to the related description of other embodiments.

[0248] Those of ordinary skill in the art can realize that the units and algorithm steps of each example described in combination with the embodiments disclosed in the present application can be realized by electronic hardware or a combination of computer software and electronic hardware. Whether the functions are executed in hardware or software depends on the specific application and design constraints of the technical solution. Professional technicians can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the present application.

[0249] In the embodiments provided by the present application, it should be understood that the disclosed apparatus / terminal and method can be implemented by other ways. For example, the above-mentioned apparatus / terminal embodiments are only schematic, and the division of the modules or units is only a logical function division, and there can be another division way in actual implementation, for example, a plurality of units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the displayed or discussed mutual coupling or direct coupling or communication connection can be indirect coupling or communication connection through some interface, device or unit, and can be electrical, mechanical or other forms.

[0250] The units described as separate components can or can not be physically separated, and the components shown as units can or can not be physical units, that is, they can be located in one place, or can be distributed on multiple network units. Part or all of the units can be selected according to actual needs to achieve the purpose of the embodiment.

[0251] In addition, each functional unit in each embodiment of the present application can be integrated in one processing unit, or each unit can be physically present separately, or two or more units can be integrated in one unit. The integrated unit can be realized in the form of hardware or in the form of a software functional unit.

[0252] The integrated module / unit, if realized in the form of a software functional unit and sold or used as an independent product, can be stored in a computer-readable storage medium. Based on such understanding, all or part of the processes in the above-mentioned embodiment methods can also be completed by a computer program instructing related hardware, and the computer program can be stored in a computer-readable storage medium. The computer program can implement the steps of each method embodiment when executed by a processor. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or some intermediate forms. The computer-readable medium can include any entity or device capable of carrying the computer program code, recording medium, U disk, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signal, telecommunication signal, and software distribution medium, etc. It should be noted that the computer-readable medium can include or exclude contents according to the requirements of legislation and patent practice in the jurisdiction, for example, in some jurisdictions, according to legislation and patent practice, the computer-readable medium does not include electrical carrier signals and telecommunication signals.

[0253] The present application is described with reference to flowcharts and / or block diagrams according to the methods, devices, and computer program products of embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of flows and / or blocks in the flowcharts and / or block diagrams can be implemented by computer program instructions. These computer program instructions can be provided to a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to produce a machine, so that the instructions executed by the computer or other programmable data processing devices produce a device that implements the functions specified in the flowcharts and / or block diagrams. Figure 1 The functions specified in one flow or multiple flows and / or blocks Figure 1 The device that implements the functions specified in one flow or multiple flows and / or blocks.

[0254] These computer program instructions can also be stored in a computer-readable storage medium that can guide the computer or other programmable data processing devices to work in a specific manner, so that the instructions stored in the computer-readable storage medium produce a manufactured product including instruction devices that implement the functions specified in the flowcharts and / or block diagrams. Figure 1one or more processes and / or blocks Figure 1 the function specified in the one or more blocks.

[0255] These computer program instructions can also be loaded into computer or other programmable data processing devices, so that a series of operational steps are performed on the computer or other programmable data processing devices to generate a computer-implemented process, so that the instructions executed on the computer or other programmable data processing devices provide a process for implementing the flow Figure 1 one or more processes and / or blocks ​ the steps of the function specified in the one or more blocks.

[0256] The above is only to illustrate the technical idea of the present application, and cannot limit the protection scope of the present application. Any modification made according to the technical idea of the present application on the basis of the technical scheme falls within the protection scope of the claims of the present application.

Claims

1. A method for evaluating the resilience of a power distribution system to urban rainstorm flooding disasters, characterized in that, The method comprises the following steps: a storm model is constructed according to rainfall and rainfall process, and time-series rainfall intensity is obtained; a runoff model and a confluence model are constructed, surface water depth variation process is determined according to the obtained time-series rainfall intensity, and surface water depth simulation results are obtained; a model is constructed to simulate outdoor equipment submergence and indoor equipment submergence process based on the surface water depth simulation results, and a power distribution system disaster scenario and a damaged equipment set are obtained; a road network model is constructed based on the power distribution system disaster scenario and the damaged equipment set, and a mobile resource path problem under urban waterlogging is modeled as a time-dependent vehicle routing problem, specifically: a submerged road traffic model is established according to storm water depth and vehicle driving speed; a discrete arrival time function is defined to meet the needs of a space-time network modeling framework; a space-time coordinate system with time index as the horizontal coordinate and road network vertex as the vertical coordinate is established to reflect the spatial changes of mobile resources in the road network at different times after the storm ends; based on the discrete arrival time function, the concept of space-time arc in the space-time coordinate system is defined, and the constraint conditions related to post-disaster vehicle routing are expressed under the concept of space-time arc; A mixed integer linear programming model is constructed based on time-dependent vehicle routing problem as the distribution system response model, the elasticity of the distribution system is quantified by using the elasticity metric index, and the obtained elasticity index is used to evaluate the elasticity of the distribution system The elasticity of urban rainstorm waterlogging disaster is evaluated, the distribution system response model under waterlogging is modeled as a collaborative optimization model, the proportion of users with power outage exceeding 12 hours to the total number of interrupted users is defined as the IEEE elasticity index, including the automatically restored or avoided user interruption through intelligent switch operation and microgrid technology, based on the solution of the collaborative optimization model, the number of persistent user interruptions and the number of avoided user interruptions are counted, and the parameterized elasticity index is determined As follows: Elasticity indicator As follows: wherein the parameters represent the duration of the power outage of interest; is an indicator function that judges whether the duration of the power outage of the node exceeds the time tmax. The collaborative optimization model is specifically as follows: wherein, denotes a set of time slot indices, denotes a set of distribution system nodes, denotes a time instant denotes a node denotes whether the load at the node denotes the number of users connected to the node denotes a node denotes a fixed time interval per time slot, denotes a relatively small positive number, denotes a set of mobile emergency resources, denotes a set of space-time arcs in a space-time network, denotes the departure time of a vehicle at a node denotes the arrival time of a vehicle at a node denotes the arrival time of a vehicle at a node denotes whether a mobile resource is on a space-time arc denotes a space-time arc 2. The power distribution system resilience assessment method against urban rainstorm flood disaster according to claim 1, characterized in that, The storm model is constructed according to rainfall and rainfall process, and time-series rainfall intensity is obtained specifically as follows: Intensity-duration-frequency curve is constructed to obtain average rainfall intensity; Chicago rain type is used for rainfall process design, rain peak coefficient is used to represent the peak time of rainfall process, rainfall duration is divided into two periods before and after the peak, and instantaneous rainfall intensity before and after the peak is obtained based on the average rainfall intensity.

3. The power distribution system resilience assessment method against urban rainstorm flood disaster according to claim 2, characterized in that, Pre- and post-peak instantaneous intensity of storm processes and are: wherein, and respectively represent the corresponding time in the peak before and after the peak period of the rainstorm duration; represents the peak position coefficient of the design rainstorm process derived from the historical rainstorm data; , , , is a coefficient related to the city where the study area is located; represents the return period.

4. The power distribution system resilience assessment method against urban rainstorm flood disaster of claim 1, wherein, The runoff model is constructed specifically as follows: wherein, is the infiltration rate at time t; is the initial infiltration rate; is the steady-state infiltration rate of the soil; is the decay coefficient; The confluence model is specifically as follows: wherein, a vector representing a conserved quantity, composed of water depth , x-direction unit-width flow rate , and y-direction unit-width flow rate ; and represent the average flow velocity of water in the x-direction and y-direction, respectively; Flux in x and y directions and is given by the equation: wherein is the gravitational acceleration.

5. The power distribution system resilience assessment method against urban rainstorm flood disaster according to claim 1, characterized in that, The model is constructed to simulate outdoor equipment submergence and indoor equipment submergence process specifically as follows: The outdoor submergence model is specifically as follows: If the rain depth at an outdoor node exceeds the critical flood protection threshold of the device , the node is shut down urgently and the nearby switches are disconnected to isolate the fault; let denote the set of flooded outdoor distribution nodes, be the water level at the outdoor node at the moment; denote the set of distribution nodes; denote the set of indoor nodes; For each flooded outdoor node whose location has a rain depth exceeding the time slot is noted as By means of a drainage simulation of the urban pipe network, the time slot in which the rain water is removed from the outdoor node is noted as ; The indoor submergence model is specifically as follows: When the distribution facilities are located indoors, the indoor flooding depth is calculated as a function of the outdoor water depth; let denote the set of distribution nodes that are flooded indoors, where is the indoor water depth at time , and the corresponding time slot is also denoted as ; the set of flooded distribution nodes is denoted as , and a binary variable is introduced to indicate whether node is normal at time , i.e., for the nodes that do not rise above the critical water level during the rainstorm, there is ; the state of the flooded nodes during the rainstorm is as follows: wherein denotes an indicator function.

6. The power distribution system resilience assessment method against urban rainstorm flood disaster of claim 5, wherein, When outdoor water depth exceeds indoor water depth, rainwater flows into the building and is calculated as follows: wherein, is the flow rate of rainwater into the building; is a flow coefficient set to 1 in the present invention; is the width of the building door through which water is expected to enter; and respectively represent the height of the outdoor and indoor water surfaces; The indoor water depth is updated as follows: wherein, is the building area of the building.

7. The power distribution system resilience assessment method against urban rainstorm flood disaster according to claim 1, characterized in that, The relationship between storm water depth and vehicle driving speed is as follows: wherein, is a road segment at a time instant; is a normal speed for a road segment ; is a maximum water depth for a road segment at a time instant; For , define a discrete arrival time function as a function , and satisfy: non-decreasing; ; Given road network and a set of time slots , define a space-time arc in the space-time network as an arc from vertex to vertex that satisfies: or ; denote this space-time arc as The constraint conditions are specifically as follows: wherein, is a mobile resource whether on a spatiotemporal arc , is a mobile resource whether on a spatiotemporal arc , is a set of spatiotemporal arcs in a spatiotemporal network, is a time slot index, is a set of time slot indices after a rainstorm, is a time slot corresponding to the end of a rainstorm, is a maximum simulation time for a model, is a set of mobile emergency resources, is a set of road network nodes, is a warehouse point for a mobile resource , is a warehouse point for a mobile resource whether on a spatiotemporal arc .

8. A power distribution system resilience assessment system for coping with urban rainstorm flood disasters, characterized in that, including: a storm module, a storm model is constructed according to rainfall and rainfall process, and time-series rainfall intensity is obtained; a surface runoff module, a runoff model and a confluence model are constructed, surface water depth variation process is determined according to the obtained time-series rainfall intensity, and surface water depth simulation results are obtained; an equipment submergence module, a model is constructed to simulate outdoor equipment submergence and indoor equipment submergence process based on the surface water depth simulation results, and a power distribution system disaster scenario and a damaged equipment set are obtained; a road submergence module, a road network model is constructed based on the power distribution system disaster scenario and the damaged equipment set, and a mobile resource path problem under urban waterlogging is modeled as a time-dependent vehicle routing problem, specifically: a submerged road traffic model is established according to storm water depth and vehicle driving speed; a discrete arrival time function is defined to meet the needs of a space-time network modeling framework; a space-time coordinate system with time index as the horizontal coordinate and road network vertex as the vertical coordinate is established to reflect the spatial changes of mobile resources in the road network at different times after the storm ends; based on the discrete arrival time function, the concept of space-time arc in the space-time coordinate system is defined, and the constraint conditions related to post-disaster vehicle routing are expressed under the concept of space-time arc; The system response module constructs a mixed integer linear programming model as a power distribution system response model based on a time-dependent vehicle routing problem, quantifies the flexibility of the power distribution system by using a flexibility metric, and quantifies the flexibility of the power distribution system based on the obtained flexibility metric The flexibility of urban rainstorm waterlogging disaster is evaluated, and the power distribution system response model under waterlogging is modeled as a collaborative optimization model. The proportion of the number of users with power outage exceeding 12 hours to the total number of interrupted users is defined as the IEEE flexibility index, which includes the automatically restored or avoided user interruption through intelligent switch operation and microgrid technology. Based on the solution of the collaborative optimization model, the number of persistent user interruptions and the number of avoided user interruptions are counted, and the parameterized flexibility index is determined As follows: Elasticity index As follows: wherein the parameters represent the duration of the power outage of interest; is an indicator function that judges whether the duration of the power outage of the node exceeds the time tmax. The collaborative optimization model is specifically as follows: in, Represents the set of time slot indices. Represents the set of nodes in a power distribution system. Indicates time node Has the load at the location been restored? Represents nodes Number of connected users This represents a fixed time interval for each time slot. Represents relatively small positive numbers. Represents a collection of mobile emergency resources. Represents the set of spatiotemporal arcs in a spatiotemporal network. Indicates in Departure time and route Arrival time, Indicates mobile resources Is it in the spacetime arc? superior.

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