Two-stage fault recovery method for improving elasticity of power distribution system

Abstract

The invention discloses a two-stage fault recovery method for improving the elasticity of a power distribution system, and the method comprises the steps: constructing a typhoon space-time evolution model, and generating a prediction fault scene; simulating the distribution line in the predicted fault scene by using a Monte Carlo simulation method to generate a plurality of fault scenes; based on the information entropy value of the fault scene and the fault multiple number, an uncertainty set is constructed, and then a robust optimization model is constructed; solving the robust optimization model, and determining a pre-layout scheme of the mobile energy storage system and the static var compensator in a pre-disaster worst fault scene; a multi-source collaborative post-disaster multi-period multi-target fault recovery model is constructed; the fault recovery model realizes recovery of a power-loss load and a fault line of a power distribution system through network reconstruction and optimal scheduling of a mobile energy storage system, a static var compensator, a maintenance team and an electric vehicle. According to the invention, the overall elasticity of the power distribution system is obviously improved, the capability of resisting disasters is enhanced, and the capability of rapidly recovering power supply is also improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of improving the resilience of power systems, and in particular relates to a two-stage fault recovery method for improving the resilience of distribution systems. Background Art

[0002] In the power system sector, improving distribution network resilience is a key technical scenario. Current research defines resilience as both resistance and recovery, and corresponding improvement strategies can be divided into two phases: pre-disaster prevention and post-disaster recovery. In the pre-disaster prevention phase, the distribution system's resilience is primarily enhanced through the rational planning of flexible resources. This includes deploying distributed active power sources such as photovoltaics, wind power, diesel generators, and mobile energy storage (MESS) to provide power support for critical loads in emergencies. In recent years, with the increasing popularity of electric vehicles (EVs) and the development of vehicle-to-grid (V2G) technology, the potential of EVs as a flexible energy storage resource has gradually attracted attention. Furthermore, integrating distributed reactive power sources such as group-switched capacitors and static VAR compensation (SVCs) into the distribution network helps stabilize voltage, especially ensuring safe and stable system operation after large-scale power outages. Furthermore, measures such as component reinforcement, soft switching, and the formation of island microgrids can effectively enhance pre-disaster resilience.

[0003] During the post-disaster recovery phase, the movement and output of distributed energy storage resources, such as MESS, are primarily dispatched to rapidly restore power to critical loads and minimize outage losses. However, compared to MESS, EVs, while numerous, have smaller individual capacities and outputs, and their participation in fault recovery scheduling requires comprehensive consideration of multiple factors, including temporal and spatial distribution, travel preferences, and user demand. While distributed energy storage can provide power support for some critical loads in the short term, long-term, ensuring stable and long-term power supply for all lost loads requires grid-level intervention to restore connectivity between the lost areas and the primary power source. Distribution systems equipped with remotely controlled switches can modify their topology through network reconfiguration, providing recovery paths for critical loads. However, network reconfiguration alone may be ineffective in severe faults. Furthermore, dispatching maintenance teams (RCs) to repair faulty lines can help restore connectivity between lost loads and the primary power source. However, due to limitations in the number and efficiency of RCs, it is difficult to complete repairs on all faulty lines in a short period of time. Therefore, flexible allocation of RC resources is necessary to improve the efficiency of repairing critical lines and restore more loads to the primary power source as quickly as possible.

[0004] However, existing research has limitations. In the pre-disaster prevention phase, most analyses are based on given fault scenarios, without fully considering the temporal and spatial uncertainty of typhoon-induced faults in the distribution system. This makes it difficult to predict the effectiveness of the resulting flexible resource pre-layout schemes under different actual fault scenarios. In the post-disaster recovery phase, most studies use a single resource or simply combine different recovery resources, with less in-depth exploration of the characteristics of various resources and their synergistic and complementary effects in the recovery process. How to rationally coordinate and dispatch limited resources to maximize recovery effectiveness remains an unresolved issue.

[0005] To address the above challenges, it is urgent to propose a two-stage fault recovery method to enhance the resilience of the distribution system, so as to effectively improve the resilience of the distribution network under extreme disasters such as typhoons. Summary of the Invention

[0006] To solve the above technical problems, the present invention provides a two-stage fault recovery method for improving the resilience of a power distribution system.

[0007] The present invention proposes a two-stage fault recovery method for improving the resilience of a power distribution system, comprising the following steps:

[0008] Build a typhoon spatiotemporal evolution model to generate predicted failure scenarios;

[0009] The Monte Carlo simulation method is used to simulate the distribution lines in the predicted fault scenario and generate several fault scenarios;

[0010] Based on the information entropy value and fault multiplicity of the fault scenario, an uncertainty set is constructed, and then a robust optimization model is constructed;

[0011] Solve the robust optimization model to determine the pre-placement plan for the mobile energy storage system and static VAR compensator under the worst-case pre-disaster fault scenario;

[0012] Construct a multi-source collaborative post-disaster multi-period multi-target fault recovery model;

[0013] The fault recovery model achieves the recovery of power distribution system lost loads and fault lines through network reconstruction and optimized scheduling of mobile energy storage systems, static VAR compensators, maintenance teams and electric vehicles.

[0014] Optionally, the process of building a typhoon spatiotemporal evolution model includes:

[0015] Based on the functional relationship between the typhoon's movement path, minimum air pressure and maximum wind speed radius, and combined with the raster data principle of the geographic information system, the area where the distribution system is located is gridded, and the wind speed values ​​​​of each unit of the distribution line in each time period are simulated and calculated, thereby completing the construction of the typhoon's spatiotemporal evolution model.

[0016] Optionally, the objective function of the robust optimization model is the economic cost under the worst fault scenario, including the power loss load cost, the pre-layout configuration cost of the mobile energy storage system and the static VAR compensator.

[0017] Optionally, the constraints of the robust optimization model include the outermost layer of flexible resource configuration and network topology constraints, the middle layer of fault scenario occurrence model constraints, and the innermost layer of load reduction constraints, mobile energy storage system output constraints, static VAR compensator compensation constraints and distribution system operation constraints.

[0018] Optionally, the objective function of the fault recovery model is to minimize the total economic cost during the fault recovery period, including the power-off load cost, switch operation cost, line fault time cost, maintenance team maintenance cost and electric vehicle discharge economic compensation cost.

[0019] Optionally, the constraints of the fault recovery model include mobile energy storage system scheduling constraints, maintenance team scheduling constraints, electric vehicle scheduling constraints, and other distribution system operation constraints;

[0020] The mobile energy storage system scheduling constraints include capacity and output constraints and time-space movement constraints; the maintenance team scheduling constraints include time-space movement constraints and nonlinear relationship constraints between maintenance efficiency and the number of maintenance teams.

[0021] The present invention also provides a computer device, comprising a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method.

[0022] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which implements the steps of the method when executed by a processor.

[0023] The present invention also provides a computer program product, comprising a computer program, which implements the steps of the method when executed by a processor.

[0024] Compared with the prior art, the present invention has the following advantages and technical effects:

[0025] This invention constructs a typhoon's spatiotemporal evolution model and generates a large number of predicted fault scenarios. It then analyzes the fault scenarios using Monte Carlo simulation, quantifies the uncertainty of the fault scenarios, and then constructs a robust optimization model for flexible resources under the worst-case fault scenario before a disaster, determining the optimal pre-layout plan for mobile energy storage systems and static VAR compensators. This technical approach not only accurately predicts the impact of typhoons on power distribution systems, generates a large number of possible fault scenarios and quantifies their uncertainties, thereby providing a scientific basis for pre-layout before a disaster, but also determines the optimal resource pre-layout plan before a disaster, enabling mobile energy storage systems and static VAR compensators to respond quickly after a disaster, providing power support for critical loads, reducing power outages, and improving power supply reliability.

[0026] During the post-disaster recovery phase, this invention achieves resource synergy and complementarity through network reconstruction and optimized scheduling of multiple resources, including mobile energy storage systems, static VAR compensators, maintenance teams, and electric vehicles. This improves recovery efficiency, reduces the pressure on individual resources, and makes the recovery process more efficient and economical. This strategy of precise pre-disaster prediction and optimized pre-layout, as well as post-disaster coordinated recovery of multiple resources, significantly enhances the overall resilience of the distribution system, strengthening its ability to withstand disasters and improving its ability to quickly restore power, thereby reducing the economic losses and impact of power outages caused by disasters on the power system. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0028] Figure 1 A schematic diagram of the geographical location of a node power distribution system and a typhoon movement process according to an embodiment of the present invention;

[0029] Figure 2 Schematic diagram of average cost and average load recovery rate of various solutions under different fault severities in an embodiment of the present invention;

[0030] Figure 3 A schematic diagram of the locations of flexible resources and faulty lines at the start of fault recovery according to an embodiment of the present invention;

[0031] Figure 4 Schematic diagram of active power output and load recovery in each time period according to an embodiment of the present invention;

[0032] Figure 5 Schematic diagram of reactive power output of each reactive power source and load recovery reactive power in each time period according to an embodiment of the present invention;

[0033] Figure 6 Schematic diagram of RC maintenance position and line status at each time period according to an embodiment of the present invention;

[0034] Figure 7 Schematic diagram of active power recovery curve of loads under various strategies according to an embodiment of the present invention. DETAILED DESCRIPTION

[0035] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0036] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0037] Example 1

[0038] This embodiment provides a two-stage fault recovery method for improving the resilience of a power distribution system, including the following steps:

[0039] Build a typhoon spatiotemporal evolution model to generate predicted failure scenarios;

[0040] The Monte Carlo simulation method is used to simulate the distribution lines in the predicted fault scenario and generate several fault scenarios;

[0041] Based on the information entropy value and fault multiplicity of the fault scenario, an uncertainty set is constructed, and then a robust optimization model is constructed;

[0042] Solve the robust optimization model to determine the pre-placement plan for the mobile energy storage system and static VAR compensator under the worst-case pre-disaster fault scenario;

[0043] Construct a multi-source collaborative post-disaster multi-period multi-target fault recovery model;

[0044] The fault recovery model achieves the recovery of power distribution system lost loads and fault lines through network reconstruction and optimized scheduling of mobile energy storage systems, static VAR compensators, maintenance teams and electric vehicles.

[0045] The feasible process of generating distribution system fault scenarios during typhoons includes:

[0046] Construction of typhoon spatiotemporal evolution model:

[0047] A typhoon is a tropical cyclone that rotates around its center and moves at a constant speed. This example uses the semi-numerical, semi-empirical YanMeng wind field model to model the spatiotemporal evolution of typhoons. The YanMeng wind field model is a pressure gradient balance equation that takes into account boundary layer friction correction and can better characterize the relationship between forces in a typhoon wind field:

[0048]

[0049] Where: v is the wind speed vector in the typhoon wind field; p is the atmospheric pressure; ρ is the air density; f is the Coriolis force coefficient; y is the wind field fitting parameter; F is the atmospheric boundary layer friction. The atmospheric pressure p can be solved according to the Holland pressure concentric circle model:

[0050]

[0051] Where: p0 is the lowest air pressure at the center; Δp is the maximum air pressure difference; r is the distance from the typhoon center; R m is the maximum wind speed radius of the typhoon; B is the pressure parameter curve, generally ranging from 0.5 to 2.5.

[0052] Distribution system line fault model:

[0053] When the force exerted by typhoon wind on the line exceeds the limit, the line's bearing capacity decreases exponentially as the strain generated increases. The failure probability exponential model under typhoon operating conditions is as follows:

[0054]

[0055] Where: V k,t and P f ,k,t are the wind speed and fault probability of the kth unit of the line in the tth period respectively; V max The maximum wind speed that the line can withstand.

[0056] The steps for generating a fault scenario are as follows:

[0057] (1) According to the raster data principle of geographic information system, the area where the distribution system is located is divided into grids with units of a certain size.

[0058] (2) Input data such as typhoon movement path, minimum air pressure and maximum wind speed radius, set the simulation step size, and use the YanMeng wind field model to obtain the wind speed value V of each unit where the distribution line is located in each period. k,t .

[0059] (3) Calculate the failure probability P of each unit in each period of the line according to the line index failure probability model f ,k,t.

[0060] (4) Monte Carlo simulation method is used to simulate the status of each line under a certain fault scenario. A random number S between 0 and 1 is generated for each unit and time period where the line is located. rand,ij,k,t , if S rand,ij,k,t Greater than P fIf ,k,t, then the kth unit of the line is considered to be fault-free during the tth period; otherwise, a fault occurs. If any unit of a line fails during any period, then the line is considered to have failed in that scenario simulation. This generates a large number of fault scenarios.

[0061] The construction of a flexible resource pre-layout model for the worst-case pre-disaster failure scenario is feasible:

[0062] Pre-positioning MESS and SVCs before a disaster allows them to participate in restoration as quickly as possible after a disaster. However, the post-disaster failure scenarios of distribution systems caused by typhoons are uncertain, and the effectiveness of pre-disaster pre-positioning solutions is closely related to the failure scenarios. Therefore, this embodiment quantifies the uncertainty of the generated predicted failure scenarios and establishes a robust optimization model. By solving the MESS and SVC pre-positioning solutions for the worst-case failure scenario, the obtained pre-positioning solutions can effectively support power restoration in possible extreme scenarios.

[0063] Furthermore, the objective function in the pre-disaster stage is the economic cost under the worst failure scenario:

[0064]

[0065] Where: C PLS is the power loss load cost, c L,i P is the economic loss of power loss load per unit power; Lsh,i Reduce active power for load; Ω B is the set of nodes in the power distribution system. MESS and C SVC are the pre-layout configuration costs of MESS and SVC, c M and c S is the unit allocation cost of the two resources; 0-1 variable β M,i,m , β S,i,s is the connection status of MESS, SVC and distribution nodes. When it is 1, it means that the resource is connected to the distribution network and pre-layout configuration costs are incurred; M and S are the sets of MESS and SVC. The min-max-min objective function includes a three-layer structure, where x is a variable that characterizes the access location of MESS and SVC and the status of line switches. The outermost min problem determines the layout of MESS, SVC and the network topology of the distribution system. u is a variable that characterizes the fault scenario of the distribution system. The middle-layer max problem determines the fault scenario with the highest power loss cost. y is a variable that characterizes the operating status of the distribution system. The innermost min problem solves the optimal load reduction strategy under a given network architecture, flexible resource deployment location and fault scenario.

[0066] Furthermore, the constraints include:

[0067] Outermost constraint:

[0068] The outermost layer determines the network topology of the MESS, SVC layout, and distribution system:

[0069] (1) MESS and SVC configuration constraints:

[0070] A distribution node can only connect to one MESS and one SVC at most:

[0071]

[0072] (2) Network topology radial constraints:

[0073] The power distribution system adheres to the principle of "closed-loop design, open-loop operation" and must maintain a radial topology during normal operation:

[0074]

[0075] Where: 0-1 variable α ij and S Sub,i F is the circuit breaker status and virtual power supply mark; Sub,i 、F ij is the virtual power supply power and virtual branch power; δ(i) and γ(i) are the child and parent node sets of node i; Ω L N is the distribution system branch collection; B is the number of nodes in the power distribution system; M is a large positive number.

[0076] Middle layer constraints:

[0077] The middle layer is a fault scenario model. This model solves the most severe power outage distribution system failure scenario, given the outermost layer's flexible resources and network topology planning decisions. This embodiment uses the fault multiplicity and information entropy of the fault scenario to quantify the uncertainty of the distribution line fault state.

[0078] According to the NK principle, the fault line multiplicity N of the distribution system fault scenario is required to be Z Within a certain range:

[0079]

[0080] Where: 0-1 variable z ij Line fault status; if the line fails, it is 0; otherwise, it is 1. N Zmax 、N Zmin The upper and lower limits of the fault severity.

[0081] In order to reduce the conservatism of the solution results when NK is used as the uncertainty set, it is also required that the information entropy value W corresponding to the fault scenario should be within a certain range:

[0082]

[0083] Where: p ij is the line failure rate; W max and W min The upper and lower limits of information entropy.

[0084] Innermost constraint:

[0085] The innermost layer determines the load reduction, the output of each power source, and the operation strategy of the distribution system:

[0086] (1) Load reduction constraints:

[0087] The load reduction should be less than the power during normal operation, and the load reactive power should be reduced in proportion to the active power:

[0088]

[0089] Where: Q Lsh,i Reducing reactive power for load; P L,i With Q L,i They are respectively the active and reactive power of the load during normal operation.

[0090] (2) MESS output constraints:

[0091] The charging and discharging of MESS cannot occur at the same time. MESS that is not connected to the distribution node is neither charging nor discharging.

[0092]

[0093] Where: 0-1 variable c i,m and d i,m is the charge and discharge status of MESS.

[0094] MESS output is within a certain range:

[0095]

[0096] Where: P Mc,i,m and P Md,i,m is the MESS charging and discharging power; P Mcmax,m and P Mdmax,m is the maximum charge and discharge power of MESS.

[0097] (3) SVC compensation constraints:

[0098] The reactive power compensation of SVC is within a certain range:

[0099]

[0100] Where: QS,i,s is the inductive reactive power generated by SVC; Q Smax,s and Q Smin,s The upper and lower limits of the inductive reactive power generated by the SVC.

[0101] (4) Distribution system operation constraints:

[0102] The safe operation of the distribution system requires satisfying power balance constraints, line voltage constraints, node voltage constraints, and line capacity constraints, as shown below:

[0103] Ignoring the smaller quadratic terms, the linearized Distflow power flow equation is used to describe the distribution system operation state, and the voltage equation is relaxed using the Big-M method. The safe operation of the distribution system requires the following:

[0104] (1) Power balance constraints:

[0105]

[0106] Where: P ij and Q ij is the active and reactive power flowing through the line; P G,i and Q G,i Active and reactive power output of the main power supply.

[0107] (2) Line voltage constraints:

[0108]

[0109] Where: U sqr,i is the square of the node voltage; R ij and X ij are the line resistance and reactance.

[0110] (3) Node voltage constraints:

[0111]

[0112] Where: U sqrmax,i and U sqrmin,i These are the upper and lower limits of the square of the node voltage during normal operation.

[0113] (4) Line capacity constraints:

[0114]

[0115] Where: S max,ij It is the maximum apparent transmission capacity of the line.

[0116] The quadratic constraint can be approximated using the following linear constraints:

[0117]

[0118] The process of building a feasible multi-period fault recovery model for post-disaster multi-resource coordination includes:

[0119] After a disaster, the distribution system experiences widespread power outages, disconnecting numerous load nodes from the main power source. This requires the dispatch of various flexible resources to quickly restore power to critical loads and repair faulty lines. Based on the resulting flexible resource pre-placement scheme, this embodiment establishes a multi-source collaborative, multi-period, and multi-objective post-disaster fault recovery model. This model minimizes fault losses through network reconstruction and the dispatch of MESS, SVC, EV, and RC.

[0120] Furthermore, the objective function of the post-disaster stage is to minimize the total economic cost during the failure recovery period:

[0121] min C DSII =C PLS +C OP +C FL +C RC +C EV (26)

[0122]

[0123] Where: C PLS is the power loss load cost; C OP is the switching cost, c OP The cost of one action. FL is the line failure time cost, c FL k is the equivalent loss generated by each fault point for every hour it exists; i,t The line fault repair status, 0 means the repair is not completed, 1 means the repair is completed and can be put into operation. RC is the RC maintenance cost, c RC The cost of repairing each RC for one hour, 0-1 variable β R,i,r,t is the connection status between RC and distribution node, R is the set of RC. EV is the economic compensation cost of EV discharge, c EV is the compensation price per unit discharge power, P Vd,v,t is the discharge power of the V2G station, V is the set of V2G stations, T is the set of fault periods; Ω F is the set of line fault nodes.

[0124] Introducing the 0-1 intermediate variable λ ij,t Linearize the absolute value term in equation (28):

[0125]

[0126] Furthermore, the constraints include:

[0127] MESS scheduling constraints:

[0128] The MESS scheduling constraints must also meet the following constraints:

[0129] (1) MESS capacity and output constraints:

[0130]

[0131] Where: E M,m,t is the capacity of MESS; E Mmax,m and E Mmin,m is the upper and lower limits of the MESS capacity; η Mc,m and η Md,m is the charge and discharge efficiency of MESS.

[0132] (2) MESS space-time movement constraints:

[0133] A MESS can only be located at one distribution node at a time:

[0134]

[0135] A distribution node can only be connected to one MESS at a time:

[0136]

[0137] When the time interval is less than the sum of the movement time and the configuration time, the connection status of the MESS distribution node at that moment is 0:

[0138]

[0139] Where: T M,ij,m is the moving time of MESS between distribution nodes; T M0,m The time required for MESS to access the node. M,ij,m The calculation formula is as follows:

[0140]

[0141] Where: v M is the average speed of MESS; D M,ij,m is the MESS travel distance.

[0142] RC scheduling constraints:

[0143] Based on the fault scenario, RCs are dispatched from the maintenance center to repair the line fault. The RC temporal and spatial mobility constraints are similar to the MESS temporal and spatial mobility constraints.

[0144] To repair critical fault lines more quickly, multiple RCs can be deployed to repair the same fault line to improve repair efficiency. Considering the actual situation, the impact of the number of RCs on repair efficiency should be nonlinear. The following constraints must be met between repair efficiency and the number of repair teams:

[0145]

[0146] Where: 0-1 variable φ i,n,t When it is 1, it means that there are n maintenance teams repairing the line fault node i in time period t; n is the number of maintenance teams repairing the same fault line in the same time period; θ n is the maintenance efficiency of n maintenance teams repairing the same fault line at the same time; δ i,t is the actual maintenance efficiency of line fault node i in period t; N R The total number of maintenance teams.

[0147] The faulty line with a maintenance degree greater than 1 can operate normally at the next moment:

[0148]

[0149] The repaired fault line will not be damaged again:

[0150]

[0151] EV scheduling constraints considering temporal and spatial distribution randomness and user demand:

[0152] Considering the randomness of EV spatiotemporal distribution, the distribution system area is divided into multiple functional zones according to their usage, and coordinates are randomly generated within each functional zone as the initial position of each EV. Assuming that the initial capacity of each EV follows a normal distribution, before the fault recovery scheduling begins, each EV drives from its initial position to the nearest V2G station to prepare for power supply:

[0153]

[0154] Where: E E0,v,e is the initial capacity of EV, E E1,v,e is the capacity of EV to reach the V2G station, ΔE E D is the amount of electricity consumed by the EV when traveling one kilometer. E,v,e is the driving distance. E v is the set of electric vehicles arriving at the vth V2G station.

[0155] In addition, considering the user's demand for vehicles, the EV capacity needs to be restored to a certain value before the fault recovery scheduling is completed:

[0156]

[0157] Where: E Emax,v,e is the upper limit of EV capacity; r E The percentage of remaining capacity.

[0158] During fault recovery scheduling, EVs also need to meet capacity and output constraints, similar to MESS scheduling constraints.

[0159] Other constraints:

[0160] The network topology radial constraints, load reduction constraints, SVC compensation constraints, power balance constraints, line voltage constraints, node voltage constraints, and line capacity constraints are similar to those above. In addition, it is necessary to ensure that the line switch state is 0 when the fault line is not repaired:

[0161]

[0162] Where: Ω LF is the set of fault lines.

[0163] And considering the user satisfaction of the load node, the load that has been restored to power supply cannot be cut off again:

[0164]

[0165] Implementable, model solving:

[0166] For the single-layer multi-objective optimization model in the post-disaster recovery phase, the YALMIP toolbox and GUROBI solver can be directly used in the MATLAB environment for solution. For the robust optimization model in the pre-disaster prevention phase, the column and constraint generation (C&CG) algorithm can be used to decompose the main problem and sub-problems, and then the solvers can be used to iteratively solve them. The specific solution process is as follows:

[0167] The compact form of the original problem of the flexible resource pre-placement model under the worst failure scenario before a disaster is as follows:

[0168]

[0169] st Ax≤a (50)

[0170] Mu≤Γ (51)

[0171] Cx1+By+G·x2·diag(u)≤h (52)

[0172] Where: x1 is divided by α ij The outermost variable outside; x2·diag(u) represents the bilinear term α ij z ij; c and b are the coefficient vectors of the objective function; a, Γ and h represent the constant vectors of the corresponding constraints; A, M, C, B and G represent the coefficient matrices of the corresponding constraints.

[0173] After decomposing the original problem into the main problem and subproblems, the bilinear term α ij z ij The two variables of have a fixed constant in the main problem and the subproblem respectively, and no linearization is required.

[0174] (1) Main question:

[0175] The expression of the main problem in the C&CG algorithm is:

[0176]

[0177] st Ax≤a (54)

[0178]

[0179] Where: k represents the number of iterations; η is the optimized value of the kth iteration subproblem; u l * is the worst failure scenario obtained in the kth iteration.

[0180] Sub-questions:

[0181] The expression of the subproblem in the C&CG algorithm is:

[0182]

[0183] st Mu≤Γ (58)

[0184] Cx1 * +By+G·x2 * ·diag(u)≤h (59)

[0185] Where: x1 * and x2 * is the flexible resource configuration and network architecture solution obtained in the kth iteration. The duality theory is used to transform the double-layer subproblem into a single-layer subproblem for solution:

[0186]

[0187] Mu≤Γ (61)

[0188] Β T π+b=0 (62)

[0189] π≥0 (63)

[0190] Where: π is the dual variable.

[0191] (3) Solution steps:

[0192] The algorithm accuracy is set to ε, and the specific solution steps are as follows:

[0193] 1) Let the lower bound of the original problem be L B =-∞, upper bound U B =+∞, the number of iterations k=1, given a set of feasible failure scenarios u0.

[0194] 2) Solve the main problem, obtain the optimal pre-layout solution and optimal value, and update the lower bound.

[0195] 3) Solve the subproblems, obtain the worst failure scenario and optimal value, and update the upper bound.

[0196] 4) If |U B -L B | / U B ≤ε, return the optimal solution, terminate the algorithm iteration, update the number of iterations k=k+1, and jump to step 2.

[0197] Implementation, case analysis:

[0198] This example is based on the improved IEEE33 distribution system, with a total system load of 3.715+j2.3MVA. Assume that the distribution system is located in the coastal area of ​​my country. Figure 1 The latitude and longitude of the load nodes and the level division settings are shown in Tables 1 and 2.

[0199] Table 1

[0200] node Longitude (°E) Latitude (°N) node Longitude (°E) Latitude (°N) 1 112.59 23.20 18 114.15 23.66 2 112.72 23.17 19 112.82 23.03 3 112.84 23.15 20 113.05 22.99 4 112.98 23.14 21 113.30 22.99 5 113.14 23.14 22 113.61 22.97 6 113.29 23.15 23 112.85 23.29 7 113.42 23.17 24 113.02 23.37 8 113.57 23.15 25 113.26 23.42 9 113.78 23.24 26 113.21 23.23 10 113.84 23.15 27 113.36 23.29 11 113.86 23.08 28 113.50 23.34 12 113.89 22.97 29 113.61 23.39 13 114.04 23.08 30 113.74 23.45 14 114.09 23.21 31 113.84 23.52 15 114.02 23.34 32 113.86 23.62 16 114.10 23.44 33 113.95 23.70 17 114.13 23.55 RC starting point 113.59 23.27

[0201] Table 2

[0202]

[0203] Analysis of the results of power distribution system fault scenario generation:

[0204] This example first simulates the wind speeds experienced by each grid cell in the distribution system based on a typhoon's spatiotemporal evolution model. It then generates a large number of fault scenarios using the Monte Carlo method. The example uses data from 2016's fourth severe typhoon, Nida, derived from tropical cyclone parameter data from the Joint Typhoon Warning Center (JTWC).

[0205] The distribution system area is divided into 100m×100m cells, and each cell is considered to have the same fault model and geographical height. The maximum wind speed that the line can withstand is set to 22m·s -1, the simulation step is 0.5h, and the wind speed value of each grid unit that changes with the typhoon evolution time is obtained using typhoon data and the YanMeng wind field model. According to the obtained wind speed value, the distribution system line fault scenario is simulated and predicted, and 1000 fault scenarios are generated using the Monte Carlo algorithm. Based on the generated fault scenarios, the probability of failure of each line in 1000 scenarios is obtained. It can be seen that the lines that are subjected to wind speeds exceeding the maximum wind speed have different degrees of failure rates, and the higher the wind speed value and the longer the time, the higher the failure probability. This shows that the fault generation model proposed in this embodiment can correctly map the relationship between the spatiotemporal evolution of typhoons and line faults.

[0206] When a typhoon makes landfall in the distribution system from the southeast, the lines on the southeast side, being the first to enter the typhoon's impact zone and close to the typhoon's center, have a higher probability of failure. Lines on the west side enter the typhoon's impact zone relatively later, when the overall wind speed has already decreased, resulting in a low or even zero line failure rate. Lines on the northeast side are spatially farther from the typhoon's center and do not pass through the maximum wind speed radius, experiencing relatively low wind speeds and similarly low line failure rates. This suggests that the failure rate of distribution lines is clearly linked to their geographic location, the typhoon's path, and the direction of landfall.

[0207] Selection of uncertainty set interval:

[0208] Based on the generated fault scenarios, the probability distribution of different fault severity in 1000 scenarios is calculated. According to the generated fault severity probability, it can be known that the fault severity of the distribution system is mainly between 4 and 6, so the N in the fault scenario uncertainty constraint is set to Zmin and N Zmax Take 4 and 6 respectively.

[0209] Then, according to formula (15), the information entropy values ​​of 1000 fault scenarios are calculated and sorted. The 10th and 90th percentiles of the information entropy value sorting are 3.3998 and 12.5056 respectively, which means that 80% of the fault scenario information entropy values ​​are distributed within this range. The higher the probability of occurrence of the corresponding entropy value of the scenario, the greater the possibility of the fault scenario occurring under extreme weather conditions. Therefore, it can be considered that the entropy value of the actual fault scenario is more reasonable within this range. Based on the above analysis results, W in the fault scenario uncertainty constraint formula (15) is min and W max Take 3.3998 and 12.5056 respectively.

[0210] Analysis of the worst-case failure scenario prediction results and flexible resource pre-layout results before a disaster:

[0211] Based on the obtained fault scenario uncertainty parameters, a flexible resource pre-placement model was developed for the worst-case pre-disaster fault scenario. The price parameter settings, as well as the MESS and SVC parameter settings, are shown in Tables 3, 4, and 5. The C&CG algorithm iteration accuracy was set to 0.001. The faulty lines for the worst-case fault scenario were found to be lines 5, 21, 33, 35, and 37. The MESS pre-placement locations were nodes 7, 14, 31, and 32, and the SVC pre-placement locations were nodes 7, 14, and 31. The load loss cost for this fault scenario was 6,760 yuan, and the pre-placement cost was 5,500 yuan.

[0212] Table 3

[0213]

[0214] Table 4

[0215]

[0216] Table 5

[0217]

[0218] In order to verify the effectiveness and economy of the pre-layout solution obtained by the method proposed in this embodiment under different fault scenarios, three groups of solutions are designed to minimize the economic cost C DSI Restoration results for 1,000 fault scenarios were solved for the objective function, and the average load recovery rate and average cost of each scheme were calculated for different fault multiplies. Scheme 1 only reconfigures the system without configuring MESS and SVC. In Scheme 2, the MESS pre-positioning locations are randomly selected from nodes 4, 18, 21, and 25 distributed throughout the distribution system, and the SVC pre-positioning locations are nodes 4, 18, and 21. Scheme 3 is the proposed pre-positioning scheme.

[0219] The recovery results of each solution are as follows Figure 2 As shown in the figure, it can be seen that the load recovery rates of Schemes 2 and 3 with pre-layout are better than those of Scheme 1 under different fault severities, and Scheme 3 has the best recovery effect, indicating that a reasonable flexible resource pre-layout scheme can effectively improve the resilience of the distribution system.

[0220] When the fault severity is low, due to the cost of pre-placement of flexible resources, the total economic cost of both Schemes 2 and 3 is higher than that of Scheme 1, which does not pre-place. As the fault severity increases, the cost difference between Scheme 3 and Scheme 1 gradually decreases, and after the fault severity reaches 9, it is lower than that of Scheme 1. The economic advantage of pre-placement resources becomes increasingly apparent as the severity of the fault scenario increases. The cost of Scheme 2 is higher than that of Scheme 1 at all fault severities, indicating that the rationality of the pre-placement solution is closely related to the economic efficiency of recovery.

[0221] Post-disaster fault recovery scheduling results and analysis:

[0222] After a disaster occurs, MESS and EVs are used as active power sources on the power supply side to restore power, and SVCs are used as reactive power sources to maintain node voltage within the limit. On the grid side, RC coordinated repairs are used to accelerate the restoration of critical fault lines, and network reconstruction is used to provide a power supply path for the power-lost loads.

[0223] The parameter settings of EV and RC are shown in Tables 6 and 7:

[0224] Table 6

[0225]

[0226] Table 7

[0227]

[0228] The geographical division of functional areas, the process of generating EV coordinates, and the arrival of EVs at V2G stations are as follows:

[0229] Considering that most car owners take refuge in residential areas during typhoon weather, it is assumed that 70% of EVs willing to respond to recovery dispatch are distributed in residential areas, 20% in work areas, and 10% in leisure areas. Monte Carlo simulation method is used to generate the EV arrival situation of each V2G station. The specific process is as follows:

[0230] (1) A random number between 0 and 1 is generated for a certain EV participating in the dispatch. If the random number is in the interval [0, 0.1), the EV is considered to be in the leisure area; if the random number is in the interval [0.1, 0.2), the EV is considered to be in the work area 1; if the random number is in the interval [0.2, 0.3), the EV is considered to be in the work area 2; if the random number is in the interval [0.3, 0.5), the EV is considered to be in the residential area 1; if the random number is in the interval [0.5, 0.7), the EV is considered to be in the residential area 2; if the random number is in the interval [0.7, 1], the EV is considered to be in the residential area 3. In this way, the areas to which 100 EVs belong are generated.

[0231] (2) For each EV, a latitude and longitude coordinate within the area to which it belongs is generated based on uniform distribution, and an initial power consumption is generated based on normal distribution.

[0232] (3) Each EV moves to the nearest V2G station. If the straight-line distance between the EV and the nearest V2G station exceeds 30 km, the EV will not participate in the power supply restoration scheduling of the distribution system.

[0233] (4) Record the number of EVs arriving at each V2G station and the total amount of power delivered. Each V2G station can only accommodate a maximum of 15 EVs charging and discharging simultaneously. That is, the maximum output power of a V2G station with more than 15 EVs arriving is the sum of the maximum output powers of the 15 EVs, as shown in Table 8:

[0234] Table 8

[0235]

[0236] Assume that the actual travel distance of all mobile resources is 1.5 times the straight-line distance between the starting point and the end point, and the moving speed is 45 km / h. -1 .

[0237] Assuming that the fault points are all midpoints of the line, the fault scenario is the worst fault scenario obtained in the previous section, and the MESS and SVC pre-layout positions are also based on the solution results of the previous section, a multi-period and multi-objective optimization model for the coordination of multiple resources after the disaster is solved. The fault recovery lasts for 16 hours, the simulation step is set to 1 hour, and the locations of each flexible resource and fault line at the start of the fault recovery are as follows: Figure 3 After a fault occurs, the distribution system first performs network reconstruction, disconnecting lines 13 and 32 and closing tie switch lines 34 and 36.

[0238] The results of each power output and load recovery in each period are as follows Figure 4 、 Figure 5 As shown in the figure, during periods 1-5, a large area of ​​distribution nodes were disconnected from the main power supply. Since the four MESSes were pre-positioned in the power outage area, they remained in place, generating active power and remained stationary. Their capacity reached its minimum in period 6. SVCs and EVs also generated power at pre-positioned nodes and V2G sites, respectively, to meet the voltage and power requirements of the distribution system.

[0239] RC dispatch maintenance results and line disconnection and fault status are as follows Figure 6As shown in Figure 1, the three RCs moved toward lines 33 and 37, which were closest to the starting point, in period 1. They arrived at their destination and began maintenance in period 3. Because simultaneous maintenance of two RCs increased efficiency, line 33 was repaired and operational by period 6. At this point, all distribution nodes except node 22 were connected to the main power source. However, due to the voltage limit of terminal node 32 and the upper limit of the SVC's reactive power compensation, some nodes were still unable to fully restore power. In period 8, line 37 was repaired and operational, and line 26 was disconnected for network reconfiguration. Power was restored to all distribution nodes except node 22, and the EVs at the V2G station began charging to meet travel demand after the fault recovery schedule concluded. Line 21 was repaired and operational by period 10. At this point, all distribution nodes were connected to the main power source, power restoration was complete, and the network topology remained unchanged. In period 15, RC1 and maintenance teams RC2 and RC3 completed repairs on lines 35 and 5, respectively, completing the distribution system fault recovery.

[0240] In order to analyze the impact of various flexible restoration resources on power restoration effects, 10 groups of different strategies were designed for comparison. The resource allocation and restoration results of the strategies are shown in Table 9. The load active power restoration curves of each strategy are shown in Figure 7 As shown in Table 9, the power outage load and resource allocation cost are shown in Table 9, where strategy 10 is the proposed recovery strategy. It can be seen from Table 9 that the proposed strategy has the highest overall recovery rate and the lowest total cost.

[0241] Table 9

[0242]

[0243] Compared with the proposed strategies, Strategy 1 does not configure any active or reactive power sources, while Strategy 2 and Strategy 3 do not configure reactive and active power sources, respectively. The power loss load costs of these three strategies are much higher than those of other strategies, indicating that both active output and reactive power compensation are required for effective power supply during load recovery.

[0244] Strategy 4 and Strategy 5 only utilize EVs as active power sources, and in Strategy 5, the V2G stations at nodes 22 and 25 are located at nodes 12 and 29. Due to the change in V2G station location, the EV energy distribution also changes. In Strategy 5, the V2G stations at nodes 12 and 29 are located within the power loss load area. Therefore, Strategy 5 achieves higher recovery levels and EV discharge compensation costs than Strategy 4, but the power loss load cost is significantly lower. This indicates that the location of the V2G station significantly influences the recovery effect. Distribution systems typically operate with a single power source and in a radial pattern. In the event of a line fault, loads located midstream and downstream are more likely to enter the power loss area. Therefore, when selecting a V2G station, in addition to considering economic efficiency during normal operation, the reliability and resilience of the distribution system under extreme conditions should also be considered.

[0245] Strategy 6 utilizes only one active power source, the MESS. Due to the MESS's higher output power, Strategy 6 achieves a higher level of power restoration during periods 1-5 compared to Strategies 4 and 5, but at the expense of higher resource allocation costs. Overall, due to the lower cost of power loss loads, Strategy 6 also offers lower total costs. As distributed energy storage, the MESS offers high output and flexibility, but is expensive and available in limited quantities. EV output is limited by the location of V2G stations and requires a certain level of power to be maintained for travel, but it offers the advantage of lower resource allocation costs. The proposed strategy combines the two to create complementary advantages. In the early stages of the fault, when the fault is most severe, the MESS and EV simultaneously output at maximum power. In the later stages of the fault, EV charging occurs, without compromising power supply and meeting the needs of vehicle owners. This strategy outperforms strategies that utilize only one active power source in terms of both recovery effectiveness and cost-effectiveness.

[0246] Strategy 7 pre-positions MESSes at randomly selected nodes 4, 18, 21, and 25, distributed throughout the distribution system. The SVC pre-positions are at nodes 4, 18, and 21. At the start of fault recovery, only one MESS in Strategy 7 is located in the outage area and can immediately provide power. The other three MESSes move toward the outage area, gradually connecting to the destination node starting in period 4 and continuing to provide power until period 10. Compared to the proposed strategy, Strategy 6's MESSes move early in the fault's severity, resulting in lower power restoration than Strategy 9. Furthermore, due to the different pre-positions, the RC repair routes also change. Strategy 7 has two faulty lines that are not repaired until period 16, resulting in higher downtime costs. This demonstrates that the MESS and SVC pre-positioning scheme derived from the robust optimization model outperforms Strategy 6 in both restoration effectiveness and cost-effectiveness.

[0247] Strategy 8 does not perform coordinated RC repairs and moves to faulted lines 21, 33, and 37 during period 1. Compared to the proposed strategy of coordinated repairs with multiple RCs, Strategy 8 completes the repairs on all three lines in less time, thus restoring power to all loads earlier. Both the switching and RC repair costs are slightly lower than those of Strategy 10. However, the time required to complete the repairs on the first line is longer, resulting in a longer initial period of widespread power outages. Overall, the restoration level is lower than that of the proposed strategy, and the total cost is higher.

[0248] Strategy 9, unlike the proposed strategy, does not involve network reconfiguration; that is, tie-switch lines 33 to 37 remain disconnected. Therefore, the RC prioritizes repairing section-switch lines 5 and 21 along the maintenance route. Since Strategy 9 completes power restoration after repairing both lines, it completes power restoration earlier than the proposed strategy, resulting in lower switching and RC repair costs. However, since lines 5 and 21 are relatively far from the RC departure station, the large-scale power outage lasts longer, resulting in higher downtime costs. Furthermore, this strategy's topology places higher demands on the SVC's reactive power compensation while maintaining operating voltage constraints, resulting in a lower overall recovery level than the proposed strategy.

[0249] The two-stage fault recovery strategy for the elastic distribution system proposed in this embodiment is feasible. First, a flexible resource pre-layout model is constructed and solved under the worst fault scenario before the disaster, and the most serious power outage fault scenario that may occur in the distribution system and the MESS and SVC pre-layout scheme under this scenario are obtained. It can be seen that in the pre-disaster prevention stage, the following effects are achieved: (1) The fault condition of the distribution line is closely related to the spatiotemporal evolution of the typhoon. In view of the uncertainty of the fault scenario under the typhoon disaster, this embodiment uses the fault multiplicity and information entropy to establish an uncertainty set. Through analysis, it can be seen that the size and distribution of the fault multiplicity and information entropy are highly correlated with the severity and probability of the fault scenario, and can better describe the uncertainty of the fault scenario. (2) Robust optimization can obtain a flexible resource pre-layout scheme under the worst fault scenario. Compared with other schemes, the power supply recovery rate can be better improved in the worse scenario, effectively improving resource utilization and the elasticity of the distribution system.

[0250] After the disaster, the network is reconfigured and the mobility and output of MESS, SVC, RC, and EV are optimized to achieve rapid recovery of the power outage load and fault line in the distribution system. By designing comparative experiments and analyzing the role of various flexible recovery resources, the effectiveness of the proposed strategy is verified. It can be seen that in the post-disaster recovery phase, the following effects are achieved: (1) Compared with the traditional scheduling strategy in which only one RC can repair a fault line, the strategy of multi-RC coordinated repair can repair the key line faster, so that the power outage load area can be restored to the main power supply faster, providing a power supply path for the key load. (2) The spatial distribution of power supply side resources MESS, SVC, and V2G sites has a great influence on the recovery effect. The closer to the downstream of the distribution system where power outages are likely to occur, the better the recovery effect. (3) Although the participation of multiple flexible resources in the recovery will increase the cost of resource allocation, the coordinated scheduling between resources can significantly reduce the cost of the power outage load, giving play to the effect of 1+1 being far greater than 2, and has obvious advantages in the effectiveness and economy of elasticity improvement.

[0251] Example 2

[0252] This embodiment further discloses a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method described in the first embodiment.

[0253] Example 3

[0254] This embodiment further discloses a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the method described in the first embodiment are implemented.

[0255] Example 4

[0256] This embodiment further discloses a computer program product, including a computer program, which implements the steps of the method described in the first embodiment when executed by a processor.

[0257] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A two-stage fault recovery method for improving the resilience of a power distribution system, characterized in that: The following steps are involved: Build a typhoon spatiotemporal evolution model to generate predicted failure scenarios; The Monte Carlo simulation method is used to simulate the distribution lines in the predicted fault scenario and generate several fault scenarios; Based on the information entropy value and fault multiplicity of the fault scenario, an uncertainty set is constructed, and then a robust optimization model is constructed; Solve the robust optimization model to determine the pre-placement plan for the mobile energy storage system and static VAR compensator under the worst-case pre-disaster fault scenario; Construct a multi-source collaborative post-disaster multi-period multi-target fault recovery model; The fault recovery model achieves the recovery of power distribution system lost loads and fault lines through network reconstruction and optimized scheduling of mobile energy storage systems, static VAR compensators, maintenance teams and electric vehicles.

2. The method according to claim 1, characterized in that The process of building a typhoon spatiotemporal evolution model includes: Based on the functional relationship between the typhoon's movement path, minimum air pressure and maximum wind speed radius, and combined with the raster data principle of the geographic information system, the area where the distribution system is located is gridded, and the wind speed values ​​​​of each unit of the distribution line in each time period are simulated and calculated, thereby completing the construction of the typhoon's spatiotemporal evolution model.

3. The method according to claim 1, characterized in that The objective function of the robust optimization model is the economic cost under the worst fault scenario, including the power loss load cost and the pre-layout configuration cost of the mobile energy storage system and static VAR compensator.

4. The method according to claim 3, characterized in that The constraints of the robust optimization model include the outermost layer of flexible resource configuration and network topology constraints, the middle layer of fault scenario occurrence model constraints, and the innermost layer of load reduction constraints, mobile energy storage system output constraints, static VAR compensator compensation constraints, and distribution system operation constraints.

5. The method according to claim 1, characterized in that The objective function of the fault recovery model is to minimize the total economic cost during the fault recovery period, including the power loss load cost, switch operation cost, line fault time cost, maintenance team maintenance cost and electric vehicle discharge economic compensation cost.

6. The method according to claim 5, characterized in that The constraints of the fault recovery model include mobile energy storage system scheduling constraints, maintenance team scheduling constraints, electric vehicle scheduling constraints, and other distribution system operation constraints; The mobile energy storage system scheduling constraints include capacity and output constraints and time-space movement constraints; the maintenance team scheduling constraints include time-space movement constraints and nonlinear relationship constraints between maintenance efficiency and the number of maintenance teams.

7. A computer device comprising a memory, a processor, and a computer program stored in the memory, wherein: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

9. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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